Discussion:
Condorcet for public proposals
MIKE OSSIPOFF
2003-12-23 09:47:47 UTC
Permalink
When I found out about BeatpathWinner's brief algorithm and computer
program, I began recommending for committees, organizations, and polls. That
was largely because the brief BeatpathWinner program was the only one that
I'd written. I had diffriculty setting aside the time that it would take to
write the much longer programs for SSD and Ranked-Pairs. So I was offering
a BeatpathWinner program because that was all I had. People asked me where
they could find a Ranked-Pairs program, and I had to say that I didn't know
where they could find a wv RP program.

But all the time when I was recommending BeatpathWinner for committees,
partly with the idea that the members of the committee, like me, would find
a brief program more convenient, I was also saying that SSD, RP, and PC are
the Condorcet versions to propose for public elections.

That's because those Condorcet versions are the ones with natural and
obvious motivation and justification. Obviously, of those 3, PC isn't as
good as the other 2.

CSSD and SSD differ in their stopping rule. SSD stops when someone is
unbeaten. CSSD stops when there are no defeats among the candidates of the
Schwartz set. When I initially suggested CSSD, no knowing about Markus's
prior proposal, I was saying to stop when there are no cycles among the
candidates of the current Schwartz set. When I heard about Markus's CSSD
proposal, which worded the stopping rule in terms of defeats in the Schwartz
set, instead of cycles, I adopted that wording, since defeats are a more
natural notion than cycles. In that way, with CSSD, it's never necessary to
mention cycles. Of course with SSD it's never necessary to mention cycles
either.

Stopping the count when someone becomes unbeaten sounds much briefer, more
natural, expected than stopping the count when there are no defeats among
the candidates of the current Schwartz set. After all, the whole reason why
a circular tie solution is needed was because initially no one was unbeaten.
What could be more natural than to stop when someone becomes unbeaten.

As I was saying before, an innermost unbeaten set is compelling--It's
obvious that the winner should come from that set. And that therefore the
candidates of that set are the ones who should have their defeats dropped.


Here's how I define SSD:


Schwartz set definition:

1. An unbeaten set is a set of candidates none of whom are beaten by anyone
outside that set.

2. An innermost unbeaten set is an unbeaten set that doesn't contain a
smaller unbeaten set.

3. The Schwartz set is the set of candidates who are in innermost unbeaten
sets.

SSD:

1. If any candidate is unbeaten, they win and the count ends.

2. Otherwise, determine which candidates are in the Schwartz set, counting
only undropped defeats.

3. Drop the weakest defeat among the members of that set. Go to 1.

[end of SSD definition]


Ranked-Pairs is also obviously motivated and justified, and that makes it
too a good proposal for public elections. Its definition is probably
briefer than that of SSD, because SSD requires the Schwartz set to be
defined. But RP loses some of its brevity when its midcount-tie-solution is
specified.

Ranked-Pairs:

To "keep" a defeat means to record it as being kept.

In order of strongest defeats first, consider each defeat in turn as
follows: Keep it doesn't conflict with already-kept defeats, by being in a
cycle with them-- i.e., by being in a cycle consisting only of it and some
already-kept defeats.

When all the defeats have been considered in that way, a candidate wins if
s/he has no kept defeats.

[end of RP definition]

Ranked-Pairs isn't a descriptive definition. If it applies to RP at all, it
could also apply to some other Condorcet versions. Steve Eppley has
suggested a better name:

Maximize Affirmed Majorities (MAM). That name well describes what MAM does.

RP can have midcount ties, situations where there are 2 or more equally
strongest as-yet unconsidered defeats. The problem is, which one should be
considered first? It's said that, for the purpose of clone-independence and
monotonicity, maybe the best way to solve that is to randomly chose the
order in which to consider them. That doesn't sound like something that the
public would like, however.

I suggested an RP midcount tie solution on this mailing list some time ago.
It's based on the idea that a defeat is nullified if it's in a cycle with
defeats that are all at least as strong as it is:

1. Call the equally strongest as-yet unconsidered defeats the "tie defeats".

2. Defeats that were kept before keeping any tie defeats are called "old
defeats".

3. A tie defeat is "qualified" if it isn't in a cycle consisting only of it
and some old defeats.

4. Keep every qualified tie defeat that is not in a cycle each of whose
members is either an old defeeat or a qualified tie defeat.

[end of "deterministic1" midcount tie solution definition]

In the EM discussion at that time, it was called deterministic1. Steve had
already considered it.

I thought that was the brief midcount tie solution, till Eric suggested
something briefer:

[using the same definitions as before]

Keep every tie defeat that isn't in a cycle consisting only of it and some
old defeats.

[end of briefer midcount tie solution]

That's so much briefer that I immediately agreed that that's the one to
offer for public proposals.

It could probably be worded so that it wouldn't be necessary to separately
define tie defeats and old defeats.

In public elections, equal defeats are so rare that it doesn't reallly
matter what the rule is for solving them. Brevity is all-importnat, and the
brief midcount tie solution is the one to include in public MAM proposals.

As I've often said, the merit difference between MAM and SSD in public
elections is negligible. The choice between those two should be based
entirely on which is more likely to be accepted. Maybe a "focus group"
public meeting or a poll should be done to chose.

If I was proposing only BeatpathWinner/CSSD for committees only because it
was the only one that I had a count program written for, maybe that isn't
the best way to choose a voting system. Maybe RP should be considered as a
method for committees. Maybe a program should be written that implements
CSSD by its own very plausible definition, rather than by BeatpathWinner.
For a committee, the choice between CSSD and CSSD would obviously depend on
whether an obvious stopping rule is more imporant than clone independence.
Will clone advantage or disadvantage really happen often enough to cause
factions to strategically introduce clones? I doiubt it.

As I said, it's been suggested that the MAM midcount tie solutions that I
described might not be clone-independent &/or monotonic. How much of a
problem is that? How likely is a faction to strategically run (or avoid)
clones, on the chance that there will be equal defeats, in circumstances
that favor or disfavor clones? Probably not so likely. How likely is someone
to downrank his favorite so as to make him win in the unlikely event that a
certain two defeats will be equal, and the other circumstances will be right
for that particular candidate to benefit from the nonmonotonicy and from
that voter's downranking strategy. It doesn't sound real likely, does it.

I've had good response to an SSD definition. SSD doesn't require any mention
of cycles. MAM requires at least mention of defeats that conflict or are
incompatible, etc. Someone might ask how defeats conflit, and then you're
defining cycles to that person. With SSD you never have to speak of cycles,
or incompatible defeats.

But SSD and MAM are both excellent public Condorcet proposals.

Sometimes we underestimate how resistant people might be to anything whose
definition is longer than a line or two. Sure, anyone who is willilng to
read the definitions of SSD and MAM will like them. But what about all those
people who will reject them without being willing to read the definition,
because they consider a short paragraph to be too long? For them, maybe
Condorcet is a better idea.

Sure SSD & MAM are better, but if people insist on something more
briefly-defined, them Plain Condorcet (PC) is the thing:

If anyone is undefeated they win. Otherwise drop the weakest defeat. Repeat
till someone is undefeated. They win.

[end of PC definition]

PC is called Basic Condorcet at the electionmethods website.

Sure, PC violates Condorcet Loser. But it would happen only rarely. It would
be a peculiarly popular Condorcet loser who has fewer people preferring
anyone else to him than anyone else does.

If a Condorcet Loser wins it would be an embarrassment. But the likely
"badness" of that winner is reduced by the fact that he has the fewest
people preferring anyone else to him.

Condorcet Loser could also be used against PC in campaigns, and that
objection would have to be answered. For one thing, Condorcet Loser can't be
used to oppose replacing Plurality with PC, because Plurality violates it
too, probably more often.

Keep thiis in persepctive. Let's not exaggerate how likely or how much of a
problem PC's ability to fail Condorcet Loser is.

Mike Ossipoff

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Anthony Duff
2004-01-27 13:26:44 UTC
Permalink
I am replying to:
http://www.mail-archive.com/election-methods-***@electorama.com/msg01542.html
From: "MIKE OSSIPOFF"
Subject: [EM] Condorcet for public proposals
Date: Tue, 23 Dec 2003 09:47:47 +0000

Mike wrote, in part,
... SSD, RP, and PC are
the Condorcet versions to propose for public elections.
That's because those Condorcet versions are the ones with natural and
obvious motivation and justification. Obviously, of those 3, PC
isn't as
good as the other 2.
As I understand: SSD and RP are excellent methods, they are identical
in virtually every reasonable election result, and it is too
difficult to definitively decide which is better. PC is a very good
method, with the merit of being straightforward and brief to explain.

Mike implies(?), something that I think is very important. If you
are going to make a serious public proposal, you have to be certain
about your proposal. If you are hesitating over the details, then
you will not inspire confidence. When it comes to a public proposal,
with a public that has little patience for details, you must have
precisely one, well defined proposal.
Sometimes we underestimate how resistant people might be to anything whose
definition is longer than a line or two. Sure, anyone who is
willilng to
read the definitions of SSD and MAM will like them. But what about
all
those
people who will reject them without being willing to read the
definition,
because they consider a short paragraph to be too long? For them, maybe
Condorcet is a better idea.
Sure SSD & MAM are better, but if people insist on something more
I agree with Mike’s thrust, that simplicity could be the deciding
factor between condorcet getting off the ground, or not.

I’d express things a little differently though. People won’t “insist
on something more briefly-defined” so much as they will fail to have
their attention held and try and get away from you, politely at
first.

The problem with SSD & RP/MAM is not just that there are extra words
in definitions and explanation of the method, but people will also
want to know why the extra details are required. Explaining the
“whys” could get particularly convoluted given that an otherwise
uninterested person may only give you a minute or two before they
decide that you are a nuisance.

I note that PC is not the simplest condorcet method. PC means
PC(winning votes). PC(margins) would be simpler and more intuitive.
Margins are intuitive. The pairwise contests are decided by margins.
The newcomer to condorcet will want to know why defeats should be
used instead of margins. This is the point where I fear that the
explanation of condorcet will become bogged down for too many people.
You have already startled this unsuspecting person with the news
that the community might express an apparent contradiction
(condorcet’s paradox), and then you try to justify a
counter-intuitive method to choose a winner.

I wonder if, rather than explaining everything, an implicit “just
trust me” approach would be better used in the first instance.
For example:
“When resolving a circular tie, measuring defeats by margins has been
shown to be vulnerable to strategic manipulation. By measuring
defeats by winning votes, that vulnerability is significantly
reduced”

Regarding circular ties:
I have been unable to discover a reasonable example for why a
sincerely voting community would produce a circular tie, except for
where ballots are largely random. Random ballots (voters making
random choices) can produce a circular tie, but if the number of
voters is very large then the relative margins involved in the ties
will be exceedingly small, and in such a case, non-random votes will
very likely dominate the result.

Sure, it is easy to contrive of multiple complex philosophies with
matching candidates that would produce a circular tie. However, in
such attempts as I have made, I have not found any good reason why
just as many other people might not have opposing correlations of
philosophies. The whole thing seems to be verging on randomness. Has
anyone got an argument for why a particular community might produce a
sincere, circular tie? Does anyone have evidence of one actually
exisiting?

On the other hand, it is easy to see why a narrowly loosing faction
may vote strategically for the specific purpose of creating a
circular tie so as to rob victory from a sincere condorcet winner.

Therefore, I suspect that should a circular tie ever eventuate, that
it would very likely be due to strategic voting. If this is true,
then admit it upfront.
If anyone is undefeated they win. Otherwise drop the weakest defeat.
Repeat
till someone is undefeated. They win.
[end of PC definition]
My criticism of this is that, by default, it is expected that there
will not be a condorcet winner. In general, when I read descriptions
of condorcet, the content is overwhelmingly concerned with the
resolution of circular ties. The main feature of condorcet is that a
full pairwise analysis is done, unlike in IRV. This should be a
selling point of condorcet, but unfortunately it is buried beneath
the detail.

I suggest that a definition of the condorcet election method being
publicly proposed should be explicit about the full pairwise
analysis, and that the possibility of a circular tie, and the
resolution of such a circular tie should be treated like a footnote.
Sure, PC violates Condorcet Loser. But it would happen only rarely.
It
would
be a peculiarly popular Condorcet loser who has fewer people
preferring
anyone else to him than anyone else does.
If a Condorcet Loser wins it would be an embarrassment. But the
likely
"badness" of that winner is reduced by the fact that he has the
fewest
people preferring anyone else to him.
Condorcet Loser could also be used against PC in campaigns, and that
objection would have to be answered. For one thing, Condorcet Loser
can't
be
used to oppose replacing Plurality with PC, because Plurality
violates it
too, probably more often.
I do not think the condorcet loser criterion is really that
important. The condorcet winner criterion is very important, and I
might even rank it as paramount. I think the symmetric relationship
between these two criteria has artificially raised the status of the
condorcet loser criterion.
I think the condorcet loser criterion is less important than an
overruled majority.
The prime example of PC electing a condorcet loser is:
20 ABCD
20 BCAD
20 CABD
13 DABC
13 DBCA
13 DCAB
D wins despite being ranked last by 60% and despite being beaten by
every other candidate.
My justification of the win by D is this: No other single candidate
can stand up, in court or in public, and complain that they should be
the winner because they beat D 60 to 39. Should A, for example, do
this, D can immediately counter by pointing out that A suffered a
worse defeat of 66 to 33. Therefore, A’s case is worse than D’s.
Condorcet is a pairwise method. Let the justifications and
complaints be made in a pairwise manner. I think this would be
convincing in a public forum.

The condorcet loser criterion is, however, emotive. To have lost
against *everyone* is a pretty bad thing. If someone wants to obsess
about this, then I would argue that in a large public election, the
result is implausible, as there will have been some other minor
candidate E, and suddenly, D is no longer a condorcet looser.

Is the problem that D is not in the smith set? The general public is
not going to make this complaint. With PC, such a set is never
mentioned.

Someone might suggest that the 39 D voters perverted the result by
deliberately creating a cycle. Clearly this is not the case, as the
cycle exists among the 60 voters who rank D last, and without a
strong cycle among those 60, the cycle among the D voters would be
ineffective.

Someone might suggest that A, B & C are effective clones, that they
represent a similar position with respect to D. This is an advanced
argument. However, a problem with it is that the extreme strength of
the cycle suggests that there are some very strong feelings
differentiating A from B from C. If they were clones, then why
didn’t nearly as many vote CBA as ABC?


Another thought: “condorcet” is an unfortunate name. It is an
unfamiliar French name. People probably won’t even agree on how it
is to be pronounced. As for the abbreviation “PC” – it has already
been used, as in “personal computer”, and in “politically correct”.
Are there any thoughts for a better name?


Anthony


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Ernest Prabhakar
2004-01-27 17:10:36 UTC
Permalink
Hi Anthony,
Post by Anthony Duff
I suggest that a definition of the condorcet election method being
publicly proposed should be explicit about the full pairwise
analysis, and that the possibility of a circular tie, and the
resolution of such a circular tie should be treated like a footnote.
I tend to agree with you.
Post by Anthony Duff
..Is the problem that D is not in the smith set? The general public is
not going to make this complaint. With PC, such a set is never
mentioned.
Actually, I"m leaning towards Smith PC (Plain Condorcet within the
Smith Set of tied winners) as perhaps the optimal tradeoff between
rigor and clarity for public elections. As you point out, in public
elections circular ties are rather unlikely to come up. But I think
the concept of a tiebreaker round actually helps in the understanding,
and using PC (least greatest defeat) as a tie breaker is far simpler to
calculate and explain than any of the alternatives I've seen.
Post by Anthony Duff
Another thought: “condorcet” is an unfortunate name. It is an
unfamiliar French name. People probably won’t even agree on how it
is to be pronounced. As for the abbreviation “PC” – it has already
been used, as in “personal computer”, and in “politically correct”.
Are there any thoughts for a better name?
Yeah, my friends (on the radical centrist list) are unanimous that the
term Condorcet has to go. :-)

I have been proposing the term 'Instant Matchup Voting', or IMV, by
analogy with Instant Runoff Voting. I compare it to a round-robin
tournament, which most people have direct experience with. I think
this leads to a simple, easy to visualize definition:

1. Each rank-ordered ballot is interpreted as a series of "Instant
Matchups"
That is A > B > C, implies one point each for the three pairwise
Matchups A > B, B > C, and A > C
Note that "A>B" is counted separately from "B>A" (i.e., winning votes)
2. Tally up the N * (N-1) Matchups, for each ordered pair of candidates
3. If one candidate beats everyone, that's the absolute winner
4. If there is a 'rock-paper-scissors' tie (A >= B, B >= C, C >= A),
the tiebreaking winner is the candidate from that group with the
'least greatest defeat'

I actually think the Smith tiebreaking round makes it easier to
understand and defend than straight PC. Terms like Smith sets, cycles,
and even circular ties can be confusing. However, using the
round-robin analogy, everyone I've talked to quickly grasps the
rock-paper-scissors concept. We could even recurse it to give a
complete ordering (which is important to many people).

While Smith PC is not quite perfect, to me this seems the simplest
possible definition that would make sense to people. I have something
close to this implemented, though I've been planning to also implement
Ranked Pairs, Beatpath, and perhaps SD so that the experts can easily
compare alternative calculations. And of course I've been distracted
by my Auto-Districting program (which was written a week ago, but I've
just started debugging).

Does anyone think Smith PC is likely to cause any severe pathologies in
a public election? Are there open questions that we could work to
resolve, if people agree it is a good idea?

-- Ernie P.
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Eric Gorr
2004-01-27 17:55:41 UTC
Permalink
Post by Anthony Duff
I suggest that a definition of the condorcet election method being
publicly proposed should be explicit about the full pairwise
analysis, and that the possibility of a circular tie, and the
resolution of such a circular tie should be treated like a footnote.
Have you read my description of the method found at:

http://www.ericgorr.net/condorcet/rankedpairs/

How would you modify it to make it better?
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Dave Ketchum
2004-01-28 03:27:38 UTC
Permalink
Post by Eric Gorr
Post by Anthony Duff
I suggest that a definition of the condorcet election method being
publicly proposed should be explicit about the full pairwise
analysis, and that the possibility of a circular tie, and the
resolution of such a circular tie should be treated like a footnote.
http://www.ericgorr.net/condorcet/rankedpairs/
How would you modify it to make it better?
Wording seemed tortured.

Help me understand how the 75 migrated from B/C to A/B.
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Eric Gorr
2004-01-28 04:21:47 UTC
Permalink
Post by Dave Ketchum
Post by Eric Gorr
Post by Anthony Duff
I suggest that a definition of the condorcet election method being
publicly proposed should be explicit about the full pairwise
analysis, and that the possibility of a circular tie, and the
resolution of such a circular tie should be treated like a footnote.
http://www.ericgorr.net/condorcet/rankedpairs/
How would you modify it to make it better?
Wording seemed tortured.
What wording?
Post by Dave Ketchum
Help me understand how the 75 migrated from B/C to A/B.
oops. Thanks for catching that. Example #2 corrected.


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Ernest Prabhakar
2004-01-28 05:28:52 UTC
Permalink
Hi Dave,
I like what Ernest writes, though I see a bit of room for improvement
and suggest "tournament" as a less foreign-sounding title (even though
its ancestry is also French).
Hmm, maybe. It is better than Condorcet, but to me tournament evokes
an image of knights jousting on horses.

Someone (sorry, I forgot who) suggested the word Pairwise is important.
I could live with the name Pairwise Matchup Voting (PMV). Pairwise
by itself seems too vague, somehow
Post by Ernest Prabhakar
Yeah, my friends (on the radical centrist list) are unanimous that
the term Condorcet has to go. :-)
I have been proposing the term 'Instant Matchup Voting', or IMV, by
analogy with Instant Runoff Voting. I compare it to a round-robin
tournament, which most people have direct experience with. I think
Ahead of much that I have seen, but I suggest tournament as even
easier to visualize from. My definition will follow yours.
Well, tournament does have the idea of a series of matches, but not
necessarily individual pairwise matchups, I don't think. We could
use the term Instant Round-Robin, which is much more explicit, but IRR
is too close to IRV. :-(
Post by Ernest Prabhakar
1. Each rank-ordered ballot is interpreted as a series of "Instant
Matchups"
That is A > B > C, implies one point each for the three pairwise
Matchups A > B, B > C, and A > C
Note that "A>B" is counted separately from "B>A" (i.e., winning votes)
2. Tally up the N * (N-1) Matchups, for each ordered pair of
candidates
3. If one candidate beats everyone, that's the absolute winner
4. If there is a 'rock-paper-scissors' tie (A >= B, B >= C, C >= A),
the tiebreaking winner is the candidate from that group with the
'least greatest defeat'
0. Voters simply rank as many of the candidates as they choose,
starting with their most-preferred.
1. Each rank-ordered ballot is interpreted as a series of matches
among all
That is, ranking A > B > C, and D and E not ranked by this voter,
implies each ranked candidate winning over each candidate ranked
later, and
over each unranked candidate.
Thus unranked candidates do not get counted as ranked over each
other.
That's a good point. I don't think we usually spend enough time
explaining how the ranking is supposed to work, so it would be good to
be more explicit.
Note that "A>B" is counted separately from "B>A" (i.e., winning
votes).
2. Tally up the number of wins for each ordered pair of candidates in
an
N*N array (with an empty diagonal, for candidates do not play against
themselves).
Good point, N*N does reduce explanation.
3. If one candidate wins when compared with each other candidate,
that's
the absolute winner.
4. If no absolute winner, we have a 'rock-paper-scissors' near tie
such as
(A >= B, B >= C, C >= A), and the tiebreaking winner is the candidate
from
that group with the 'least greatest defeat'.
NOTE: I consider 'least greatest defeat' unacceptably opaque for this
purpose, and ask for help in providing simpler words.
Fair enough. How about "whose worst loss is the smallest"? Or
simply "lost by the smallest margin" (a little ambiguous, but sounds
simpler) - can always go into more detail elsewhere.
BTW: Debatable whether voters should be permitted to rank candidates
as equal.
Is there any good reason not to? Implicit equal ranking certainly
makes it clearer about how unlisted candidates are counted. Any if at
all possible, it seems good to give people the option of equality
rather than forcing a random choice. Has anyone presented a clear
argument for or against equal ranking?
If so then, for each pair of equal candidates, count 1/2 win for
each (thus if two voters rank A=B=C then A>B, B>A, A>C, C>A, B>C, and
C>B each get credited one full win).
That doesn't make any sense to me. If two candidates are ranked, I
think that neither should get the win -- at least if we're doing
winning votes (wv) For example, if all the candidates that most people
don't rank at the bottom of the list get a win against each other, then
one single vote in favor could make that person the 'wv' winner!
Right?

Any more thoughts on the implications of Smith PC on strategy, assuming
we can hammer out a decent, simple explanation?

-- Ernie P.

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Kevin Venzke
2004-01-28 05:54:19 UTC
Permalink
Ernest,
Post by Ernest Prabhakar
BTW: Debatable whether voters should be permitted to rank candidates
as equal.
Is there any good reason not to? Implicit equal ranking certainly
makes it clearer about how unlisted candidates are counted. Any if at
all possible, it seems good to give people the option of equality
rather than forcing a random choice. Has anyone presented a clear
argument for or against equal ranking?
Maybe it's easier to tamper with ballots if more than one candidate can
be given the same rank? That's all I can think of.
Post by Ernest Prabhakar
If so then, for each pair of equal candidates, count 1/2 win for
each (thus if two voters rank A=B=C then A>B, B>A, A>C, C>A, B>C, and
C>B each get credited one full win).
That doesn't make any sense to me. If two candidates are ranked, I
think that neither should get the win -- at least if we're doing
winning votes (wv)
Giving half-votes is the Margins (and Symmetric-Completion) interpretation.
I suggest the same method be used for both expressed and truncated equal
rankings. I can't think why there should be a difference in treatment.


Kevin Venzke
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Dave Ketchum
2004-01-28 15:31:49 UTC
Permalink
Post by Ernest Prabhakar
Hi Dave,
I like what Ernest writes, though I see a bit of room for improvement
and suggest "tournament" as a less foreign-sounding title (even though
its ancestry is also French).
Hmm, maybe. It is better than Condorcet, but to me tournament evokes an
image of knights jousting on horses.
Someone (sorry, I forgot who) suggested the word Pairwise is important.
I could live with the name Pairwise Matchup Voting (PMV). Pairwise by
itself seems too vague, somehow
This thread is looking for something for the public, rather than what we
might enjoy within our group.

While tournament comes from the time of knights, it gets used for golf
tours, etc., in the modern world.

I do not demand winning this debate, but think tournament should be
considered.
Post by Ernest Prabhakar
Post by Ernest Prabhakar
Yeah, my friends (on the radical centrist list) are unanimous that
the term Condorcet has to go. :-)
I have been proposing the term 'Instant Matchup Voting', or IMV, by
analogy with Instant Runoff Voting. I compare it to a round-robin
tournament, which most people have direct experience with. I think
Ahead of much that I have seen, but I suggest tournament as even
easier to visualize from. My definition will follow yours.
Well, tournament does have the idea of a series of matches, but not
necessarily individual pairwise matchups, I don't think. We could use
the term Instant Round-Robin, which is much more explicit, but IRR is
too close to IRV. :-(
Post by Ernest Prabhakar
1. Each rank-ordered ballot is interpreted as a series of "Instant
Matchups"
That is A > B > C, implies one point each for the three pairwise
Matchups A > B, B > C, and A > C
Note that "A>B" is counted separately from "B>A" (i.e., winning votes)
2. Tally up the N * (N-1) Matchups, for each ordered pair of candidates
3. If one candidate beats everyone, that's the absolute winner
4. If there is a 'rock-paper-scissors' tie (A >= B, B >= C, C >= A),
the tiebreaking winner is the candidate from that group with the
'least greatest defeat'
0. Voters simply rank as many of the candidates as they choose,
starting with their most-preferred.
1. Each rank-ordered ballot is interpreted as a series of matches
among all
That is, ranking A > B > C, and D and E not ranked by this voter,
implies each ranked candidate winning over each candidate ranked
later, and
over each unranked candidate.
Thus unranked candidates do not get counted as ranked over each
other.
That's a good point. I don't think we usually spend enough time
explaining how the ranking is supposed to work, so it would be good to
be more explicit.
Note that "A>B" is counted separately from "B>A" (i.e., winning
votes).
2. Tally up the number of wins for each ordered pair of candidates in an
N*N array (with an empty diagonal, for candidates do not play against
themselves).
Good point, N*N does reduce explanation.
ALSO is easier to program.
Post by Ernest Prabhakar
3. If one candidate wins when compared with each other candidate, that's
the absolute winner.
4. If no absolute winner, we have a 'rock-paper-scissors' near tie such as
(A >= B, B >= C, C >= A), and the tiebreaking winner is the candidate from
that group with the 'least greatest defeat'.
NOTE: I consider 'least greatest defeat' unacceptably opaque for this
purpose, and ask for help in providing simpler words.
Fair enough. How about "whose worst loss is the smallest"? Or
simply "lost by the smallest margin" (a little ambiguous, but sounds
simpler) - can always go into more detail elsewhere.
I think I like winning votes rather than margins.

Also hope we can avoid the word "defeat" here.

Do NOT want ambiguity - perhaps someone else can help.
Post by Ernest Prabhakar
BTW: Debatable whether voters should be permitted to rank candidates
as equal.
Is there any good reason not to? Implicit equal ranking certainly makes
it clearer about how unlisted candidates are counted. Any if at all
possible, it seems good to give people the option of equality rather
than forcing a random choice. Has anyone presented a clear argument
for or against equal ranking?
Complicates the definition a bit.

Complicates ballot construction - without it the ">" is implied.

Perhaps explicit equal ranking simplifies ballot construction: Let voter
rank each candidate by number, with equal numbers for equality, and gaps
in numbers permitted (4,3,1, ,3 for candidates A thru E ranks C first, B
and E equal and next, A following, and D unranked).

I deliberately excluded unranked candidates from getting any credit.
Post by Ernest Prabhakar
If so then, for each pair of equal candidates, count 1/2 win for
each (thus if two voters rank A=B=C then A>B, B>A, A>C, C>A, B>C, and
C>B each get credited one full win).
That doesn't make any sense to me. If two candidates are ranked, I
think that neither should get the win -- at least if we're doing winning
votes (wv) For example, if all the candidates that most people don't
rank at the bottom of the list get a win against each other, then one
single vote in favor could make that person the 'wv' winner! Right?
I am following the wv path. Thus I do not want A and B penalized for some
voters ranking them equal rather than about half of these voters ranking
A>B and the other half ranking B>A.

Ok, I am having trouble as to whether the above paragraph matters that
much for deciding on a winner - certainly does not affect margins in this
particular race. Doing these counts does get different numbers in the
array when A and B are both good candidates and often ranked as equals
than when they are both unranked lemons.

BTW - the entire array contents BETTER be public - it has much useful
information beyond the simple deciding on a winner.
Post by Ernest Prabhakar
Any more thoughts on the implications of Smith PC on strategy, assuming
we can hammer out a decent, simple explanation?
-- Ernie P.
--
***@clarityconnect.com people.clarityconnect.com/webpages3/davek
Dave Ketchum 108 Halstead Ave, Owego, NY 13827-1708 607-687-5026
Do to no one what you would not want done to you.
If you want peace, work for justice.

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Rob Speer
2004-01-28 19:20:50 UTC
Permalink
Post by Dave Ketchum
This thread is looking for something for the public, rather than what we
might enjoy within our group.
While tournament comes from the time of knights, it gets used for golf
tours, etc., in the modern world.
I do not demand winning this debate, but think tournament should be
considered.
I also approve of the word "tournament".

People _understand_ tournaments. People watch sports, where winners are
decided by systems that are far more complex and obscure than Condorcet.

In fact, here's a way I sometimes explain Condorcet vs. plurality:

Say you have a bunch of basketball teams, and you want to find out which
one is the best. Do you have them all run onto a court at once and fight
over the ball? No - you have them compete two at a time, and hold a
tournament.

Current plurality voting is like all the teams running onto the court at
once. Condorcet is like a round robin tournament.

Plurality just shows who's good at grabbing the ball, or grabbing
attention. Condorcet shows who's actually good at the game, that is,
being preferred by the people.
--
Rob Speer

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Adam Tarr
2004-01-28 20:38:15 UTC
Permalink
Post by Rob Speer
I also approve of the word "tournament".
Tournament isn't bad, but I think it's a trifle inaccurate, since nearly
all sporting tournaments (College World series and a few others being
notable exceptions) are single elimination. While a single elimination
matchup voting scheme would be Condorcet compliant, it's not what we're
really advocating.

I prefer "round robin voting" or "matchup voting", but I think "tournament
voting" is OK too,
Post by Rob Speer
Say you have a bunch of basketball teams, and you want to find out which
one is the best. Do you have them all run onto a court at once and fight
over the ball? No - you have them compete two at a time, and hold a
tournament.
Current plurality voting is like all the teams running onto the court at
once. Condorcet is like a round robin tournament.
It seems like boxing is an easier analogy. Say you have ten boxers and you
want to know who is the best.

Plurality - throw them in the ring, the last one standing is the winner.

IRV - have a referee in the ring who pulls out anyone who's getting badly
beaten. Last one in the ring is the winner.

Borda - the boxer with the most landed punches wins.

Condorcet - have them fight one-on-one in a round robin.

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Dave Ketchum
2004-01-30 01:03:32 UTC
Permalink
Post by Adam Tarr
Post by Rob Speer
I also approve of the word "tournament".
Tournament isn't bad, but I think it's a trifle inaccurate, since nearly
all sporting tournaments (College World series and a few others being
notable exceptions) are single elimination. While a single elimination
matchup voting scheme would be Condorcet compliant, it's not what we're
really advocating.
I prefer "round robin voting" or "matchup voting", but I think
"tournament voting" is OK too,
My dictionary says the kind of round robin we are discussing is a kind of
tournament:
Point for you in being more precise.
I still like tournament, seeing it as correct and more salable.

Golf has tournaments in which many, if not all, players play at the same
time, and their score is the sum of what they do over many holes.
Post by Adam Tarr
Post by Rob Speer
Say you have a bunch of basketball teams, and you want to find out which
one is the best. Do you have them all run onto a court at once and fight
over the ball? No - you have them compete two at a time, and hold a
tournament.
Current plurality voting is like all the teams running onto the court at
once. Condorcet is like a round robin tournament.
It seems like boxing is an easier analogy. Say you have ten boxers and
you want to know who is the best.
Plurality - throw them in the ring, the last one standing is the winner.
Each referee (voter) gets one vote as to which is best.

Approval -

Each referee (voter) votes for as many as they consider to be

acceptable, but cannot indicate which of these they consider to be best.
Post by Adam Tarr
IRV - have a referee in the ring who pulls out anyone who's getting
badly beaten. Last one in the ring is the winner.
Tempting BUT:

Each referee (voter) gets one vote as to which is best. Each voter

is also allowed to rank second, etc,, preferences such that, if their first

choice loses, the first of their preferences are ignored.
Post by Adam Tarr
Borda - the boxer with the most landed punches wins.
Condorcet - have them fight one-on-one in a round robin.
My shot (admittedly looks too wordy):
Each voter lists all the candidates that they want to indicate as
better-than-last in preference order, such that listing "A" ">" "B" in
this order shows preference for A over B, no matter what other candidates
may be listed.

NOTE: We need extra effort on Condorcet vs IRV because these two are similar.
--
***@clarityconnect.com people.clarityconnect.com/webpages3/davek
Dave Ketchum 108 Halstead Ave, Owego, NY 13827-1708 607-687-5026
Do to no one what you would not want done to you.
If you want peace, work for justice.

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Adam Tarr
2004-01-30 01:46:53 UTC
Permalink
Post by Dave Ketchum
Post by Adam Tarr
Post by Rob Speer
I also approve of the word "tournament".
Tournament isn't bad, but I think it's a trifle inaccurate, since nearly
all sporting tournaments (College World series and a few others being
notable exceptions) are single elimination. While a single elimination
matchup voting scheme would be Condorcet compliant, it's not what we're
really advocating.
I prefer "round robin voting" or "matchup voting", but I think
"tournament voting" is OK too,
My dictionary says the kind of round robin we are discussing is a kind of
Point for you in being more precise.
I still like tournament, seeing it as correct and more salable.
Fine by me.
Post by Dave Ketchum
Golf has tournaments in which many, if not all, players play at the same
time, and their score is the sum of what they do over many holes.
True, although that's not a good analogy because there are no pairwise
comparisons going on (except in match play, when golf does become a single
elimination event).
Post by Dave Ketchum
Post by Adam Tarr
It seems like boxing is an easier analogy. Say you have ten boxers and
you want to know who is the best.
Plurality - throw them in the ring, the last one standing is the winner.
Each referee (voter) gets one vote as to which is best.
(other such examples snipped)

Oh, come on. The point was to have an analogy. If we're voting on who
wins, then that's not an analogy, that's the same thing.

-Adam

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Steve Eppley
2004-01-28 19:27:05 UTC
Permalink
Post by Kevin Venzke
Post by Ernest Prabhakar
BTW: Debatable whether voters should be permitted to
rank candidates as equal.
-snip-
Post by Kevin Venzke
Post by Ernest Prabhakar
That doesn't make any sense to me. If two candidates are
ranked, I think that neither should get the win --
at least if we're doing winning votes (wv)
Giving half-votes is the Margins (and Symmetric-Completion)
interpretation. I suggest the same method be used for both
expressed and truncated equal rankings. I can't think why
there should be a difference in treatment.
My Feasibility criterion requires allowing each voter to
leave as many candidates unranked as she wants, since there
might be a huge number of candidates. (Feasibility also
requires the time to tally the votes must be a small
polynomial function of the number of voters and the number
of candidates.)

To satisfy certain criteria (e.g., my Minimal Defense
criterion which is based on Mike Ossipoff's Strong
Defensive Strategy criterion) and assuming voters may only
express orders of preference, it's necessary to (at least)
allow each voter to rank as many candidates as she wants at
the bottom (or leave them unranked, which is to be treated
as the bottom) and to count 0 votes, not 1/2 vote, for and
against each candidate in the pairings of bottommost
candidates.

It's possible to satisfy an even stronger criterion, and
without having to worry about the "wv" vs "margins" issue,
if voters are allowed to insert a special dividing line in
their orders of preference:

Sincere Defense criterion
-------------------------
For all subsets of alternatives X and Y, if more than
half of the voters prefer every alternative in X
over every alternative in Y, then there must exist
a set of admissible voting strategies for that majority
that does not require any misrepresention of preferences
yet ensures all of Y will be defeated (and finish below
all of X if the method produces a social ordering).

Both margins and "wv" methods are capable of satisfying
Sincere Defense, if they're designed right. For example,
MAM can be tweaked as follows:

(See www.alumni.caltech.edu/~seppley for the definition
of MAM, a list of criteria it satisfies, and proofs.)

Let SpecialMajorities denote the subset {(x,y) in
Majorities such that the number of votes that rank
x over the dividing line over y exceeds the number
of votes that rank y over the dividing line over x}.

When sorting the majorities (primarily from largest to
smallest in untweaked MAM) adjust the sort order so that
the special majorities precede all other majorities
(which means the majorities are now sorted secondarily
from largest to smallest).

It is easy to show that the set of special majorities is
acyclic, which means none of them needs to be discarded.
(They can all be "affirmed", in MAM-speak.)

I'm reluctant to propose the dividing line "enhancement"
for use in public elections anytime soon, because I'm
concerned many voters would try to use it as some sort of
"sincere approval" threshold, rather than as the strategic
device it's intended to be. (Note that the concept of
"sincere approval" cannot be derived from conventional
"rational choice" models of individual preferences.) I
would wait to propose it until years after society adopts
good voting methods, to allow time for misleading
absolutist concepts like "approval" to fade from the
culture.

---Steve (Steve Eppley ***@alumni.caltech.edu)

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Ernest Prabhakar
2004-01-30 19:18:34 UTC
Permalink
Hi all,

Thanks for all your input. I've rewritten my IMV proposal to reflect
as much of the comments as I agreed with. :-) I hope to post this on
my site next week, along with a Python implementation. The audience of
this document is primarily people who do *not* have experience in
either set theory or electoral reform. Thus, I have tried to carefully
define my terms, and leave much of the jargon in endnotes. However, I
do also want to be correct in the terminology I do use, so experts
(such as yourselves :-) don't get unnecessarily annoyed.

I would welcome any further comments, as well as additional URLs to
recommend for people who want to learn more. The name, however, is
fixed. :-)

Yours,
Ernest "I want my IMV" Prabhakar


Instant Matchup Voting:
Improving the Roots of Democracy

The Problem
Voter participation and majority rule are often considered the heart of
democracy. However, the most common form of "one person, one vote"
elections in the U.S. (usually called Plurality or First Past the Post)
implicitly assumes there are only two candidates. When there are more
than two candidates, not only is there a risk that no candidate will
get an absolute majority, but voters are faced with the dilemma between
voting 'strategically' (for the lesser of two evils) vs. voting
'sincerely' (with their conscience). This also tends to promote a
two-party system, which despite its many merits (such as the ability to
ensure governable coalitions), is vulnerable to systemic bias (as
evidenced by low voter turnout, due to a perception that neither party
offers a meaningful choice). The end result is that candidates lack a
true majoritarian mandate, due both to low voter turnout and the
possibility of a split vote.

Our Solution
To address these problems, we recommend an alternate election system
called Instant Matchup Voting [1]. Instant Matchup Voting, or IMV,
treats an election as a series of simultaneous one-on-one matchups,
like a round-robin tournament. Each voter's ballot describes the
results of one complete round of matchups between each pair of
candidates. The candidate who gets the majority of votes in all their
matchups is the winner. In the unlikely event of a tie (where no
candidate wins all their matches) the tied candidate with the fewest
votes against them wins.

The Benefits
This system allows voters to fully express their preferences among the
available candidates, and generally makes it possible for them to vote
sincerely without having to worry about strategy [3]. It also tends to
discourage mudslinging in multi-candidate elections, since there is an
incentive to have the other candidate's supporters vote you for second
or third place. Perhaps more importantly, it allows non-traditional and
third-party candidates to run without fear of becoming spoilers,
increasing the range of meaningful choices available to voters.

Instant Matchup Voting
The formal procedure for IMV has five standard phases, plus three
tiebreaking phases:

1. Votes
Each voter votes for all the candidates they like, indicating order of
preference.

Consider an example in a five-candidate election, where a voter likes A
most, B next, and C even less, but doesn't care at all for D or E. In
that case, their ballot would be ranked "A > B > C"

2. Matchups
Each ballot defines the result of matchups between all the candidates
in a election.

Thus, the ballot A > B > C would be interpreted as:
A > B, A > C, A > D, A > E
B > C, B > D, B > E
C > D, C > E


3. Pairwise Matrix
The results from all the ballots is summed up in what is called a
'pairwise matrix', where the rows indicate votes -for- a candidate, and
the columns indicate votes -against- a candidate.

So, given the following results from 9 voters:
4 votes of A > B > C (over D and E)
3 votes of D > C > B (over A and E)
2 votes of B > A (over C, D and E)

The pairwise matrix would be:
A B C D E
A - 4 6 6 6
B 5 - 6 6 9
C 3 3 - 5 7
D 3 3 3 - 3
E 0 0 0 0 -


4. Win tabulation
Using the matrix, tabulate the wins for each candidate.

For the case above, we have:
A> C:6/3, D:6/3, E:6/0
B> A:5/4, C:6/3, D:6/3, E:9/0
C> D:5/3, E:7/0
D> E:3/0
E> -nobody-

Note: "A> D:6/3" means 6 votes for A > D vs. 3 votes for D > A

5. Majority winner
The candidate who wins all their matchups is the majority winner

In the case above, B wins all their matchups. In particular, B beats A,
since a majority of voters indicated that they prefer B over A. True,
some of those voters would ideally have preferred D or C, but since
they can't have that they're still happier with B than A. By using all
the information from every voter, IMV is one of the most efficient
forms of voting available, in terms of maximizing the wishes of the
majority.

6. First-round ties
In rare cases there may be no majority winner. [4]. In this case, we
declare a 'first round tie' (also known as a Smith Set[2]) between the
candidate with the least losses [5], and all the candidates which don't
lose to that candidate or another member of the Smith Set.

For example, consider 9 ballots of the form:
2 votes of A > B > C (over D and E)
4 votes of D > C > B (over A and E)
3 votes of E > A (over B, C and D)

This gives a win table of:
A> B:5/4, C:5/4, D:5/4
B> E:6/2
C> B:4/2, E:6/2
D> B:4/2, C:4/2, E:4/3
E> A:3/2

or, equivalently, a loss table of:
A< E:2\3
B< A:4\5, C:2\4, D:2\4
C< A:4\5, D:2\4
D< A:4\5
E < B:2\6, C:2\6, D:3\4

Thus, A < E, E < (B, C, D), so the Smith Set is [A,B,C,D,E] - a five
way tie!

7. Tiebreaker
The tiebreaker is the member of the Smith Set who had the least number
of people voting against them.

For the example in (6), the most votes against each candidate is:
A:3, B:5, C:5, D:5, E:6
Thus, A is the tiebreaking winner with only 3 votes against them --
though in this exceptional case they not the majority winner.

8. Second-round ties
If two or more candidates have the least number of people voting
against them (within statistical uncertainties[6]), these then form a
second-round tie. If there is no alternative mechanism available[7],
the winner is picked at random from within the second-round tie.

Ernest N. Prabhakar, Ph.D.
Founder, RadicalCentrism.org
January 30, 2004

RadicalCentrism.org is an anti-partisan think tank based near
Sacramento, California, which is seeking to develop a new paradigm of
civil society encompassing politics, economics, psychology, and
philosophy. We are dedicated to developing and promoting the ideals of
Reality, Character, Community & Humility as expressed in our Radical
Centrist Manifesto: The Ground Rules of Civil Society.

Notes
[1]
IMV is a variant of what is called Smith PC(wv) -- short for Plain
Condorcet using winning-votes within the Smith Set[2]. See
http://www.wikiepedia.org/wiki?condorcet for more details.
[2]
The Smith Set is those candidates which beat all the candidates outside
the set, but beat or tie (do not lose to) each other.
[3]
To be precise, it is mathematically impossible to have a perfect voting
system free of any strategic considerations. However, we believe Smith
PC (wv) is the simplest system that meets most of the important
criteria. More complicated tiebreaking formulas might resist strategic
manipulation better on certain occasions, but only under what we
consider extraordinary and unlikely circumstances (at least for large
public elections).
[4]
This can only happen if we have a 'rock-paper-scissors' situation (also
called a circular tie), where A beats B, and B beats C, but C beat A.
This is very unlikely in normal public elections -- since each
individual ballot requires a strict ranking among candidates -- but is
possible if, for example, a significant fraction of the population
casts ballots that don't reflect a linear Left-Right political
spectrum.
[5]
If several candidates have the maximum number of wins, pick the one
which beats the other such candidates. If there is a circular tie among
them, include them all in the Smith Set.
[6]
Voting machines and processes, like all human activities, are not
infinitely accurate. If the difference between two votes is less than
the achievable precision, it is statistically insignificant, and
therefore random. In such cases, we believe it is better to be
explicitly random than to use arbitrary criteria to create a false
level of precision. Of course, this requires having a well-established
error rate (level of uncertainty) before the election, to avoid
uncertainty about the uncertainty!
[7]
In some environments, there is an alternate mechanism available for
'true' tiebreakers. Either an alternate body (e.g., the House of
Representatives) can break the tie, or (for small groups) it may be
feasible to re-run the election and hope that the results will shift.
However, in other cases no alternate mechanism is available, but a
decision is still necessary. For these cases, we specify random choice
in order that IMV may be completely specified, especially for computer
analysis of voting methods.

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Adam Tarr
2004-01-30 20:06:40 UTC
Permalink
Here are some suggestions (really, only two suggestions, but one of them
In the unlikely event of a tie (where no candidate wins all their
matches) the tied candidate with the fewest votes against them wins.
I think calling this situation a "tie" only generates confusion and makes
the method seem weak. Just saying "In the unlikely event where no
candidate wins all their matches..." seems fine.
Instant Matchup Voting
The formal procedure for IMV has five standard phases, plus three
In keeping with my suggestion to avoid referring to cyclic ambiguities as
ties... "five standard phases, and three more phases in certain rare cases"
3. Pairwise Matrix
The results from all the ballots is summed up in what is called a
'pairwise matrix', where the rows indicate votes -for- a candidate, and
the columns indicate votes -against- a candidate.
I think the pairwise matrix step you show should be moved entirely to the
"notes" section. In the step before, you showed how to break a vote down
into its matchups. In the step after, you show what to do with the vote
totals. All that the pairwise matrix is, is a way to display results. It
confuses the casual viewer and takes them away from the general flow of how
Condorcet works (which you did a great job describing up to that part, by
the way). If you leave this in the body, you'll lose a lot of people who
were following you just fine up to there.
6. First-round ties
I'd call this, "procedure when no majority winner exists" or somesuch.
8. Second-round ties
If two or more candidates have the least number of people voting against
them (within statistical uncertainties[6]), these then form a second-round
tie. If there is no alternative mechanism available[7], the winner is
picked at random from within the second-round tie.
I would just call this "ties" as oppose to second-round ties. This is (in
the context of plain Condorcet) an actual tie, as oppose to what we were
looking at before.

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Ernest Prabhakar
2004-02-09 07:21:58 UTC
Permalink
Hi all,

Well, after digesting Eric Gorr's deterministic variant of MAM (if he,
and I, understand it correctly), I have rewritten my IMV proposal to
use that instead of Smith PC, under the new name "Multiple Matchup
Voting" - since it is based on ranking the results of multiple
matchups. I've also added Adam's suggestion of hiding the Pairwise
Matrix in favor of simplicity.

The terminology is probably a little rough (since I'm writing this late
at night), but I still welcome your comments. I think I have a good
idea how to implement this, but I want to make sure I understand the
basic algorithm first.

-- Ernie P.

Multiple Matchup Voting:
Improving the Roots of Democracy

http://RadicalCentrism.org/mm_voting.html

A. The Problem
Voter participation and majority rule are often considered the heart
of democracy. However, the most common form of voting in the U.S. --
"one person, one vote" (technically known as Plurality or First Past
the Post) -- implicitly assumes there are only two candidates. When
there are more than two candidates, not only is there a risk that no
candidate will get an absolute majority, but voters are faced with the
dilemma between voting 'strategically' (for the lesser of two evils)
vs. voting 'sincerely' (what their conscience feel is the 'best'
candidate). This also tends to promote a two-party system, which
despite its many merits (such as the ability to ensure governable
coalitions), is vulnerable to systemic bias (as evidenced by low voter
turnout, due to a perception that neither party offers a meaningful
choice). The end result is that candidates lack a true majoritarian
mandate, due both to low voter turnout and the possibility of a split
vote.

B. Our Solution
To address these problems, we recommend an alternate election system
we call Multiple Matchup Voting [1], where voter rank the candidates in
order of preference. Multiple Matchup Voting, or MMV, treats the
ballots as the result of simultaneous one-on-one matchups, like a
round-robin tournament. Each voter's ballot describes the results of
one complete round of matchups between each pair of candidates. The
results of the matchups are used to compile an ordered list of
candidates. This guarantees[2] that the winner is the majority
preference under all circumstances, regardless of the number of
candidates.

C. The Benefits
This system allows voters to fully express their preferences among the
available candidates, and generally makes it possible for them to vote
sincerely without having to worry about strategy [3]. It also tends to
discourage mudslinging in multi-candidate elections, since there is an
incentive to have the other candidate's supporters vote for you as
second or third place. Perhaps more importantly, it allows
non-traditional and third-party candidates to run without fear of
becoming spoilers, increasing the range of meaningful choices available
to voters.

D. Multiple Matchup Voting
The formal procedure for MMV has five phases:

1. Voting
Each voter votes for all the candidates they like, indicating order of
preference if any.

Consider an example in a five-candidate election, where a voter likes
A most, B next, and C even less, but doesn't care at all for D or E. In
that case, their ballot would be ranked "A > B > C > D = E". This can
be shortened to "A > B > C" since unranked candidates are considered to
be at the bottom and equivalent. Similarly, if another voter liked E
most, considered D and C tied for second, and ranked B over A, their
ballot would be "E > D = C > B > A" (with the last "> A" being
optional, since its redundant).

2.Matchups Defined
Each ballot defines the result of one round of matchups between all
the candidates in a election.

Thus, the ballot A > B > C would be interpreted as:
A > B, A > C, A > D, A > E
B > C, B > D, B > E
C > D, C > E

while "E > D = C > B > A" would be:
E > D, E > C, E > B, E > A
D > B, D > A
C > B, C > A
B > A


3. Matchups Counted
When all the balots are counted, this gives a final score for each
matchup. [4].

Say we have nine voters, who voted as follows
4: A > B > C
3: E > D = C > B
2: C > A > D

this gives:
6/3: A > B
4/5: A > C
6/3: A > D
6/3: A > E
4/5: B > C
4/5: B > D
4/3: B > E
6/0: C > D
6/3: C > E
2/3: D > E

Note how some matchups add up to less than 9, because some candidates
were ranked equal by some voters. Also, the total number of matchups
for N candidates is always N * (N-1)/2, or 10 for N = 5.

4. Matchups Ranked
Next, the matchups are ranked in order of the largest winner. If two
matchups have the same winner, the one with the smallest loser (largest
margin) is listed first. If the matchups are completely identical, it
is called a pairwise tie; while common in small committees, such ties
are extremely unlikely in public elections.

The ballots above would thus be reordered to give:
6/0: C > D
6/3: A > B
6/3: A > D
6/3: A > E
6/3: C > E
5/4: C > A
5/4: C > B
5/4: D > B
5/4: E > B
3/2: E > D


5. Candidates ordered
This list of matchups is traversed in order, from the largest win
down. The candidates are sorted into a list that is consistent with
that order, with the following caveats:

(i) In the unlikely event that a matchup later in the list conflicts
with the previously-determined order[5], that matchup is discarded
(this is why the ordering of matchups is significant).

(ii) In the even unlikelier case where several members of a pairwise
tie might conflict with each other, all such conflicting matchups are
discarded. [6].

Stepping through the ordered list of matchups, we find (using (X,Y) for
unordered candidates):
1: C > D
2: A > B, C > D
3: A > B, (A,C) > D
4: A > (B,E), (A,C) > D
5: A > B, (A,C) > (D,E)
6: C > A > (B,D,E) [implies C > B]
7: C > A > (B,D,E) [thus unchanged]
8: C > A > D > (B,E)
9: C > A > D > E > B
10: C > A > D > E > B [E > D discarded as inconsistent]


6. Winner selection
Thus, with MMV will always have a strict ordering of candidates
(unless all the pairwise matchups for multiple candidate are precisely
identical). The top candidate, obviously, is the winner. If there
really is a true tie among the top candidates, then the winner would
need to be chosen from the top candidates by random draw, or some
external mechanism.

E. Conclusions

Since Multiple Matchup Voting uses all the information available, and
weights larger majorities over lesser ones (in case of conflict), it is
always gauranteed to reflect the majority preference of the electorate.
While this sort of electoral reform may not solve all our political
problems, it will help involve more voters -- and candidates -- in the
electoral process, which can only strengthen our democratic
institutions.
Ernest N. Prabhakar, Ph.D.
Founder, RadicalCentrism.org
February 8, 2004

RadicalCentrism.org is an anti-partisan think tank based near
Sacramento, California, which is seeking to develop a new paradigm of
civil society encompassing politics, economics, psychology, and
philosophy. We are dedicated to developing and promoting the ideals of
Reality, Character, Community & Humility as expressed in our Radical
Centrist Manifesto: The Ground Rules of Civil Society.

Notes
[1]
MMV could also stand for Majority Maximization Voting, as it is based
on a deterministic form of Steve Eppley's Maximize Affirmed Majorities
(MAM) system, which in turn is a variant of Tideman's well-studied
Ranked Pairs algorithm. See http://www.wikiepedia.org/wiki?condorcet
for more details. This deterministic variant was first suggested to me
by Eric Gorr of http://www.condorcet.org/.
[2]
Under a suitable definition of majority preference. See Note 5.
[3]
To be precise, it is mathematically impossible to have a perfect voting
system free of any strategic considerations. However, with Maximize
Affirmed Majorities sincere voting is usually the optimal strategy. It
is theoretically possible for one party to attempt to vote
'insincerely' (at the risk of electing a non-preferred candidate) to
avoid electing the true consensus winner, but in that case there are
defensive strategies that other parties can use to preserve the
intended winner. The deterministic variant(somemtimes called MAM-d) is
not quite as well studied as MAM, but so far appears to possess all the
same desireable properties.
[4]
This tabulation is usually done via what is called a 'pairwise
matrix', where the rows indicate votes -for- a candidate, and the
columns indicate votes -against- a candidate. This is often used in
voting systems associated with the Condorcet Criteria, which states
that any candidate which is unanimously preferred to each other
candidate on the basis of pairiwse matchups should win the election.

For example, given the following results from 9 voters:
4 votes of A > B > C (over D and E)
3 votes of D > C > B (over A and E)
2 votes of B > A (over C, D and E)

The pairwise matrix (sometimes called the Condorcet matrix) would be:
A B C D E
A - 4 6 6 6
B 5 - 6 6 9
C 3 3 - 5 7
D 3 3 3 - 3
E 0 0 0 0 -


[5]
This can only happen if we have a 'rock-paper-scissors' situation (also
called a circular tie), where A beats B, and B beats C, but C beat A.
This is very unlikely in normal public elections -- since each
individual ballot requires a strict ranking among candidates -- but is
possible if, for example, a significant fraction of the population
casts ballots that don't reflect a linear Left-Right political
spectrum.
[6]
For example, say that the current ordering is "A > B, C > D", and
there is a pairwise tie between the next two items, "B > C" and "D >
A". Since the former would imply "A > D" and the latter would imply "C
B", they are inconsistent with each other, and would both be
discarded. Again, this is an extremely unnatural occurence, but is
included here for theoretical completeness.

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Eric Gorr
2004-02-09 14:10:49 UTC
Permalink
Post by Ernest Prabhakar
Well, after digesting Eric Gorr's deterministic variant of MAM (if
he, and I, understand it correctly),
It's actually not my variant. First got the method description from
Mike and would like to find a better name for it.
--
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"Therefore the considerations of the intelligent always include both
benefit and harm." - Sun Tzu
== Insults, like violence, are the last refuge of the incompetent... ===
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Dave Ketchum
2004-01-28 03:29:47 UTC
Permalink
I like what Ernest writes, though I see a bit of room for improvement and
suggest "tournament" as a less foreign-sounding title (even though its
ancestry is also French).

On Tue, 27 Jan 2004 09:10:36 -0800 Ernest Prabhakar wrote, per subject:

Re: [EM] Condorcet for public proposals - IMV
Post by Ernest Prabhakar
Hi Anthony,
Post by Anthony Duff
I suggest that a definition of the condorcet election method being
publicly proposed should be explicit about the full pairwise
analysis, and that the possibility of a circular tie, and the
resolution of such a circular tie should be treated like a footnote.
I tend to agree with you.
Cycles are possible, so they better get attended to, however rarely they
may be expected (one general rule to be remembered is that whatever is
possible, but not prepared for, WILL happen - regardless of theoretical odds).

But they should not get in the way of explaining the heart of the basic
method.
Post by Ernest Prabhakar
Post by Anthony Duff
..Is the problem that D is not in the smith set? The general public is
not going to make this complaint. With PC, such a set is never
mentioned.
Looking back to what Anthony wrote - his voters AGREED that D was a lemon
- any method that declares such a lemon to be sweet had better start
defending or revising.
Post by Ernest Prabhakar
Actually, I"m leaning towards Smith PC (Plain Condorcet within the Smith
Set of tied winners) as perhaps the optimal tradeoff between rigor and
clarity for public elections. As you point out, in public elections
circular ties are rather unlikely to come up. But I think the concept
of a tiebreaker round actually helps in the understanding, and using PC
(least greatest defeat) as a tie breaker is far simpler to calculate and
explain than any of the alternatives I've seen.
Post by Anthony Duff
Another thought: “condorcet” is an unfortunate name. It is an
unfamiliar French name. People probably won’t even agree on how it
is to be pronounced. As for the abbreviation “PC” – it has already
been used, as in “personal computer”, and in “politically correct”.
Are there any thoughts for a better name?
Yeah, my friends (on the radical centrist list) are unanimous that the
term Condorcet has to go. :-)
I have been proposing the term 'Instant Matchup Voting', or IMV, by
analogy with Instant Runoff Voting. I compare it to a round-robin
tournament, which most people have direct experience with. I think this
Ahead of much that I have seen, but I suggest tournament as even easier to
visualize from. My definition will follow yours.
Post by Ernest Prabhakar
1. Each rank-ordered ballot is interpreted as a series of "Instant Matchups"
That is A > B > C, implies one point each for the three pairwise
Matchups A > B, B > C, and A > C
Note that "A>B" is counted separately from "B>A" (i.e., winning votes)
2. Tally up the N * (N-1) Matchups, for each ordered pair of candidates
3. If one candidate beats everyone, that's the absolute winner
4. If there is a 'rock-paper-scissors' tie (A >= B, B >= C, C >= A),
the tiebreaking winner is the candidate from that group with the
'least greatest defeat'
Tournament:
0. Voters simply rank as many of the candidates as they choose, starting with
their most-preferred.
1. Each rank-ordered ballot is interpreted as a series of matches among all

candidates in the election:
That is, ranking A > B > C, and D and E not ranked by this voter,

implies each ranked candidate winning over each candidate ranked later, and

over each unranked candidate.

Thus unranked candidates do not get counted as ranked over each other.

Note that "A>B" is counted separately from "B>A" (i.e., winning votes).
2. Tally up the number of wins for each ordered pair of candidates in an

N*N array (with an empty diagonal, for candidates do not play against
themselves).

3. If one candidate wins when compared with each other candidate, that's

the absolute winner.
4. If no absolute winner, we have a 'rock-paper-scissors' near tie such as

(A >= B, B >= C, C >= A), and the tiebreaking winner is the candidate from

that group with the 'least greatest defeat'.


NOTE: I consider 'least greatest defeat' unacceptably opaque for this
purpose, and ask for help in providing simpler words.

BTW: Debatable whether voters should be permitted to rank candidates as
equal. If so then, for each pair of equal candidates, count 1/2 win for
each (thus if two voters rank A=B=C then A>B, B>A, A>C, C>A, B>C, and C>B
each get credited one full win).
Post by Ernest Prabhakar
I actually think the Smith tiebreaking round makes it easier to
understand and defend than straight PC. Terms like Smith sets, cycles,
and even circular ties can be confusing. However, using the
round-robin analogy, everyone I've talked to quickly grasps the
rock-paper-scissors concept. We could even recurse it to give a
complete ordering (which is important to many people).
While Smith PC is not quite perfect, to me this seems the simplest
possible definition that would make sense to people. I have something
close to this implemented, though I've been planning to also implement
Ranked Pairs, Beatpath, and perhaps SD so that the experts can easily
compare alternative calculations. And of course I've been distracted
by my Auto-Districting program (which was written a week ago, but I've
just started debugging).
Does anyone think Smith PC is likely to cause any severe pathologies in
a public election? Are there open questions that we could work to
resolve, if people agree it is a good idea?
-- Ernie P.
--
***@clarityconnect.com people.clarityconnect.com/webpages3/davek
Dave Ketchum 108 Halstead Ave, Owego, NY 13827-1708 607-687-5026
Do to no one what you would not want done to you.
If you want peace, work for justice.

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Kevin Venzke
2004-01-28 01:03:15 UTC
Permalink
Anthony,
Post by Anthony Duff
I note that PC is not the simplest condorcet method. PC means
PC(winning votes). PC(margins) would be simpler and more intuitive.
Margins are intuitive. The pairwise contests are decided by margins.
The newcomer to condorcet will want to know why defeats should be
used instead of margins.
I disagree on a couple of points.
1. I don't see how Margins is simpler. When resolving scenarios with
pen and paper, Margins requires an extra subtraction step to find every
defeat strength.
2. I don't see why the margin, measured as the absolute number of votes
difference, is intuitive. If anything, the relative margin seems more
intuitive; that is, a 14-2 contest would have strength of "7x," not 6.
3. Does the newcomer to Condorcet really want to know that? Whenever
I introduce people to election methods, I don't bring up Margins very
early on, and I've yet to have it suggested to me.

I believe it is intuitive to measure defeat strength as the (absolute)
number of voters who can complain if the defeat is tossed out.

It might be more intuitive (in a different way) to measure defeat strength
as the number of non-abstaining voters (in that contest), but then voters
on the losing side might regret participating in the contest. Also, we
need a secondary measure if all voters participate in certain contests.
Post by Anthony Duff
I wonder if, rather than explaining everything, an implicit “just
trust me” approach would be better used in the first instance.
“When resolving a circular tie, measuring defeats by margins has been
shown to be vulnerable to strategic manipulation. By measuring
defeats by winning votes, that vulnerability is significantly
reduced”
I use examples which illustrate how WV works, and in passing note how
Margins would have differed. I haven't yet found it necessary to discuss
differences in strategy, as whether or not Margins is more intuitive, it
doesn't seem to provide more intuitive *winners*.
Post by Anthony Duff
Has anyone got an argument for why a particular community might produce a
sincere, circular tie? Does anyone have evidence of one actually
exisiting?
What is wrong with:
35 A>B
20 B
45 C ?
Post by Anthony Duff
I do not think the condorcet loser criterion is really that
important. The condorcet winner criterion is very important, and I
might even rank it as paramount. I think the symmetric relationship
between these two criteria has artificially raised the status of the
condorcet loser criterion.
I think the condorcet loser criterion is less important than an
overruled majority.
I was recently considering a criterion to be called "Raynaud Loser,"
dictating that the method should not elect the loser of the strongest
pairwise contest.

If you care about not overruling majorities, strength has to be by WV.
Post by Anthony Duff
20 ABCD
20 BCAD
20 CABD
13 DABC
13 DBCA
13 DCAB
D wins despite being ranked last by 60% and despite being beaten by
every other candidate.
My justification of the win by D is this: No other single candidate
can stand up, in court or in public, and complain that they should be
the winner because they beat D 60 to 39. Should A, for example, do
this, D can immediately counter by pointing out that A suffered a
worse defeat of 66 to 33. Therefore, A’s case is worse than D’s.
Condorcet is a pairwise method. Let the justifications and
complaints be made in a pairwise manner. I think this would be
convincing in a public forum.
Someone might suggest that A, B & C are effective clones, that they
represent a similar position with respect to D.
This is what I see.
Post by Anthony Duff
This is an advanced
argument. However, a problem with it is that the extreme strength of
the cycle suggests that there are some very strong feelings
differentiating A from B from C. If they were clones, then why
didn’t nearly as many vote CBA as ABC?
I'm afraid I don't find this very convincing, since each voter will know
whether they preferred the clones to D or vice versa.
Post by Anthony Duff
Another thought: “condorcet” is an unfortunate name. It is an
unfamiliar French name. People probably won’t even agree on how it
is to be pronounced. As for the abbreviation “PC” – it has already
been used, as in “personal computer”, and in “politically correct”.
Are there any thoughts for a better name?
I like "pairwise methods." For "PC" itself I prefer "MinMax." But foremost
I would use the term "pairwise" to describe the method as different from
others.


Kevin Venzke
***@yahoo.fr


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Dave Ketchum
2004-06-21 05:23:04 UTC
Permalink
On Mon, 21 Jun 2004 03:46:48 +0200 (CEST) Kevin Venzke continued insisting
that WV is the same as Margins except that:
Margins counts explicit and implied equality,
While WV does not.

So I quote his Jan post below, which agrees with my memory on this detail:
WV simply uses winners' vote counts in resolving cycles.
Margins requires an extra subtraction step to determine margin
between winner's vote count and loser's vote count.

I argue that explicit equal ranking should be included in WV to make these
counts comparable as related to voters' intent.

I argue that counting equal ranking has no value in margins since it would
not affect the margins, BUT would do the same counting as for WV for
consistency.

Dave

On Wed, 28 Jan 2004 02:03:15 +0100 (CET) Kevin Venzke wrote:

Subject: Re: [EM] Condorcet for public proposals
Post by Ernest Prabhakar
Anthony,
Post by Anthony Duff
I note that PC is not the simplest condorcet method. PC means
PC(winning votes). PC(margins) would be simpler and more intuitive.
Margins are intuitive. The pairwise contests are decided by margins.
The newcomer to condorcet will want to know why defeats should be
used instead of margins.
I disagree on a couple of points.
1. I don't see how Margins is simpler. When resolving scenarios with
pen and paper, Margins requires an extra subtraction step to find every
defeat strength.
2. I don't see why the margin, measured as the absolute number of votes
difference, is intuitive. If anything, the relative margin seems more
intuitive; that is, a 14-2 contest would have strength of "7x," not 6.
3. Does the newcomer to Condorcet really want to know that? Whenever
I introduce people to election methods, I don't bring up Margins very
early on, and I've yet to have it suggested to me.
I believe it is intuitive to measure defeat strength as the (absolute)
number of voters who can complain if the defeat is tossed out.
It might be more intuitive (in a different way) to measure defeat strength
as the number of non-abstaining voters (in that contest), but then voters
on the losing side might regret participating in the contest. Also, we
need a secondary measure if all voters participate in certain contests.
Post by Anthony Duff
I wonder if, rather than explaining everything, an implicit "just
trust me" approach would be better used in the first instance.
"When resolving a circular tie, measuring defeats by margins has been
shown to be vulnerable to strategic manipulation. By measuring
defeats by winning votes, that vulnerability is significantly
reduced"
I use examples which illustrate how WV works, and in passing note how
Margins would have differed. I haven't yet found it necessary to discuss
differences in strategy, as whether or not Margins is more intuitive, it
doesn't seem to provide more intuitive *winners*.
Post by Anthony Duff
Has anyone got an argument for why a particular community might produce a
sincere, circular tie? Does anyone have evidence of one actually
exisiting?
35 A>B
20 B
45 C ?
Post by Anthony Duff
I do not think the condorcet loser criterion is really that
important. The condorcet winner criterion is very important, and I
might even rank it as paramount. I think the symmetric relationship
between these two criteria has artificially raised the status of the
condorcet loser criterion.
I think the condorcet loser criterion is less important than an
overruled majority.
I was recently considering a criterion to be called "Raynaud Loser,"
dictating that the method should not elect the loser of the strongest
pairwise contest.
If you care about not overruling majorities, strength has to be by WV.
Post by Anthony Duff
20 ABCD
20 BCAD
20 CABD
13 DABC
13 DBCA
13 DCAB
D wins despite being ranked last by 60% and despite being beaten by
every other candidate.
My justification of the win by D is this: No other single candidate
can stand up, in court or in public, and complain that they should be
the winner because they beat D 60 to 39. Should A, for example, do
this, D can immediately counter by pointing out that A suffered a
worse defeat of 66 to 33. Therefore, A's case is worse than D's.
Condorcet is a pairwise method. Let the justifications and
complaints be made in a pairwise manner. I think this would be
convincing in a public forum.
Someone might suggest that A, B & C are effective clones, that they
represent a similar position with respect to D.
This is what I see.
Post by Anthony Duff
This is an advanced
argument. However, a problem with it is that the extreme strength of
the cycle suggests that there are some very strong feelings
differentiating A from B from C. If they were clones, then why
didn't nearly as many vote CBA as ABC?
I'm afraid I don't find this very convincing, since each voter will know
whether they preferred the clones to D or vice versa.
Post by Anthony Duff
Another thought: "condorcet" is an unfortunate name. It is an
unfamiliar French name. People probably won't even agree on how it
is to be pronounced. As for the abbreviation "PC" - it has already
been used, as in "personal computer", and in "politically correct".
Are there any thoughts for a better name?
I like "pairwise methods." For "PC" itself I prefer "MinMax." But foremost
I would use the term "pairwise" to describe the method as different from
others.
Kevin Venzke
--
***@clarityconnect.com people.clarityconnect.com/webpages3/davek
Dave Ketchum 108 Halstead Ave, Owego, NY 13827-1708 607-687-5026
Do to no one what you would not want done to you.
If you want peace, work for justice.

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Kevin Venzke
2004-06-21 07:00:04 UTC
Permalink
Dave,
Post by Dave Ketchum
On Mon, 21 Jun 2004 03:46:48 +0200 (CEST) Kevin Venzke continued insisting
Margins counts explicit and implied equality,
While WV does not.
WV simply uses winners' vote counts in resolving cycles.
Margins requires an extra subtraction step to determine margin
between winner's vote count and loser's vote count.
Either works. The subtraction step gives the same results as though you had
counted half-votes.
Post by Dave Ketchum
I argue that explicit equal ranking should be included in WV to make these
counts comparable as related to voters' intent.
I argue that counting equal ranking has no value in margins since it would
not affect the margins, BUT would do the same counting as for WV for
consistency.
Counting half-votes: Doesn't affect the margins
Counting no votes: Doesn't affect the margins

So you DO realize that your count rule, with a Margins "interpretation of
the counts," gives exactly the same winners as Margins?

Kevin Venzke
***@yahoo.fr






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Dave Ketchum
2004-06-21 20:13:21 UTC
Permalink
PLEASE stick to the issue!!!

Recently you claimed that WV and Margins are identical, so my last
iteration here quoted YOUR ASSERTION that they are different, as I have
been claiming.

As to whether counting equality matters under Margins, we seem agreed that
it does not.
Post by Kevin Venzke
Dave,
Post by Dave Ketchum
On Mon, 21 Jun 2004 03:46:48 +0200 (CEST) Kevin Venzke continued insisting
Margins counts explicit and implied equality,
While WV does not.
WV simply uses winners' vote counts in resolving cycles.
Margins requires an extra subtraction step to determine margin
between winner's vote count and loser's vote count.
Either works. The subtraction step gives the same results as though you had
counted half-votes.
What you imply is not quite true:
Since Margins is in the business OF MARGINS, it cares not whether
half-votes were counted, since they do not affect this detail.
BUT what is significant is that counting half-votes DOES affect the
numbers used by WV, where they therefore make a difference.
Post by Kevin Venzke
Post by Dave Ketchum
I argue that explicit equal ranking should be included in WV to make these
counts comparable as related to voters' intent.
I argue that counting equal ranking has no value in margins since it would
not affect the margins, BUT would do the same counting as for WV for
consistency.
Counting half-votes: Doesn't affect the margins
Counting no votes: Doesn't affect the margins
So you DO realize that your count rule, with a Margins "interpretation of
the counts," gives exactly the same winners as Margins?
What you say about Margins is true - BUT talking about this side issue
distracts from agreeing or disagreeing as to whether there is a difference
between WV and Margins.
Post by Kevin Venzke
Kevin Venzke
--
***@clarityconnect.com people.clarityconnect.com/webpages3/davek
Dave Ketchum 108 Halstead Ave, Owego, NY 13827-1708 607-687-5026
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If you want peace, work for justice.

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Kevin Venzke
2004-06-22 19:52:34 UTC
Permalink
Dave,
Post by Dave Ketchum
PLEASE stick to the issue!!!
Recently you claimed that WV and Margins are identical, so my last
iteration here quoted YOUR ASSERTION that they are different, as I have
been claiming.
I asked you to quote my assertion that they are identical, not that they are
different. I don't claim they are identical.
Post by Dave Ketchum
As to whether counting equality matters under Margins, we seem agreed that
it does not.
Good.
Post by Dave Ketchum
Post by Kevin Venzke
Post by Dave Ketchum
WV simply uses winners' vote counts in resolving cycles.
Margins requires an extra subtraction step to determine margin
between winner's vote count and loser's vote count.
Either works. The subtraction step gives the same results as though you had
counted half-votes.
Since Margins is in the business OF MARGINS, it cares not whether
half-votes were counted, since they do not affect this detail.
BUT what is significant is that counting half-votes DOES affect the
numbers used by WV, where they therefore make a difference.
When I said "either works" I was talking about Margins.
Post by Dave Ketchum
Post by Kevin Venzke
So you DO realize that your count rule, with a Margins "interpretation of
the counts," gives exactly the same winners as Margins?
What you say about Margins is true - BUT talking about this side issue
distracts from agreeing or disagreeing as to whether there is a difference
between WV and Margins.
We agree that there is a difference. I consider that to be the side issue, though.

Kevin Venzke
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Forest Simmons
2004-01-28 02:23:34 UTC
Permalink
Post by Anthony Duff
From: "MIKE OSSIPOFF"
Subject: [EM] Condorcet for public proposals
Date: Tue, 23 Dec 2003 09:47:47 +0000
Mike wrote, in part,
... SSD, RP, and PC are
the Condorcet versions to propose for public elections.
That's because those Condorcet versions are the ones with natural
and
obvious motivation and justification. Obviously, of those 3, PC
isn't as
good as the other 2.
As I understand: SSD and RP are excellent methods, they are identical
in virtually every reasonable election result, and it is too
difficult to definitively decide which is better. PC is a very good
method, with the merit of being straightforward and brief to explain.
Mike implies(?), something that I think is very important. If you
are going to make a serious public proposal, you have to be certain
about your proposal. If you are hesitating over the details, then
you will not inspire confidence. When it comes to a public proposal,
with a public that has little patience for details, you must have
precisely one, well defined proposal.
Why not give the voters a choice between several well defined proposals?

Do we believe in democracy or not?

Forest

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Markus Schulze
2004-01-27 17:40:43 UTC
Permalink
Dear Anthony,
Post by Anthony Duff
I suggest that a definition of the condorcet election method being
publicly proposed should be explicit about the full pairwise
analysis, and that the possibility of a circular tie, and the
resolution of such a circular tie should be treated like a footnote.
I don't agree with you.

For example: Suppose someone promotes Tideman's ranked pairs method.
This method satisfies Condorcet, monotonicity, independence of clones,
reversal symmetry, etc.. When he promotes only the Condorcet criterion
and treats the ranked pairs method only in a footnote then the readers
will mistakenly believe that the main reason or even the sole reason
why he promotes this method is that it satisfies Condorcet. However,
in so far as this method also satisfies monotonicity, independence of
clones, reversal symmetry, etc. this method is a very good method even
when the readers don't consider the Condorcet criterion to be important.

Therefore, instead of promoting Condorcet methods in general and
mentioning Tideman's ranked pairs method only in a footnote, I suggest
to promote Tideman's ranked pairs method in general and to mention that
this method happens to satisfy the Condorcet criterion only in a footnote.

In my opinion, the Condorcet criterion should be treated as one criterion
among many criteria. Otherwise there is the danger that when a given
reader doesn't consider the Condorcet criterion to be important then he
will consider Tideman's ranked pairs method to be completely worthless.

Markus Schulze
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Dave Ketchum
2004-01-29 01:41:25 UTC
Permalink
My suggestion about a better name: Ranked Voting or Ranked Voting Method, etc.
I am not too excited about tournament or instant matchup.
Tournament sounds like a game rather than something more serious. Instant Matchup is a technically better name than Ranked Voting, but it requires the public to think too deeply to the next level. They have to think about how the winner is actually selected rather than what they have to do when they go to the polls. When they go to the polls they rank the candidates. They can understand that easily, therefore Ranked Voting or Vote Ranking is an understandable name.
Those who care to understand how and why the results are matched will really "get it" and be the biggest advocates. The general populace will be happy with the knowledge that by using a Ranked Voting system they are being better represented. The superficial understanding will be all they need or want.
Thanks for your 2 cents.

I suspect "Ranked Voting" is a loser, for that describes IRV as well as us.

I claim we have better rights to Tournament, for we count ALL that the
voter says, while IRV often ignores significant ranking.
That is my 2 cents worth for now.
Chris
--
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Steve Eppley
2004-01-28 20:42:28 UTC
Permalink
Ernie Prabhakar wrote:
-snip-
Post by Ernest Prabhakar
I like what Ernest writes, though I see a bit of room
for improvement and suggest "tournament" as a less
foreign-sounding title (even though its ancestry
is also French).
-snip-
Post by Ernest Prabhakar
Well, tournament does have the idea of a series of matches, but not
necessarily individual pairwise matchups, I don't think. We could
use the term Instant Round-Robin, which is much more explicit, but IRR
is too close to IRV. :-(
I occasionally use the term Instant Round-Robin, but it's a
generic term for all methods that exhaustively tally all
the pairwise voted preferences, so it shouldn't be
appropriated for a particular voting method. The same
holds for the other terms you're considering.

You could keep the "Round-Robin" and replace the "Instant"
if you're concerned about the similarity with IRV. For
examples:

Simultaneous Round-Robin
Preference Order Round-Robin

By the way, I detest using terms like "defeat" and "winning
votes" when referring to pairwise majority outranking.
Those terms are misleading since a candidate ranked below
another by a majority is not really "defeated" and may
actually be the one elected. In the social choice
literature, a common phrase for winning votes is "the size
of the supporting coalition" (or the shorter "support
size") where the term "support" is defined in the pairwise
relative sense. May I suggest replacing "wv" with "ssc"
(size of supporting coalition) and replacing "margins" with
"ssc-soc" (size of supporting coalition minus size of
opposing coalition)?

---Steve (Steve Eppley ***@alumni.caltech.edu)

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Ernest Prabhakar
2004-01-29 14:27:47 UTC
Permalink
Hi Steve,
Post by Steve Eppley
By the way, I detest using terms like "defeat" and "winning
votes" when referring to pairwise majority outranking.
Yeah, I agree those terms get a bit geeky. I'll try to find a better
phrase.
Post by Steve Eppley
Those terms are misleading since a candidate ranked below
another by a majority is not really "defeated" and may
actually be the one elected. In the social choice
literature, a common phrase for winning votes is "the size
of the supporting coalition" (or the shorter "support
size") where the term "support" is defined in the pairwise
relative sense. May I suggest replacing "wv" with "ssc"
(size of supporting coalition) and replacing "margins" with
"ssc-soc" (size of supporting coalition minus size of
opposing coalition)?
I do like the term 'pairwise majority' - I may use that.

-- Ernie P.
***@alumni.caltech.edu
Caltech '95

ps When were you at Caltech?
Post by Steve Eppley
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Markus Schulze
2004-01-29 11:55:37 UTC
Permalink
Hallo,
The Libertarian Free State Project uses PC. They wanted something
especially briefly defined, because, all else being reasonably equal,
a brief definition is easier to justify. Maybe we should listen to
them for public proposals too. There's so little experience that
it's impossible to say.
MinMax (aka PC) violates reversal symmetry and independence of clones.
The Libertarian Free State Project uses MinMax to decide which state
is the most suitable state for their purposes. Of course, independence
of clones was not an issue when they decided to use MinMax since you
cannot nominate e.g. 10 different New Hamshires.

******
Duff's point was well-taken that we put too much emphasis on the circular
tiebreakers, because those are what distinguish all these methods we
propose. It's quite true that the important message for public advocacy
is the pairwise-count itself, and the election of a CW if there is one.
I'm not saying that CC compliance is enough. But the pairwise count
principle is a good first step when introducing these methods. The circular
tie solution is what gives the method further properties and advantages,
beyoned CC, but maybe the pairwise-count should be the up-front offering.
As was suggested, that should be the main offering, and the circular tie
solution should be offered as a footnote.
When you promote Condorcet in general and treat the concrete tie-breaker
only in a footnote, then the following will happen:

1) Your opponents will argue that your proposal isn't defined when there
is no Condorcet candidate (see Craig Carey).
2) Your opponents will use arguments that are valid only for other
tie-breakers, claiming that since you don't have a strong opinion about
which tie-breaker should be used it isn't clear which tie-breaker will
be adopted when Condorcet is adopted.
3) Your opponents will use arguments that are valid only for other
tie-breakers, claiming that although you promote a different tie-breaker
the fact that their tie-breaker leads to unintuitive results demonstrates
that there must be something wrong with Condorcet's ideas.

Therefore, I suggest to promote a concrete election method, to mention only
in a footnote that this method happens to satisfy the Condorcet criterion,
and to treat the Condorcet criterion only as one criterion among many criteria.

Markus Schulze
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Adam Tarr
2004-01-29 18:02:23 UTC
Permalink
Post by Markus Schulze
MinMax (aka PC) violates reversal symmetry and independence of clones.
The Libertarian Free State Project uses MinMax to decide which state
is the most suitable state for their purposes. Of course, independence
of clones was not an issue when they decided to use MinMax since you
cannot nominate e.g. 10 different New Hamshires.
Yes, but (for instance) you could nominate both north and south Dakota,
when all Dakota advocates agree that North Dakota is the better of the two.
Post by Markus Schulze
The circular
tie solution is what gives the method further properties and advantages,
beyoned CC, but maybe the pairwise-count should be the up-front offering.
As was suggested, that should be the main offering, and the circular tie
solution should be offered as a footnote.
When you promote Condorcet in general and treat the concrete tie-breaker
(bad things snipped)
Those are certainly true if you fail to define your tie-breaker
altogether. But if the nuts and bolts of the method are fully explained,
just not emphasized, then there's no rational reason that your opponents
could use those tactics.

For example, you have a pamphlet that talks about using a ranked ballot,
and using the rankings to generate all the one-on-one, pairwise election
totals. Then say that you elect the candidate with the "best" results
against all other candidates, adding that "generally one candidate will win
every contest he or she is involved in." Then, at the end of the pamphlet,
"technical explanation of (name of method)", have a nice, well-illustrated
description of how you work through the election (something like what Eric
has put together for ranked pairs on his website).

The point is, you don't hide the tiebreaking procedure, you just don't
emphasize it. The typical man-on-the-street probably won't even think to
ask, "what if there's a circular tie in pairwise preferences?", but if he
does, then he's probably smart enough to understand the answer.

-Adam

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Dave Ketchum
2004-01-30 01:03:22 UTC
Permalink
Post by Adam Tarr
Post by Markus Schulze
MinMax (aka PC) violates reversal symmetry and independence of clones.
The Libertarian Free State Project uses MinMax to decide which state
is the most suitable state for their purposes. Of course, independence
of clones was not an issue when they decided to use MinMax since you
cannot nominate e.g. 10 different New Hamshires.
Yes, but (for instance) you could nominate both north and south Dakota,
when all Dakota advocates agree that North Dakota is the better of the two.
Post by Markus Schulze
The circular
tie solution is what gives the method further properties and advantages,
beyoned CC, but maybe the pairwise-count should be the up-front
offering.
As was suggested, that should be the main offering, and the circular tie
solution should be offered as a footnote.
When you promote Condorcet in general and treat the concrete tie-breaker
(bad things snipped)
Those are certainly true if you fail to define your tie-breaker
altogether. But if the nuts and bolts of the method are fully
explained, just not emphasized, then there's no rational reason that
your opponents could use those tactics.
I am trying for better than Adam's following words:

Usually one candidate is best in each of its comparisons with other
candidates - and therefore wins.

Otherwise we have a near (or possibly true) tie such as A>B AND B>C AND
C>A, and must resolve which of these inequalities to ignore.

(seems to me there should be that much up front for everyone to read -
even the man-on-the-street should get that much - as Adam says, details
need to be conveniently available to all who care)
Post by Adam Tarr
For example, you have a pamphlet that talks about using a ranked ballot,
and using the rankings to generate all the one-on-one, pairwise election
totals. Then say that you elect the candidate with the "best" results
against all other candidates, adding that "generally one candidate will
win every contest he or she is involved in." Then, at the end of the
pamphlet, "technical explanation of (name of method)", have a nice,
well-illustrated description of how you work through the election
(something like what Eric has put together for ranked pairs on his website).
The point is, you don't hide the tiebreaking procedure, you just don't
emphasize it. The typical man-on-the-street probably won't even think
to ask, "what if there's a circular tie in pairwise preferences?", but
if he does, then he's probably smart enough to understand the answer.
-Adam
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Chris Hahn
2004-01-28 20:56:14 UTC
Permalink
My suggestion about a better name: Ranked Voting or Ranked Voting Method, etc.

I am not too excited about tournament or instant matchup.

Tournament sounds like a game rather than something more serious. Instant Matchup is a technically better name than Ranked Voting, but it requires the public to think too deeply to the next level. They have to think about how the winner is actually selected rather than what they have to do when they go to the polls. When they go to the polls they rank the candidates. They can understand that easily, therefore Ranked Voting or Vote Ranking is an understandable name.

Those who care to understand how and why the results are matched will really "get it" and be the biggest advocates. The general populace will be happy with the knowledge that by using a Ranked Voting system they are being better represented. The superficial understanding will be all they need or want.

That is my 2 cents worth for now.

Chris

-----Original Message-----
From: "Ernest Prabhakar"<***@mac.com>
To: "Dave Ketchum"<***@clarityconnect.com>
Cc: election-methods-***@electorama.com, "Anthony Duff"<***@yahoo.com.au>
Date: Tue Jan 27 21:28:52 PST 2004
Subject: Re: [centroids] [EM] Condorcet for public proposals - Tounament
Post by Ernest Prabhakar
Hi Dave,
I like what Ernest writes, though I see a bit of room for improvement
and suggest "tournament" as a less foreign-sounding title (even though
its ancestry is also French).
Hmm, maybe. It is better than Condorcet, but to me tournament evokes
an image of knights jousting on horses.
Someone (sorry, I forgot who) suggested the word Pairwise is important.
I could live with the name Pairwise Matchup Voting (PMV). Pairwise
by itself seems too vague, somehow
Post by Ernest Prabhakar
Yeah, my friends (on the radical centrist list) are unanimous that
the term Condorcet has to go. :-)
I have been proposing the term 'Instant Matchup Voting', or IMV, by
analogy with Instant Runoff Voting. I compare it to a round-robin
tournament, which most people have direct experience with. I think
Ahead of much that I have seen, but I suggest tournament as even
easier to visualize from. My definition will follow yours.
Well, tournament does have the idea of a series of matches, but not
necessarily individual pairwise matchups, I don't think. We could
use the term Instant Round-Robin, which is much more explicit, but IRR
is too close to IRV. :-(
Post by Ernest Prabhakar
1. Each rank-ordered ballot is interpreted as a series of "Instant
Matchups"
That is A > B > C, implies one point each for the three pairwise
Matchups A > B, B > C, and A > C
Note that "A>B" is counted separately from "B>A" (i.e., winning
votes)
2. Tally up the N * (N-1) Matchups, for each ordered pair of
candidates
3. If one candidate beats everyone, that's the absolute winner
4. If there is a 'rock-paper-scissors' tie (A >= B, B >= C, C >= A),
the tiebreaking winner is the candidate from that group with the
'least greatest defeat'
0. Voters simply rank as many of the candidates as they choose,
starting with their most-preferred.
1. Each rank-ordered ballot is interpreted as a series of matches
among all
That is, ranking A > B > C, and D and E not ranked by this voter,
implies each ranked candidate winning over each candidate ranked
later, and
over each unranked candidate.
Thus unranked candidates do not get counted as ranked over each
other.
That's a good point. I don't think we usually spend enough time
explaining how the ranking is supposed to work, so it would be good to
be more explicit.
Note that "A>B" is counted separately from "B>A" (i.e., winning
votes).
2. Tally up the number of wins for each ordered pair of candidates in
an
N*N array (with an empty diagonal, for candidates do not play against
themselves).
Good point, N*N does reduce explanation.
3. If one candidate wins when compared with each other candidate,
that's
the absolute winner.
4. If no absolute winner, we have a 'rock-paper-scissors' near tie
such as
(A >= B, B >= C, C >= A), and the tiebreaking winner is the candidate
from
that group with the 'least greatest defeat'.
NOTE: I consider 'least greatest defeat' unacceptably opaque for this
purpose, and ask for help in providing simpler words.
Fair enough. How about "whose worst loss is the smallest"? Or
simply "lost by the smallest margin" (a little ambiguous, but sounds
simpler) - can always go into more detail elsewhere.
BTW: Debatable whether voters should be permitted to rank candidates
as equal.
Is there any good reason not to? Implicit equal ranking certainly
makes it clearer about how unlisted candidates are counted. Any if at
all possible, it seems good to give people the option of equality
rather than forcing a random choice. Has anyone presented a clear
argument for or against equal ranking?
If so then, for each pair of equal candidates, count 1/2 win for
each (thus if two voters rank A=B=C then A>B, B>A, A>C, C>A, B>C, and
C>B each get credited one full win).
That doesn't make any sense to me. If two candidates are ranked, I
think that neither should get the win -- at least if we're doing
winning votes (wv) For example, if all the candidates that most people
don't rank at the bottom of the list get a win against each other, then
one single vote in favor could make that person the 'wv' winner!
Right?
Any more thoughts on the implications of Smith PC on strategy, assuming
we can hammer out a decent, simple explanation?
-- Ernie P.
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Markus Schulze
2004-01-31 14:22:09 UTC
Permalink
Hallo,

the term "Ranked Voting" is already used by the CVD for IRV.

As far as I know, the term "tournament" usually refers to
decision processes where the final winner only depends on
who wins against who and not on the strengths of these wins.

For Ernest's proposal, I suggest terms like "Smith-MinMax"
or "Smith-Simpson-Kramer".

Markus Schulze
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Adam Tarr
2004-01-31 17:48:27 UTC
Permalink
Post by Markus Schulze
For Ernest's proposal, I suggest terms like "Smith-MinMax"
or "Smith-Simpson-Kramer".
While these are certainly accurate names for the method, Ernest's goal was
to come up with a name that catchy and that instantly gives some idea of
the method to a layman. "Instant Matchup Voting" does this job pretty well
- it might not be exactly what I would have picked , but it's a very good
choice.

For comparison, note that IRVists have been successful plugging IRV, as
oppose to "Hare-STV".

-Adam

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N***@ecybermind.net
2004-02-01 02:48:08 UTC
Permalink
Post by Adam Tarr
While these are certainly accurate names for the method, Ernest's goal was
to come up with a name that catchy and that instantly gives some idea of
the method to a layman. "Instant Matchup Voting" does this job pretty well
- it might not be exactly what I would have picked , but it's a very good
choice.
My preference would be "Pair Competition Ranking" or something similiar.
Instant makes sense in the Runoff context but not in the Condorcet context,
Voting isn't the focus of tabulation methods, and Matchup would tend to be
interpreted as being synonomous with "equivalent" which is not the intended
meaning.

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Ernest Prabhakar
2004-02-02 17:08:57 UTC
Permalink
Hello,
Post by N***@ecybermind.net
Post by Adam Tarr
While these are certainly accurate names for the method, Ernest's goal was
to come up with a name that catchy and that instantly gives some idea of
the method to a layman. "Instant Matchup Voting" does this job pretty well
- it might not be exactly what I would have picked , but it's a very good
choice.
My preference would be "Pair Competition Ranking" or something
similiar.
Instant makes sense in the Runoff context but not in the Condorcet context,
Um, could you elaborate on why Instant doesn't make sense to you? As
a Condorcetist, I do think of multi-candidate elections as if they were
in fact a series of one-on-one matchups. Doing Condorcet via ranked
ballots is a way of getting that effect "instantly." I realize the
usual view is to start from the pairwise matrix, but I consider that
merely historic convention, and not of interest to 'the masses'. As
Adam said, it might make sense to drop the matrix entirely in the main
description, and just discuss wins.
Post by N***@ecybermind.net
Voting isn't the focus of tabulation methods, and Matchup would tend to be
interpreted as being synonomous with "equivalent" which is not the intended
meaning.
I'm sorry, I don't understand that sentence at all. Could you perhaps
be more explicit. To me, voting is what the voters do when they create
ballots. Each ballot reflects the results of a series of matchups.
That is, I'm trying to describe this algorithm in terms of how the
*voters* perceive it, not in terms of how the *counters* calculate it.
My impression is that the people on this list tend to be
algorithmists, so they have a very different perspective than 'normal
'voters.

While the term "Instant Matchup Voting" may not be immediately obvious
to everyone, the point is to tie the name to a description that seems
intuitively meaningful, so that after people hear the description it
makes sense at a conceptual level. The other terms I've seen suggest
are not particularly more transparent (at least to me), plus they don't
seem to flow as naturally into a clear definition.

-- Ernie P.

P.S. For the record, I am a marketing person, not a mathematician,
thus I prefer a catchier name as long as it isn't blatantly inaccurate.

P.P.S. To Markus point - I'm sure there may be better technical names
than Smith PC, and I would be happy to mention them in the footnote,
but the point is (as Adams said) to come up with a catchy 'brand name'
for this particular interpretation. Which also avoids arguments about
whether this is 'really' Smith PC.
Post by N***@ecybermind.net
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Markus Schulze
2004-02-01 11:31:18 UTC
Permalink
Dear Mike,
Post by Markus Schulze
For Ernest's proposal, I suggest terms like "Smith-MinMax"
or "Smith-Simpson-Kramer".
Simpson-Kramer doesn't resemble PC. I refer Markus to the
_Journal of Economic Perspective_, for Winter '95. It's been
a long time since I looked at that article, but it seems to
me that Simpson-Kramer is based a candidate's votes-for in
pairwise-comparisons, without distinguishing between the
candidate's defeats and his victories.
Actually, I am not even aware that Simpson and Kramer
discussed incomplete individual preferences.

Markus Schulze
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Markus Schulze
2004-02-01 20:04:16 UTC
Permalink
Hallo,

in my opinion, Steve Eppley's "Maximize Affirmed Majorities"
(MAM) method would be a very good public proposal:
http://www.alumni.caltech.edu/~seppley

This method satisfies Condorcet, monotonicity, independence of
clones, reversal symmetry, and many other desirable criteria.
Therefore, MAM is a very good method even when a given reader
doesn't consider the Condorcet criterion to be important. In
my opinion, the fact that Smith//MinMax violates independence
of clones is a very serious problem when you have to argue
against IRV.

Unlike e.g. Smith//MinMax, MAM is based on only one principle
and it isn't a combination of different principles.

MAM is a modification of Tideman's ranked pairs method. The
fact that Nicolaus Tideman is a professor at a university in
the USA, the fact that he is a citizen of the USA, and the
fact that his ranked pairs method has already been published
in scientific journals are important campaign strategic
advantages.

"Maximize Affirmed Majorities" is a good fight name. Maybe,
"Maximize Affirmation Method" is better.

In my opinion, for a public proposal those versions of ranked
pairs where at first a "tie-breaking ranking of the candidates"
(TBRC) using the "random voter hierarchy" (RVH) is calculated
and then this TBRC is used to get a complete ranking of the
pairwise defeats are better than those versions where at first
all potential ranked pairs winners are calculated and then
the winner is chosen randomly from the potential winners.
Calculating all potential winners instead of calculating only
one potential winner makes sense only when you have a good
idea what to do with them.

Markus Schulze
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Brian Olson
2004-06-23 07:58:24 UTC
Permalink
On the rule "if a vote ranks two choices equally, give them both a
point (or a fraction of a point)" it makes a difference in
Winning-Votes (wv) because it will affect the strength of the defeats
and the eventual beatpath found.

Suppose you take the example

*49 A
*24 B
*27 C>B

http://bolson.org:8080/v/et?vrr=-clist&if=-
cname&cand=3&data=*49+A%0D%0A*24+B%0D%0A*27+C%3EB

and change it into

*49 A>C=B
*24 B
*27 C>B

http://bolson.org:8080/v/et?vrr=-clist&if=-
cname&cand=3&data=*49+A%3EC%3DB%0D%0A*24+B%0D%0A*27+C%3EB


The winner for WV changes from B to C. Margins-Beatpath is unaffected
and always choses A.

Brian Olson
http://bolson.org/

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