Discussion:
Might IRV adoption be inevitable?
Venzke Kevin
2003-02-25 08:23:41 UTC
Permalink
I wonder if the only reason IRV has more apparent
backing than approval or Condorcet is because it would
permit our present politicians to be elected even more
easily. Approval and Condorcet would permit
compromise candidates to emerge and be elected. All
IRV will do is to keep third party candidates from
affecting the election. If you were a Republican or
Democrat politician, what's not to like about IRV?
Whereas, the adoption of approval or Condorcet might
terminate your career.

Maybe I'm pessimistic, but I think there's no real
interest in improving on Plurality. If you write to
legislators about IRV's defects, you might persuade
them the opposite way. They might see that IRV would
make their jobs safer.

Stepjak

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Alex Small
2003-02-25 15:39:11 UTC
Permalink
Post by Venzke Kevin
I wonder if the only reason IRV has more apparent
backing than approval or Condorcet is because it would
permit our present politicians to be elected even more
easily.
I think most individuals who vote for IRV do so because they know
plurality is flawed and IRV is the only alternative they've heard of. An
individual voter who supports IRV is an ally to those who support
Approval, Condorcet, and Proportional Representation, because the odds are
that he would be receptive to other methods if he knew they existed.

Even if IRV doesn't break the duopoly, if it enables third parties to
consistently poll 10% or more among the first-place votes, I think it will
prompt public outcries for Proportional Representation. Although there
are differences of opinion on this list regarding PR methods, many people
here support some form of PR.



Alex


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Dave Ketchum
2003-02-26 04:41:12 UTC
Permalink
Post by Alex Small
Post by Venzke Kevin
I wonder if the only reason IRV has more apparent
backing than approval or Condorcet is because it would
permit our present politicians to be elected even more
easily.
I think most individuals who vote for IRV do so because they know
plurality is flawed and IRV is the only alternative they've heard of. An
individual voter who supports IRV is an ally to those who support
Approval, Condorcet, and Proportional Representation, because the odds are
that he would be receptive to other methods if he knew they existed.
I like the thought, but still do not want to promote IRV:
If I promote IRV, my word turns to mud if I then admit I knew of
something better and did not try to sell it.
Once they invest in IRV equipment they want neither the dollar nor
learning cost of doing a replacement.
Post by Alex Small
Even if IRV doesn't break the duopoly, if it enables third parties to
consistently poll 10% or more among the first-place votes, I think it will
prompt public outcries for Proportional Representation. Although there
are differences of opinion on this list regarding PR methods, many people
here support some form of PR.
I question your claim about outcries - especially when the topic becomes
what flavor of PR to pick.

Anyway, PR is no help for electing mayors or governors.
Post by Alex Small
Alex
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e***@cox.net
2003-02-25 15:32:39 UTC
Permalink
Post by Venzke Kevin
I wonder if the only reason IRV has more apparent
backing than approval or Condorcet is because it would
permit our present politicians to be elected even more
easily.
Wouldn't surprise me. Alls fair in love, war and politics. :-)
--
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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
2003-02-26 04:40:05 UTC
Permalink
Post by Venzke Kevin
I wonder if the only reason IRV has more apparent
backing than approval or Condorcet is because it would
permit our present politicians to be elected even more
easily. Approval and Condorcet would permit
compromise candidates to emerge and be elected. All
IRV will do is to keep third party candidates from
affecting the election. If you were a Republican or
Democrat politician, what's not to like about IRV?
Whereas, the adoption of approval or Condorcet might
terminate your career.
The above makes no sense, for IRV and Condorcet use identical ballots and,
most of the time, award identical winners. That is:
Both get rid of Plurality's spoiler problem, which should be
attractive to politicians.
Both thus encourage voting for third party compromise candidates,
which could make successful politicians nervous.

IRV has VOCAL backers, who thus purchase apparent approval.

Those of us who promote Condorcet note that, while IRV protects
against Plurality's spoiler problem, it has a spoiler problem of its own
when third party candidates get significant votes.

While Approval beats Plurality, it restricts voter expressions of their
likely desires.
Post by Venzke Kevin
Maybe I'm pessimistic, but I think there's no real
interest in improving on Plurality. If you write to
legislators about IRV's defects, you might persuade
them the opposite way. They might see that IRV would
make their jobs safer.
???
Post by Venzke Kevin
Stepjak
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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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Venzke Kevin
2003-02-27 18:49:13 UTC
Permalink
On Tue, 25 Feb 2003 09:23:41 +0100 (CET) Venzke
Post by Venzke Kevin
I wonder if the only reason IRV has more apparent
backing than approval or Condorcet is because it
would
Post by Venzke Kevin
permit our present politicians to be elected even
more
The above makes no sense, for IRV and Condorcet use
identical ballots and,
most of the time, award identical winners.
They are only likely to award identical winners when
the voters and candidates think the rules are IRV when
they're voting and entering the race, respectively.
This is because more than two candidates may be viable
under Condorcet rules. Under IRV, usually only two
candidates can really win, and the voters know it and
vote that way; the "compromise candidates" know it,
too, and don't enter the race.
Both get rid of Plurality's spoiler problem,
IRV only reliably does this when the voters
acknowledge that they have to give favor to one of the
two lesser evils. But how different is that from
Plurality?
which should be
attractive to politicians.
Condorcet eliminates the spoiler problem by permitting
voters to vote (more) sincerely, and (thus) by making
more candidates viable. Why on earth would that be
attractive to our present politicians?
Both thus encourage voting for third party
compromise candidates,
which could make successful politicians nervous.
At the risk of being repetitive:
They don't have to be too nervous with IRV. If a
third party candidate becomes a spoiler, the winner
will still be a "lesser evil."
But they *would* have to be very nervous under
Condorcet rules, because they could lose.

If you put voting systems in order of to what degree
they preserve the problem of the election of the
lesser of two evils, I would draw it like this:
IRV - Plurality - Approval - Condorcet.
My conclusion is that people who support IRV, while
understanding the objections to it, must have a
different motivation. I suspect consequently that
support for IRV can't be easily converted to support
for a different system.

Stepjak

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Jan Kok
2003-02-27 20:53:36 UTC
Permalink
----- Original Message -----
From: "Venzke Kevin" <***@yahoo.fr>
To: <election-methods-***@eskimo.com>
Sent: Thursday, February 27, 2003 11:49 AM
Subject: Re: [EM] IRV and Condorcet operating identically
Post by Venzke Kevin
On Tue, 25 Feb 2003 09:23:41 +0100 (CET) Venzke
Post by Venzke Kevin
I wonder if the only reason IRV has more apparent
backing than approval or Condorcet is because it
would
Post by Venzke Kevin
permit our present politicians to be elected even
more
The above makes no sense, for IRV and Condorcet use
identical ballots and,
most of the time, award identical winners.
^^^^^^^^^^^^^^^^
...
Post by Venzke Kevin
If you put voting systems in order of to what degree
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Post by Venzke Kevin
they preserve the problem of the election of the
IRV - Plurality - Approval - Condorcet.
I'm curious if anyone can mathematically justify such statements as "Voting
method A exhibits property P 'more often' than method B"?

Say there is an infinite set of scenarios S, and say A and B each exhibit P
for subsets Sa and Sb of S. If Sa is a proper subset of Sb, then it would
be reasonable to say that A exhibits P "less often" than does B.
(Unfortunately it doesn't give one a sense of "_how_much_ less often" P is
exhibited by A compared to B.)

But what if Sa and Sb "overlap", i.e. Sa intersect Sb is a proper subset of
both Sa and Sb, or Sa and Sb are both non-null but the intersection is null?
Then the only way I can see to compare "how often" A and B exhibit P is to
somehow assign probabilities to the scenarios, i.e. what percent of actual
elections are members of Sa and Sb?

Is there a generally accepted way of assigning such probabilities (which
would involve lots of assumptions about distribution of voter preferences,
candidate characteristics, voter strategy, etc., etc.)?

As a concrete example, can someone show that some Condorcet method fails
Favorite Betrayal "less often" than IRV?

Cheers,
- Jan

P.S. I ran some crude simulations a few months ago with no strategy
(sincere voting) which showed that IRV and Condorcet SSD chose different
winners something like 30% of the time.


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Alex Small
2003-02-28 01:54:22 UTC
Permalink
Post by Jan Kok
I'm curious if anyone can mathematically justify such statements as
"Voting method A exhibits property P 'more often' than method B"?
Well, for methods that use strictly ranked ballots to pick among N
candidates I would represent all possible electorates with an N!
dimensional vector space. Each direction would correspond to the number
of voters with a given (sincere, normally) preference order.

I'd look at an N!-1 dimensional "slice" of that vector space given by the
constraint that

Sum(j=1,N!)V(j)=1 and V(j)>=0

where V(j) is the percentage of voters with preference order j.

Within this region, I'd identify the areas in which property P is
satisfied by a particular method and use standard integration to compute a
volume, and divide that volume by the total volume of the region in
question.

I don't think that this method could be interpreted as giving a
probabilistic answer to the question "how often" because it assumes that
all possible scenarios are equally probable. Still, it allows transitive
comparisons, i.e. if property P1 occurs more often than property P2, and
P2 occurs more often than P3, then P1 occurs more often then P3.

One easy application of this method is to figure out "how often" there
will be a Condorcet winner. With N candidates we have N(N-1)/2 pairwise
contests. Since each contest has 2 possible outcomes (ignoring ties)
there are 2^(N(N-1)/2) possible breakdowns for the pairwise results. Each
combination of pairwise results covers a fraction 2^(-N(N-1)/2) of the
total electoral space.

Now, say that we have a Condorcet winner. Among the other N-1 candidates
there are (N-1)(N-2)/2 pairwise contests and 2^((N-1)(N-2)/2) possible
ways that the pairwise contests among them could break down. Each of
those outcomes covers a fraction 2^(-N(N-1)/2) of the total volume of
electoral space (for a fixed number of voters). A little algebra shows
that the region in which candidate A is the Condorcet winner covers a
fraction
2^(1-N) of electoral space.

Finally, since there are N possible Condorcet winners, the fraction of
electoral space in which a Condorcet winner exists is N*2^(1-N).

A quick sanity check indicates that for 2 candidates, the above formula
says that 100% of electoral space has a Condorcet winner, as we'd expect.

The interpretation is that as we add more candidates, to be a CW one must
win more and more pairwise contests. This becomes harder and harder to
do, so the fraction of electoral space in which a CW exists becomes
smaller and smaller as we add more candidates.



Alex


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Craig Carey
2003-02-28 08:05:12 UTC
Permalink
Post by Jan Kok
Sent: Thursday, February 27, 2003 11:49 AM
Subject: Re: [EM] IRV and Condorcet operating identically
...
Post by Jan Kok
Post by Jan Kok
Post by Dave Ketchum
The above makes no sense, for IRV and Condorcet use
identical ballots and,
most of the time, award identical winners.
^^^^^^^^^^^^^^^^
...
Post by Jan Kok
I'm curious if anyone can mathematically justify such statements as "Voting
method A exhibits property P 'more often' than method B"?
...
Post by Jan Kok
As a concrete example, can someone show that some Condorcet method fails
Favorite Betrayal "less often" than IRV?
...

As far as I know, it was not true that there is a definition of the
FBC favourite betrayal thing. Ossipoff always sought to have rules that
did not actually test methods, but which in a very vague way, allowed him
to certify methods. The certification -- eg. FBC certification -- appears
to have no reality. No matter how inchoate and boundless the generosity
is towards the authors of messages saying FBC exists, there still seems
to be no possible path to a conclusion that that whatever-it-was, did
exist.

There is a questionable presumption inside of the question. The question
can be ignored (in the interim, or else for a longer time or forever) and
Mr Kok can provide the exact reasoning that was used when the conclusion
that FBC was worth asking a question about, was arrived at.

Mr Ossipoff never got FBC defined. Other members suggested that they
could and in private e-mail gave up on creating a replacement for the
Ossipoff FBC. There may never every be an FBC rule while there is an
agreement that it has to be acceptable to MIKE OSSIPOFF of the
United States of America.
Post by Jan Kok
P.S. I ran some crude simulations a few months ago with no strategy
(sincere voting) which showed that IRV and Condorcet SSD chose different
winners something like 30% of the time.
So what (?) (neither method is correct). Also, the number of candidates
ought be stated.


-----------------------------
Post by Jan Kok
Post by Jan Kok
I'm curious if anyone can mathematically justify such statements as
"Voting method A exhibits property P 'more often' than method B"?
Well, for methods that use strictly ranked ballots to pick among N
candidates I would represent all possible electorates with an N!
dimensional vector space. Each direction would correspond to the number
of voters with a given (sincere, normally) preference order.
Given what exactly ?

It says "sincere, normally", and so I ask:

what exactly are the ideas of normality and sincerity,

It looks like information about sincerity exists for each ballot paper
and it might cause some to be rejected.

--

If there are 4 candidates, then we want to be able to use 65
dimensions rather than 64, to describe the counts of the papers.

Strangely Mr Small says that the number of dimensions is N!, i.e.
1*2*3*4 = 24.

Doubtless it is one of the big problems necessitating an eternal
and total rejection of the thinking of Mr Small, i.e. that thing
he calls the "electoral space", in the context of a method (i.e.
a sequence of polytopes or shapes in the full dimension) being
tested.

---
Post by Jan Kok
Post by Jan Kok
I'm curious if anyone can mathematically justify such statements as
"Voting method A exhibits property P 'more often' than method B"?
Well, for methods that use strictly ranked ballots to pick among N
candidates I would represent all possible electorates with an N!
The correct answer appears to be a simple "no'.

The method would be perfectly stable and unchanging and the
statement to be justified did presume that.

So the statement won't be justifiable.

---

A note to Mr Schulze: I contradicted this wrong statement at my
mailing list. It had algebra in it.

------------------------------------------------------------------
Post by Jan Kok
Date: Wed Feb 26, 2003 12:09 pm
Subject: Re: [EM] Might IRV adoption be inevitable?
Post by Jan Kok
I wonder if the only reason IRV has more apparent
backing than approval or Condorcet is because it would
...
Post by Jan Kok
And in so far as there is no known version of proportional
representation by the [Alternative Vote method] that has been
proven to meet monotonicity,
...
------------------------------------------------------------------

The method of Vermont, as described by Mr Kok in this
message, seems to be perfectly monotonic, and it is a variant
of the Alternative Vote:

http://groups.yahoo.com/group/election-methods-list/message/10947
Post by Jan Kok
Date: Tue Feb 25, 2003 8:55 am
Subject: [EM] Vermont IRV is nonstandard
I have online here an argument demonstrating that that method
of Vermont is monotonic:

http://groups.yahoo.com/group/politicians-and-polytopes/message/220

It can be called the 2nd is a sequence of methods that has
k-candidate IFPP attached to a preprocessing stage that
deletes enough candidates.

The 3rd in the sequence is apparently far better than the
Alternative Vote.

A description of the method is this:

It is the 3 candidate Alternative Vote but with a
pre-processing candidate-deleting stage that has all the
expected transferring [i.e. preferences are deleted], and
also, [if 1 winner only then] there is a 1/3 [IFPP] quota
(applied after the other preprocessing) that sometimes
finds two losers.

Replacing IRV is certainly not a prime purpose of the
members at the Politicians and Polytopes mailing list. It
is too slight to interact with, I suppose.






Craig Carey

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Jan Kok
2003-03-01 00:57:44 UTC
Permalink
----- Original Message -----
From: "Craig Carey" <***@ijs.co.nz>
To: <election-methods-***@eskimo.com>
Sent: Friday, February 28, 2003 1:05 AM
Subject: Re: [EM] "More often" (was: IRV and Condorcet operating
identically)
Post by Craig Carey
Post by Jan Kok
Sent: Thursday, February 27, 2003 11:49 AM
Subject: Re: [EM] IRV and Condorcet operating identically
...
Post by Jan Kok
Post by Jan Kok
Post by Dave Ketchum
The above makes no sense, for IRV and Condorcet use
identical ballots and,
most of the time, award identical winners.
^^^^^^^^^^^^^^^^
...
Post by Jan Kok
I'm curious if anyone can mathematically justify such statements as "Voting
method A exhibits property P 'more often' than method B"?
...
Post by Jan Kok
As a concrete example, can someone show that some Condorcet method fails
Favorite Betrayal "less often" than IRV?
...
As far as I know, it was not true that there is a definition of the
FBC favourite betrayal thing.
From http://www.electionmethods.org/evaluation.htm: "By voting another
candidate over his favorite, a voter should never get a result that he
considers preferable to every result he could get without doing so."

Are you saying the definition is not clear enough to be usable, or what?

I have seen a few posts go by about "Strong FBC." Is that related to
Ossipoff's definition?
Post by Craig Carey
Ossipoff always sought to have rules that
did not actually test methods, but which in a very vague way, allowed him
to certify methods.
Would you explain what you mean by "testing" and "certifying" and what is
the difference?
Post by Craig Carey
The certification -- eg. FBC certification -- appears
to have no reality. No matter how inchoate and boundless the generosity
is towards the authors of messages saying FBC exists, there still seems
to be no possible path to a conclusion that that whatever-it-was, did
exist.
Again, I don't understand.
Post by Craig Carey
There is a questionable presumption inside of the question. The question
can be ignored (in the interim, or else for a longer time or forever) and
Mr Kok can provide the exact reasoning that was used when the conclusion
that FBC was worth asking a question about, was arrived at.
I frequently see claims that method A exhibits some property P "more often"
than method B, and I was wondering how one would go about justifying such a
statement. I can't swear that I've seen the claim that "Condorcet fails FBC
less often than IRV," but I bet some Condorcet supporters would agree with
it. For example, this passage from
http://www.electionmethods.org/evaluation.htm goes part of the way when it
says "the probability is very small...":

"Election methods that meet this criterion provide no incentive for voters
to betray their favorite candidate by voting another candidate over him. FBC
is the only criteria that favors Approval over Condorcet. In fact, it is the
only criteria that favors any of the methods listed in Table 1 over
Condorcet. Although Condorcet technically fails to comply with FBC, the
probability is very small that a voter can cause a preferable result by not
voting for his or her favorite in a Condorcet system."

Many third party supporters, including myself, tear their hair out in
frustration over the lesser of two evils problem. FBC is (for me, anyway)
one of the easiest criteria to understand, and to understand the
implications of a voting method failing the criterion: it causes people to
vote for the lesser of two evils, rather than voting their favorite, and it
causes the true level of support for third parties to be underreported. If
a method passes FBC, voters can freely vote their favorite. Thus, I am very
interested in methods that pass FBC.

I know that Condorcet fails FBC, but the claim is that it does so with "low
probability". So, I want to know what that really means; how to quantify
the degree of failure; how to compare the degree of failure between
different methods.
Post by Craig Carey
Mr Ossipoff never got FBC defined. Other members suggested that they
could and in private e-mail gave up on creating a replacement for the
Ossipoff FBC. There may never every be an FBC rule while there is an
agreement that it has to be acceptable to MIKE OSSIPOFF of the
United States of America.
Post by Jan Kok
P.S. I ran some crude simulations a few months ago with no strategy
(sincere voting) which showed that IRV and Condorcet SSD chose different
winners something like 30% of the time.
So what (?) (neither method is correct). Also, the number of candidates
ought be stated.
I was saying that, contrary to the claim in the original title of this
thread, IRV and Condorcet don't operate identically in about 30% of the
elections that I simulated. I don't have the details at hand (and as I said
the simulations were somewhat crude, not taking strategy into account, for
example) but I think the 30% figure would apply for about four candidates
and about four issues (e.g. abortion, gun control, foreign affairs) that
voters use to evaluate and choose candidates.
Post by Craig Carey
-----------------------------
Post by Jan Kok
Post by Jan Kok
I'm curious if anyone can mathematically justify such statements as
"Voting method A exhibits property P 'more often' than method B"?
Well, for methods that use strictly ranked ballots to pick among N
candidates I would represent all possible electorates with an N!
dimensional vector space. Each direction would correspond to the number
of voters with a given (sincere, normally) preference order.
Given what exactly ?
what exactly are the ideas of normality and sincerity,
I think what he meant was, "with a given sincere preference order."
He was using "normally" in the sense of "usually," i.e. you might sometimes
consider voted preference order.

I'll send this mail now and consider the rest later.

- Jan
Post by Craig Carey
It looks like information about sincerity exists for each ballot paper
and it might cause some to be rejected.
--
If there are 4 candidates, then we want to be able to use 65
dimensions rather than 64, to describe the counts of the papers.
Strangely Mr Small says that the number of dimensions is N!, i.e.
1*2*3*4 = 24.
Doubtless it is one of the big problems necessitating an eternal
and total rejection of the thinking of Mr Small, i.e. that thing
he calls the "electoral space", in the context of a method (i.e.
a sequence of polytopes or shapes in the full dimension) being
tested.
---
Post by Jan Kok
Post by Jan Kok
I'm curious if anyone can mathematically justify such statements as
"Voting method A exhibits property P 'more often' than method B"?
Well, for methods that use strictly ranked ballots to pick among N
candidates I would represent all possible electorates with an N!
The correct answer appears to be a simple "no'.
The method would be perfectly stable and unchanging and the
statement to be justified did presume that.
So the statement won't be justifiable.
---
A note to Mr Schulze: I contradicted this wrong statement at my
mailing list. It had algebra in it.
------------------------------------------------------------------
Post by Jan Kok
Date: Wed Feb 26, 2003 12:09 pm
Subject: Re: [EM] Might IRV adoption be inevitable?
Post by Jan Kok
I wonder if the only reason IRV has more apparent
backing than approval or Condorcet is because it would
...
Post by Jan Kok
And in so far as there is no known version of proportional
representation by the [Alternative Vote method] that has been
proven to meet monotonicity,
...
------------------------------------------------------------------
The method of Vermont, as described by Mr Kok in this
message, seems to be perfectly monotonic, and it is a variant
http://groups.yahoo.com/group/election-methods-list/message/10947
Post by Jan Kok
Date: Tue Feb 25, 2003 8:55 am
Subject: [EM] Vermont IRV is nonstandard
I have online here an argument demonstrating that that method
http://groups.yahoo.com/group/politicians-and-polytopes/message/220
It can be called the 2nd is a sequence of methods that has
k-candidate IFPP attached to a preprocessing stage that
deletes enough candidates.
The 3rd in the sequence is apparently far better than the
Alternative Vote.
It is the 3 candidate Alternative Vote but with a
pre-processing candidate-deleting stage that has all the
expected transferring [i.e. preferences are deleted], and
also, [if 1 winner only then] there is a 1/3 [IFPP] quota
(applied after the other preprocessing) that sometimes
finds two losers.
Replacing IRV is certainly not a prime purpose of the
members at the Politicians and Polytopes mailing list. It
is too slight to interact with, I suppose.
Craig Carey
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Dave Ketchum
2003-02-28 09:26:45 UTC
Permalink
We seem to disagree as to the difference between IRV and Condorcet, so
time for an example:

Given:
C - a least of evils with 40 SOLID support.
L - a least of evils with 60 SOLID support.
U - an up and coming third party candidate attractive to some L voters.

40 C
0-29 U,L - some, but minority, support by L voters for U (here I lump
together 0 votes for U,L thru 29 votes for U,L, since results are
identical for the group).
60-31 L - remaining L voters.
IRV and Condorcet both drop U as a minority, and L wins.

40 C
31-39 U,L - U is gaining.
29-21 L
IRV drops the minority L voters and C wins over U.
Condorcet sees 40C>35U, 35U>25L, 60L>40C - hopefully we agree that L
wins here.
Not liking C winning here is why I fight for Condorcet.

40 C
41-60 U,L
19-0 L
IRV awards to U.
Condorcet sees 60L>40C, 50U>40C, 50U>10L - U wins since no cycle.

For BOTH of these ranked ballot methods the third party support that was a
spoiler in Plurality voting gets measured, but does not disturb results.

Make third party support a bit stronger and IRV has a spoiler problem
while Condorcet does not.

Make third party support strong enough and both agree that third party
candidates CAN win.

Thus with both, but especially with Condorcet, voters can vote their
desires with expectation that their votes will count.
Post by Venzke Kevin
On Tue, 25 Feb 2003 09:23:41 +0100 (CET) Venzke
Post by Venzke Kevin
I wonder if the only reason IRV has more apparent
backing than approval or Condorcet is because it
would
Post by Venzke Kevin
permit our present politicians to be elected even
more
The above makes no sense, for IRV and Condorcet use
identical ballots and,
most of the time, award identical winners.
They are only likely to award identical winners when
the voters and candidates think the rules are IRV when
they're voting and entering the race, respectively.
This is because more than two candidates may be viable
under Condorcet rules. Under IRV, usually only two
candidates can really win, and the voters know it and
vote that way; the "compromise candidates" know it,
too, and don't enter the race.
Huh! Even in Plurality, where the spoiler problem made winning very
difficult for "compromise candidates", they FOR SURE did enter the race.
With Plurality's spoiler problem gone they have a better chance.

Really better to talk of ranked ballots and not say too much about
IRV/Condorcet - proper voter thinking is identidal except when voters
know that in theory IRV can be gimmicked with sufficient knowledge, and
dream that they know enough to do that successfully.
Post by Venzke Kevin
Both get rid of Plurality's spoiler problem,
IRV only reliably does this when the voters
acknowledge that they have to give favor to one of the
two lesser evils. But how different is that from
Plurality?
In BOTH IRV and Condorcet the voters need to know that they had best vote
for one of the major candidates - that, unlike Plurality, they can vote
their true desire first without worry about spoilers (except IRV has a
bit of spoiler trouble).
Post by Venzke Kevin
which should be
attractive to politicians.
Condorcet eliminates the spoiler problem by permitting
voters to vote (more) sincerely, and (thus) by making
more candidates viable. Why on earth would that be
attractive to our present politicians?
A politician who has retired to a safe elected home may not see any joy.

A politician who worries about Plurality spoiler problems should be
looking for something better.

A politician who thinks of being a third candidate should be interested.

Remember that, while general elections are often owned by one party,
primaries are fair game, even within parties that expect to win in Nov.
Post by Venzke Kevin
Both thus encourage voting for third party
compromise candidates,
which could make successful politicians nervous.
They don't have to be too nervous with IRV. If a
third party candidate becomes a spoiler, the winner
will still be a "lesser evil."
But they *would* have to be very nervous under
Condorcet rules, because they could lose.
I tried to clarify the similarity of IRV and Condorcet above.
Post by Venzke Kevin
If you put voting systems in order of to what degree
they preserve the problem of the election of the
IRV - Plurality - Approval - Condorcet.
My conclusion is that people who support IRV, while
understanding the objections to it, must have a
different motivation. I suspect consequently that
support for IRV can't be easily converted to support
for a different system.
So we disagree, for in this listing I would place IRV next to Condorcet.
Post by Venzke Kevin
Stepjak
--
***@clarityconnect.com http://www.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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Markus Schulze
2003-02-26 12:09:57 UTC
Permalink
Dear participants,
Post by Venzke Kevin
I wonder if the only reason IRV has more apparent
backing than approval or Condorcet is because it would
permit our present politicians to be elected even more
easily.
I guess that the main reason why so many people support IRV
is that these people consider IRV to be the first step to
proportional representation by the single transferable vote.
And in so far as there is no known version of proportional
representation by the single transferable vote that has been
proven to meet monotonicity, I guess that many activists
see no point in insisting that the promoted preferential
single-winner method should meet monotonicity.

Markus Schulze

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James Gilmour
2003-03-01 17:26:10 UTC
Permalink
Post by Markus Schulze
Post by Venzke Kevin
I wonder if the only reason IRV has more apparent
backing than approval or Condorcet is because it would
permit our present politicians to be elected even more
easily.
I guess that the main reason why so many people support IRV
is that these people consider IRV to be the first step to
proportional representation by the single transferable vote.
I don't think there any necessary connection between promoting IRV and promoting
PR by STV. It may be different elsewhere, but here in the UK the objectives the
promoters of IRV and of STV-PR are certainly very different.

Our main electoral reform campaigns are about PR - making local councils,
Assemblies and Parliaments more properly representative of those who voted. In
the UK context, STV-PR is the most appropriate system to achieve that. (I know we
have introduced MMP=AMS and Closed Party Lists, but that was to allow the
government party - Labour - to keep control of its own candidates and elected
members.)

Most who argue for IRV in public elections here, do so as a means of preventing
any move towards PR. They want to retain the single-member districts at all
costs. They have different reasons for this. I think a few may genuinely believe
in the alleged "special merits" of representation from single-member districts,
despite all the evidence to the contrary. In most cases, it is probably just a
cynical attempt to retain power for the IRV advocate's political party when the
voting stats show that with any reasonable system of PR, their party would be out
of power or in a minority or coalition administration. Some party apparatchiks
don't want STV-PR in particular because it would shift the balance of control away
from the political party machine and give more power to the voters - and they
don't want that!

We have very few directly elected single-office public elections in the UK.
However, when advocates of STV-PR are asked about such elections, they usually
recommend IRV (despite all its defects).

James



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Markus Schulze
2003-02-28 11:36:42 UTC
Permalink
"(3) The instant runoff count committee shall sort and count votes for
candidates. If, in the first round, no candidate received a majority of
first choices, all candidates shall be eliminated except the two candidates
with the greatest number of first choices. Ballots which rank eliminated
candidates and which indicate one of the final candidates as an alternate
choice shall be counted as votes for whichever of the final candidates is
ranked higher for that office on each ballot. In each round, each ballot
is counted as one vote for the highest ranked advancing candidate on that
ballot."
A note to Mr Schulze: I contradicted this wrong statement at my
mailing list. It had algebra in it.
------------------------------------------------------------------
Post by Jan Kok
Date: Wed Feb 26, 2003 12:09 pm
Subject: Re: [EM] Might IRV adoption be inevitable?
Post by Venzke Kevin
I wonder if the only reason IRV has more apparent
backing than approval or Condorcet is because it would
...
Post by Jan Kok
And in so far as there is no known version of proportional
representation by the [Alternative Vote method] that has been
proven to meet monotonicity,
...
------------------------------------------------------------------
The method of Vermont, as described by Mr Kok in this
message, seems to be perfectly monotonic, and it is a variant
of the Alternative Vote.
Dear Craig, I wrote (26 Feb 2003) that "there is no known version of
proportional representation by the single transferable vote that has
been proven to meet monotonicity." The method in Jan Kok's 25 Feb 2003
mail is a single-winner method and not a method of proportional
representation by the single transferable vote. Furthermore, the
method in Jan Kok's 25 Feb 2003 mail violates monotonicity. Example:

8 voters vote A > C > B.
5 voters vote B > A > C.
4 voters vote C > B > A.

The winner is candidate B. However, when 2 ACB voters change their
opinion to CAB, then this example looks as follows:

6 voters vote A > C > B.
5 voters vote B > A > C.
4 voters vote C > B > A.
2 voters vote C > A > B.

Now, candidate A is the winner. This is a clear violation of
monotonicity.

Markus Schulze

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Stephane Rouillon
2003-02-28 13:54:57 UTC
Permalink
Markus--

does Condorcet (Ranked Pair with winning-votes to be precise)
meet monotonicity ?

Steph

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Craig Carey
2003-02-28 22:41:51 UTC
Permalink
I found the mistake in my argument that the Vermont method is
monotonic. That argument appeared in my Politicians and Polytopes
mailing list.

The error occurs in the line "(A wins) = (Hb < Ha)".

At 2003\02\28 11:20 +0000 Thursday & at 02\28 14:25 +0000 Friday,
I wrote:
-------------------------------------------------------------------
(Case 1) Candidate A ranked 3rd or worse.
Case =. (a<b)(a<c) or (a<b)(a<d) or (a<b)(a<e) or ...
· · · · · · · · · · · (a<c)(a<d) or (a<c)(a<e) or ... or ...
(A wins) = False
-----------------------------
(Case 2) Candidate A ranked 1st or 2nd.
Case =. (b<a or c<a)(b<a or d<a)(b<a or e<a) and ...
· · · · · · · · · · (c<a or d<a)(c<a or e<a) and ...
· · · · · · · · · · · · · · · · (d<a or e<a) and ...
(A wins) = (Hb < Ha)
Ha=(sum of weights of papers naming A, except when B is before A)
-------------------------------------------------------------------

Unfortunately the more complex method is now assumed by me to be
a method that will Not be monotonic.

Sorting cuts into case, and when the cases are reassembled, then
the method very easily fails the test of monotonicity at the
boundaries between the cases. The Vermont method does a lot less
sorting than the Alternative Vote.

With this being the EM List, we can say that "research never starts".

The SSD method uses sorting so it is easily cutting and joining
while not trying to make the joins pass the test of monotonicity.

Possibly .. either sorting is removed or the cuts are tilted.

----
"(3) The instant runoff count committee shall sort and count votes for
candidates. If, in the first round, no candidate received a majority of
first choices, all candidates shall be eliminated except the two candidates
with the greatest number of first choices. Ballots which rank eliminated
candidates and which indicate one of the final candidates as an alternate
choice shall be counted as votes for whichever of the final candidates is
ranked higher for that office on each ballot. In each round, each ballot
is counted as one vote for the highest ranked advancing candidate on that
ballot."
...
------------------------------------------------------------------
Post by Jan Kok
Date: Wed Feb 26, 2003 12:09 pm
Subject: Re: [EM] Might IRV adoption be inevitable?
...
Post by Jan Kok
And in so far as there is no known version of proportional
representation by the [Alternative Vote method] that has been
proven to meet monotonicity,
...
------------------------------------------------------------------
...
Now, candidate A is the winner. This is a clear violation of
monotonicity.
Correction: Mr Schulze was right in saying that an AV-like method
that passes the test of monotonicity and that is defined explicitly
for all numbers candidates, and that need not be optimal, is not known.


I tried to improve on the Vermont method and did not seem to succeed.

The Vermont method might be better than the Alternative Vote. It is
not shown and starting off as very unimpressive method since being
identical to the Alternative Vote, it can wrap 33% of the voters into
a monotonicity defect. A huge fraction particularly when the exact
solution is already known for that case.


//////////////////////////



The 3 candidate Alternative Vote has "(A wins)" defined by either of
these:

(1): (A wins) = (b<a)(b<c)(c+bc<a+ba) or (c<a)(c<b)(b+cb<a+ca)

(2): (A wins) = (b<a or c<a) and (c+bc<a+ba or c<b) and (b+cb<a+ca or b<c)

The 2nd form resembles the 3 candidate 1 winner IFFP equation for when
candidate A wins:

(A wins) = (b+c<2a) and (c+bc<a+ba or c<b) and (b+cb<a+ca or b<c)

On sorting that and showing the c<b<a case winners, this is IFPP:

(A wins) = (b+cb<a+ca) or (2b<a+c)
(B wins) = (a+ca<b+cb)(a+c<2b)
(C wins) = False

Below I construct variants of the Vermont method; and make them resemble
the IFPP style.

None of the variants pass the test of monotonicity.

The Alternative Vote worsens at a fairly aggressive pace as candidates
are added (especially when checking for how forcefully the method is
demanding insincerity). The Vermont method has a lot less sorting.
STV has lacks proportionality and the Alternative Vote certainly
does not when 3 candidates (and maybe in general).

---------------

Assume that the papers are these, and there are 3 candidates.
Ties are mishandled (shapes of different dimensions are union-ed).

Sort so that c<b<a.
___ z0
A__ a0, a=a0+ab+ac
AB_ ab
AC_ ac
B__ b0, b=b0+ba+bc
BA_ ba
BC_ bc
C__ c0, c=c0+ca+cb
CA_ ca
CB_ cb

A variant of the "Vermont" method is created.
In that method, candidate C is eliminated in stage 1, leaving this:
___ z0
A__ a0, a=a0+ab+ac
AB_ ab
A__ ac
B__ b0, b=b0+ba+bc
BA_ ba
B__ bc
___ c0, c=c0+ca+cb
A__ ca
B__ cb

The above is an identical election point/example to this:
___ z0+c0
A__ a0+ac+ca
AB_ ab
B__ b0+bc+cb
BA_ ba

I create a parameterized formula, and then use the rules of
truncation resistance and monotonicity, to remove all of the parameters
except one. This is tried:
(A wins) =
. . [(b0+bc+cb) + p*ba < (a0+ac+ca) + p*ab]
. . OR [2(b0+bc+cb) + q*ba < 2r*(a0+ac+ca) + s*ab]

Assuming truncation resistance implies that shifting votes between
(A) to (AB) won't alter A's win-lose status. That implies that p=1 and
2r = s. That leads to this:

(A wins) = (b+cb < a+ca) or [2(b0+bc+cb) + q*ba < 2r*(a+ca)]

C is already eliminated and there is 1 winner, so (B loses) = (A wins).

(B loses) = (b+cb < a+ca) or [2(b0+bc+cb) + q*ba < 2r*(a+ca)]

Truncation resistance has B's win-lose status be unaffected by all
shifting of votes/weight between the papers (BA) and (B).

Hence q =2. That leads to this:

(A wins) = (b+cb < a+ca) or (b+cb < r*(a+ca))

When r=1, then varian is the original EM List Vermont method.
It is identical to the Alternative Vote.

After re-lettering is done to restore the other 5 cases:

a<b<c ==> (A wins) = False
a<c<b ==> (A wins) = False
b<a<c ==> (A wins) = (c+bc < a+ba) and [r*(c+bc) < a+ba]
b<c<a ==> (A wins) = (c+bc < a+ba) or [c+bc < r*(a+ba)]
c<a<b ==> (A wins) = (b+cb < a+ca) and [r*(b+cb) < a+ca]
c<b<a ==> (A wins) = (b+cb < a+ca) or [b+cb < r*(a+ca)]

When r=1, then
I tested with these values of r:

0/1, 1/8, 1/6, 1/5, 1/4, 1/3, 3/8, 2/5, 1/2, 3/5, 5/8,
2/3, 3/4, 4/5, 5/6, 7/8, 8/7, 6/5, 5/4, 4/3, 3/2, 8/5,
5/3, 2/1, 5/2, 8/3, 3/1, 4/1, 5/1, 6/1, 8/1,

For all those values of r, the (A wins) expression was not
monotonic. They all have 5 or 9 faces (allowing negatives).

Here is the code that I used:
-------------------------------------------------------
procedure win_a(a,b,ba,bc,c,ca,cb); begin
return
(b<a)and(a<c) and ( (c+bc < a+ba) and (r*(c+bc) < a+ba) ) or
(b<c)and(c<a) and ( (c+bc < a+ba) or (c+bc < r*(a+ba)) ) or
(c<a)and(a<b) and ( (b+cb < a+ca) and (r*(b+cb) < a+ca) ) or
(c<b)and(b<a) and ( (b+cb < a+ca) or (b+cb < r*(a+ca)) );
end;
procedure wr(rr); begin
% see if A becomes a loser when changing (B) into (A)
Pos:=(0<=a)and(0<=b)and(0<=ba)and(0<=bc)and
(0<=c)and(0<=ca)and(0<=cb); % ineffective
g1 := sub({r=rr}, win_a(a,b,ba,bc,c,ca,cb));
g2 := sub({r=rr}, win_a(a+t,b-t,ba,bc,c,ca,cb));
h1 := (0<t) and Pos and g1 and (not g2);
h1 := (100 = a+b+ba+bc+c+ca+cb) and stri h1;
tt := rlqea ex ({t,a,b,ba,bc,c,ca,cb}, h1); % (Exists t,..)
write "tt = ",tt;
end;
-------------------------------------------------------


The tangent polytopes constraining the normal vectors of
wins-regions are of a quantity that equals the number of
winners. I deleted that since cutting out the wrong argument
saying the Mr Schulze was wrong.

Perhaps Mr Schulze could venture to give some ideas on how to
tilt the divides between the cases?.

E.g. devise linear combinations prior to the sorting or
something.


The CVD has a new plan. Rob Ritchie decided it was too
risky to say that "we too regard that you are right to get no
winner but the best winner that you sought". Instead the
latest brochure is gilded like something from an early
Anold movie and talking about rates and what it means to
the voter. It might mean very little if each candidate for
mayorship offers a similar rate over the next few terms.

That aside, they say that the definition of IRV is a first
principle. The majority principle. IRV is not a church being
built over common interests.

Megaphone prblems: : what about the single day when
y'all vote for the mayor?. Interested in controlling the
selection of the mayor using a fair method ?.

Duh!. the CVD must be thinking of IRV promoting referenda
elections since using a right wing theme to advance it
random-side-of-left model of greatness.


___________________________________________________________________

Corrections:

At 03\02\28 21:05 +1300 Friday, Craig Carey wrote to EM List;
...
Post by Jan Kok
I'm curious if anyone can mathematically justify such statements as
"Voting method A exhibits property P 'more often' than method B"?
...
The method would be perfectly stable and unchanging and the
statement to be justified did presume that.
I'd reword that to:

. . . . . . . . . . . .... did impose a presumption that that was not so.




G. A. Craig Carey


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Markus Schulze
2003-03-01 01:05:25 UTC
Permalink
Dear Craig,
Post by Craig Carey
Correction: Mr Schulze was right in saying that an AV-like method
that passes the test of monotonicity and that is defined explicitly
for all numbers candidates, and that need not be optimal, is not known.
What is an "AV-like method"? What does "explicitly defined" mean in
this context? Could you give a concrete example of a method that is
well defined but not "explicitly defined"? What does "optimal" mean
in this context?

Markus Schulze

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Markus Schulze
2003-03-01 01:16:58 UTC
Permalink
FBC is the only criteria that favors Approval
over Condorcet.
Condorcet violates the participation criterion.
Approval Voting meets the participation criterion.

Markus Schulze

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Stephane Rouillon
2003-03-01 14:49:13 UTC
Permalink
Sorry for not knowing,

what is the participation criterion?

Steph
Post by Markus Schulze
FBC is the only criteria that favors Approval
over Condorcet.
Condorcet violates the participation criterion.
Approval Voting meets the participation criterion.
Markus Schulze
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Craig Carey
2003-03-01 20:58:47 UTC
Permalink
At 03\03\01 09:49 -0500 Saturday, Stephane Rouillon wrote:
...
Post by Stephane Rouillon
what is the participation criterion?
Steph
Post by Markus Schulze
FBC is the only criteria that favors Approval
over Condorcet.
Condorcet violates the participation criterion.
Approval Voting meets the participation criterion.
And the missing third sentence is: both statements are so
unimportant as to be best ignored.

There is no clue there on the weightiness of the claims. I am
sure that they are not important. Certainly that view can locked
down if the definition of the "criterion" is not available.

To the extent possible, please regard the following comments being
about an election having only the papers (AB), (B), and (C). For
that election, the Condorcet method has an undefined region of
quite a big size.

It is controversial to create a weak rule and see that it passes
some methods and not others. Instead a plausible rule that fails
all the methods that need to pass can be used, but it is length
(or bigness) of the worst failure is measured. It looked
interesting when 2 winner 4 candidate STV was proven at the STV
mailing list to be not monotonic with the support rise harmed
being about 17%.

Quite so. Shulze can tell us why he missed out using enough words.
Whether or not the participation axiom is a good friend of IRV or
not, it not figured out by me yet. However it is certainly a rule
that can be not used during design for being too weak. It could
be of interest when failing methods. Questions on its goodness can
be ignored while the details are not here. I really can't be bothered
considering whether Mr Schulze was correct in saying that the rule
failed one of those two methods. There can be two cases: the
participation axiom or whatever, is implied by a better rule or it
isn't. Then it can be rejected as a rule to not use, in both cases.
The idea that faulty methods can have their credibility raised by
getting a pass under a weaker rule, is fragile since the weaker
rule or strong (in this pro-monotonicity style) is susceptible to
being sabotaged by impurities in the support rise that should not
harm.

Also people that say that FBC is this and that, all of which are
untrue (while the comments are groper fish and the direction of the
groping is not too obvious, and maybe Ossipoff can post up some
equations), all seems to have more readily trusted and quoted by
some of the EM List new members, than what the stuff that Mr Schulze
writes.

Is this the same as the Participation Axiom ?. Is the person who
is the authority on rewording the definition of the
"participation criterion", Mr B Cretney?.

Problem 1. The rule says that when votes for a candidate disappear
then it does not change from a loser into a winner. Maybe only
FPTP papers were thought of. But this seems to be a example where
it should be possible to say that if A loses the first then it
should lose the second. The possible problem is that the rule
either rules out this alteration or it is incomplete/vague:

.1000 A
. . 2 B
. . 3 C
. 400 BCA
. . x S

.1000 A
. . 2 B
. . 3 C
. 400 BC <-- so A has to stay losing, (participation axiom)
. . x S

There might very easily be a problem: this is OK for the
"participation criterion" but whoever defined it, didn't get the
definition to allow this.

In a past message, Mr Schulze initially didn't see that the
preceding preferences would need to be kept constant. (In this
example the "BC" papers).

I can only complain about the "criteron"-ization of rules.
Literature is hardly better if calling it an "axiom" when it is
not used in a theory.

So Condorcet meets the partipation criterion, and hence the
rule ("criterion") excuses the method every time it can't find
any winners in one of the two cases.

Suppose the method returns whatever, and the rule handles the
result by converting it into a scalar value using this?:

Term := {} /= (L . Winners)

There "." is an operator to intersect sets. The rule then
processes that term using OR, AND, Exists, and For_All.

Does Condorcet return and undefined value (a third value of the
2 valued Boolean scheme) ?, or does it just make the set of
Winners be an empty set.


CASE 1:
If Condorcet (etc) returns an undefined value, then the rule does
not fail it and it does not pass it, but instead it returns an
undefined result. To fix that, the undefined value has to be
explicitly converted into either true or false.

CASE 2
A fairly natural thing for a method that gets the wrong number of
winners, is to return whatever it could return. For that case
the rule is very likely to unforgiving over a failure to get the
number of winners correct. Extra text/symbols may have to be
added before Condorcet can be passed.

There is no problem with multivalued methods: the result of the
rule is multivalued. Also the rules can easily handle all ties
correctly. It is up to the method to hide all internal ties, i.e.
flats of undefined "outcomes" where the winner sets on both sides
are the same. The simplest thing to do is to fail the method and
force the method design and fill up the cuts that have the same
winners on both sides.

A question is: is there a rarely seen philosophy that likes to
rename rules as criterion and thinks that when that is done,
then methods that can't always get the number of winners right,
are passed, and WITHOUT the extra code making it forgive the
lapse, being added to the quantifier logic of the rule.

I guess we sould see the classic Shulze brevity in respose to
this. The target here is the http://www.condorcet.org/ group.

At 03\03\01 09:49 -0500 Saturday, Stephane Rouillon wrote:
...
Post by Stephane Rouillon
what is the participation criterion?
With me having the rules down to about 3:
* Right number of winners (no undefined values)
* P2 ( 2(AB) = (ABC)+(ABD) if all candidates = {A,B,C,D}, etc.)
* Interim Equal suffrage (defined with 2 statements about
preference shifting)

Maybe the 1st two could be merged into the 3rd. To impose a
right number of winners rule, can be done by making the touching
rigid (snap-rotatable) polytope that defines the acceptable
normal vectors, be empty.

With P2, the touching polytope of Equal Suffrage is cut up into
a subspace and the quite possibly the definition of Equal Suffrage
is changed.

______________

G. A. Craig Carey

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Dave Ketchum
2003-03-02 07:38:37 UTC
Permalink
Post by Craig Carey
...
Post by Stephane Rouillon
what is the participation criterion?
Steph
Post by Markus Schulze
FBC is the only criteria that favors Approval
over Condorcet.
Condorcet violates the participation criterion.
Approval Voting meets the participation criterion.
And the missing third sentence is: both statements are so
unimportant as to be best ignored.
There is no clue there on the weightiness of the claims. I am
sure that they are not important. Certainly that view can locked
down if the definition of the "criterion" is not available.
To the extent possible, please regard the following comments being
about an election having only the papers (AB), (B), and (C). For
that election, the Condorcet method has an undefined region of
quite a big size.
Seems like "undefined region" is an unfortunate label. Agreed that
Condorcet has cycles, and that its basic definition allows these to exist
but does not provide a resolution for them.

STILL, this problem is recognized and I do not hear anyone being dumb
enough to propose actual use of Condorcet without completing the
definition of the method by specifying how to process cycles (while it is
true that there is debate as to exactly what to do with them).

For a method to be complete and ready for actual use in elections it MUST
specify response for every possible collection of ballots (papers).

IRV also has an undefined region, while smaller - what to do when two weak
candidates are equal, and thus neither can be discarded as weakest.
Post by Craig Carey
It is controversial to create a weak rule and see that it passes
some methods and not others. Instead a plausible rule that fails
all the methods that need to pass can be used, but it is length
(or bigness) of the worst failure is measured. It looked
interesting when 2 winner 4 candidate STV was proven at the STV
mailing list to be not monotonic with the support rise harmed
being about 17%.
______________
G. A. Craig Carey
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James Gilmour
2003-03-02 12:01:42 UTC
Permalink
Dave wrote (in part)
IRV also has an undefined region, while smaller - what to do when two weak
candidates are equal, and thus neither can be discarded as weakest.
If by this you mean a tie, the standard UK rules (as used in UK public elections)
state that the Returning Officer should first look back to earlier stages of the
count and exclude whichever of the candidates had the fewer votes at the earliest
stage where their votes were unequal. If their votes were equal at all stages,
the Returning Officer is to determine by lot between the candidates "and the
candidate on whom the lot falls shall be excluded".

There is no measure of "representation" in this final resolution, but when you
have a complete tie, what else can you do?

James

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Craig Carey
2003-03-02 13:08:12 UTC
Permalink
...
Post by Dave Ketchum
Post by Craig Carey
about an election having only the papers (AB), (B), and (C). For
that election, the Condorcet method has an undefined region of
quite a big size.
Seems like "undefined region" is an unfortunate label. Agreed that
Condorcet has cycles, and that its basic definition allows these to exist
but does not provide a resolution for them.
STILL, this problem is recognized and I do not hear anyone being dumb
enough to propose actual use of Condorcet without completing the
definition of the method by specifying how to process cycles (while it is
true that there is debate as to exactly what to do with them).
...

It is not OK to say that
it would be dumb to use Condorcet because: it can't always return the
right number of winners.

Condorcet could be quite good under fairness testing that got weakened
to forgive it for whenever the rule probed into its region that got the
wrong number of winners.

Fixing it is a no gain situation. I myself weaken tests so that
Condorcet slumps if fixed.
Post by Dave Ketchum
IRV also has an undefined region, while smaller - what to do when two weak
candidates are equal, and thus neither can be discarded as weakest.
...

IRV is Mr Ritchie's method isn't it?.

Doesn't USA clean up its nuclear wastes by trucking them to steel refinery
factories. Wasn't that how the CVD's Mr Ritchie who was planning that??.


A rule testing a method can overlook the ties.

Here is 2 solutions for ties in the space of the weights of the ballot
papers:

(1) say all ties are mishandled at the top of the analysis.
I.e. most of the "<"s might actually mean "<=". That seems OK

(2) A computer does not accept that. So my lax, stri, strieq functions
can expand and contract solids to include or exclude their surfaces and
cuts.


What is the best way (for this topic), to define a function (named
"stri", say ("stri" is for "strict"), that cuts out the surface of its
argument ?.

Question:
What should "stri (x=0) or ((y=0) and (z=0))" equal ?:

(a): False [since the space is 3-D and R is the union of polytopes of
a lower dimension (ie. x=0 is a plane)].

(b): False [since all equalities. (It is known that x,y,z are free
rather than, say, equal to 0)]

(c): "(x=0)' [since that is all the highest dimensional part of the
polytope]

My REDLOG code uses (b); I presume that the (c) is the best choice.
Because I use "(b)", I have two "stri" functions: one contracts solids
but leaves the x=y flats, and the other deletes those.

This whole topic of ties is so easy.




Craig Carey

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Dave Ketchum
2003-03-03 01:06:09 UTC
Permalink
Post by Craig Carey
...
Post by Dave Ketchum
Post by Craig Carey
about an election having only the papers (AB), (B), and (C). For
that election, the Condorcet method has an undefined region of
quite a big size.
Seems like "undefined region" is an unfortunate label. Agreed that
Condorcet has cycles, and that its basic definition allows these to exist
but does not provide a resolution for them.
STILL, this problem is recognized and I do not hear anyone being dumb
enough to propose actual use of Condorcet without completing the
definition of the method by specifying how to process cycles (while it is
true that there is debate as to exactly what to do with them).
...
It is not OK to say that
it would be dumb to use Condorcet because: it can't always return the
right number of winners.
Condorcet could be quite good under fairness testing that got weakened
to forgive it for whenever the rule probed into its region that got the
wrong number of winners.
Fixing it is a no gain situation. I myself weaken tests so that
Condorcet slumps if fixed.
I do not see "weaken tests" as being an acceptable response to a method
being incomplete. Also, I do not understand (or likely need to
understand) "slumps" as used here.

I brought up IRV (see below) as a topic to emphasize necessity for methods
to be complete before being offered for use in actual elections (and, if
the goal is anything less than public elections, I do not get enough
amusement from EM to be worth bothering).

Thus, to be complete as a method, Condorcet must provide for returning the
required number of winners - something those serious about Condorcet do
attend to.
Post by Craig Carey
Post by Dave Ketchum
IRV also has an undefined region, while smaller - what to do when two weak
candidates are equal, and thus neither can be discarded as weakest.
...
IRV is Mr Ritchie's method isn't it?.
... (Craig offers thoughts on methods to solve this problem of ties).


In another post, James Gilmour offers the solution used in public
elections in the UK.
Post by Craig Carey
This whole topic of ties is so easy.
It is easy if AND ONLY IF it is attended to before declaring the method to
be complete and ready to be used in an actual election.

There is no acceptable solution if method completion is left until an
actual election displays the lack and no decision can be made without
human input - human input that cannot be guaranteed free from human bias.
Post by Craig Carey
Craig Carey
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Markus Schulze
2003-03-01 19:35:12 UTC
Permalink
Dear Steph,

the participation criterion says that it is not possible
to worsen the outcome by participating:

Suppose that candidate A is the winner. Suppose that
a set of voters, where each voter strictly prefers
candidate B to candidate A, is added to the original
profile. Then candidate B must not become the new winner.

Moulin demonstrated that the Condorcet criterion and the
participation criterion are incompatible. (Herve Moulin,
"Condorcet's Principle Implies the No Show Paradox,"
Journal of Economic Theory, vol. 45, pp. 53-64, 1988.)

Markus Schulze

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Stephane Rouillon
2003-03-01 21:12:19 UTC
Permalink
I suppose you meant:

Suppose that candidate A is the winner. Suppose that
a set of voters, where each voter strictly prefers
candidate A to candidate B, is added to the original
profile. Then candidate B must not become the new winner.

Steph
Post by Markus Schulze
Dear Steph,
the participation criterion says that it is not possible
Suppose that candidate A is the winner. Suppose that
a set of voters, where each voter strictly prefers
candidate B to candidate A, is added to the original
profile. Then candidate B must not become the new winner.
Moulin demonstrated that the Condorcet criterion and the
participation criterion are incompatible. (Herve Moulin,
"Condorcet's Principle Implies the No Show Paradox,"
Journal of Economic Theory, vol. 45, pp. 53-64, 1988.)
Markus Schulze
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Markus Schulze
2003-03-01 20:11:24 UTC
Permalink
Dear James,
Post by Venzke Kevin
I wonder if the only reason IRV has more apparent
backing than approval or Condorcet is because it would
permit our present politicians to be elected even more
easily.
I guess that the main reason why so many people support IRV
is that these people consider IRV to be the first step to
proportional representation by the single transferable vote.
And in so far as there is no known version of proportional
representation by the single transferable vote that has been
proven to meet monotonicity, I guess that many activists
see no point in insisting that the promoted preferential
single-winner method should meet monotonicity.
I don't think there any necessary connection between promoting
IRV and promoting PR by STV. (...) Most who argue for IRV in
public elections here, do so as a means of preventing any move
towards PR.
Is this statement only valid for IRV supporters? Or do you think
that also Approval Voting supporters and Condorcet supporters
rather hurt than help the move towards PR-STV? In your opinion,
which single-winner method should those people who want
to promote PR-STV for parliamentary elections promote for
single-winner elections when they don't want their effort
for better single-winner elections to hurt their effort for
the introduction of PR-STV?

******
Post by Venzke Kevin
We have very few directly elected single-office public elections
in the UK. However, when advocates of STV-PR are asked about such
elections, they usually recommend IRV (despite all its defects).
Which election method do you recommend for directly elected
single-office public elections?

Markus Schulze

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James Gilmour
2003-03-01 23:35:56 UTC
Permalink
Post by Markus Schulze
Post by James Gilmour
I don't think there any necessary connection between promoting
IRV and promoting PR by STV. (...) Most who argue for IRV in
public elections here, do so as a means of preventing any move
towards PR.
Is this statement only valid for IRV supporters? Or do you think
that also Approval Voting supporters and Condorcet supporters
rather hurt than help the move towards PR-STV?
There are no supporters of Approval Voting and no supporters of Condorcet voting
in the UK. At least, no one is promoting either of these systems for use in
public elections.

Apart from the army of "Keep First-Past-The-Post" supporters, the main opponents
of STV-PR promote MMP(= AMS) or some form of Party List PR. Both MMP and Party
List are highly defective and fall far short of delivering what STV-PR can give to
the voters.
Post by Markus Schulze
Markus then asked: In your opinion,
which single-winner method should those people who want
to promote PR-STV for parliamentary elections promote for
single-winner elections when they don't want their effort
for better single-winner elections to hurt their effort for
the introduction of PR-STV?
In the UK context, IRV is the obvious choice, primarily because it is the same
system of voting (preferential with fully transferable votes) applied to a
single-seat election. But this is only for directly elected posts like Mayor (or
Governor), not local representatives (council members) where IRV is sometimes
suggested as a 'stepping stone' towards PR. It isn't.

NB We do not have any voting technology problems of the kind that affect voting
reform decisions in the USA, at least not yet. Nearly all UK public elections are
recorded on paper ballots and counted by hand. We do now have some machine
counting of paper ballots and there have been several pilots with a variety of
electronic systems, and more pilots are planned. Note also that in Ireland in the
2002 general election, they used a totally electronic system for STV-PR in three
constituencies and it worked well.
Post by Markus Schulze
Post by James Gilmour
We have very few directly elected single-office public elections
in the UK. However, when advocates of STV-PR are asked about such
elections, they usually recommend IRV (despite all its defects).
Which election method do you recommend for directly elected
single-office public elections?
For the moment, IRV, and that is the one I use. I shall be supervising the IRV
count for the election of the Rector of the University of Edinburgh next Friday
evening. There are five candidates and all students and staff of that University
can vote.

James

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Alex Small
2003-03-02 06:52:05 UTC
Permalink
Post by Markus Schulze
Is this statement only valid for IRV supporters? Or do you think
that also Approval Voting supporters and Condorcet supporters
rather hurt than help the move towards PR-STV
I have suggested before, and I'll suggest again, that almost any
single-winner election method better than plurality will lead to calls for
PR (of some sort, everybody has his favorite method) in the US.

Despite IRV's flaws, adoption of IRV would probably lead to third-party
candidates getting more first-place votes than the measly 2% or so that
they usually get in the US. Remember that when there are 3 candidates, a
candidate with less than 25% of the first place votes will always be
eliminiated, and cannot act as a "spoiler" by knocking somebody else out
of the second round and then losing. If election returns consistently
showed 15% or more support for a particular third party (a quite plausible
scenario under IRV) the unrepresentative nature of single member districts
will become obvious. I call this plausible because the flaws of IRV will
not rear their head when the third candidate gets 15%, but the flaws of
single-memberf districts will become obvious.

If we adopt a method that leads to a significant number of third party
candidates winning legislative offices then we can be even more confident
of PR being adopted. First of all, the third party legislators will
presumably push for PR. Second, the legislature will probably be a very
poor reflection of the composition of the electorate with three or more
parties.

When you only have two parties, even with gerrymandering the party that's
most popular in the state is usually (but not always) the one that draws
the districts. OK, there are states where one party controls the Senate
and the other the House (or Assembly, or whatever that state calls it),
but those states usually do not have a strong partisan preference. (e.g.
As a Wisconsinite by birth and upbringing I can tell you that it made
perfect sense when WI had a GOP Assembly, a Democrat Senate, a
GOP-dominated House delegation, 2 Democrat US Senators, a GOP governor,
and a trend of voting Democrat in Presidential races.)

Anyway, any election reform that gives third parties a chance to at least
earn more support (even if they rarely win) will make more obvious the
flaws of single-member districts. I think we could then see PR become a
serious issue.



Alex


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Markus Schulze
2003-03-01 23:19:37 UTC
Permalink
Dear Steph,
Post by Markus Schulze
Suppose that candidate A is the winner. Suppose that
a set of voters, where each voter strictly prefers
candidate A to candidate B, is added to the original
profile. Then candidate B must not become the new winner.
Yes. You're right.

Markus Schulze

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Craig Carey
2003-03-02 02:28:43 UTC
Permalink
Post by Markus Schulze
Dear Steph,
Post by Markus Schulze
Suppose that candidate A is the winner. Suppose that
a set of voters, where each voter strictly prefers
candidate A to candidate B, is added to the original
profile. Then candidate B must not become the new winner.
Yes. You're right.
When Mr Schulze is brief then wrong too (maybe in general).

Firstly voters should be changed to papers.

The rule is one that is undesirable and it would not be an axiom.
So far Mr Sculze has not said that it is important. Complaining
about that would seem appropriate but the definition was not
available.

Now, we still have no definition.


This is to be allowed rather than prohibited (Mr Schulze appears
to be speaking against it):

The "We" in the text described ballot papers grouped by their
leading preferences.

----------------------------------------------------------------
We'll take A and if not available then B, and we'll take C and
if C's not available, then D.
----------------------------------------------------------------

Take is like desire. Mr Rouillon might otherwise write in and
suggest he could learn something when that is not likely to be
true: whatever that desire is, if it is not represented by an
equation that it can't be about rules uses in the design of
methods or for when they are rejected. I don't use rules to
reject (e.g. STV) that were not tested by having them axioms.
A bad option is to call a "rule" a "criterion". Presumably the
motive is that can reject methods. That fix seems to only
reduce the chance of the rules being rejected. But we need to
know who it was that came up with the idea of calling a rule
a criterion, before the non-monotonic topic of achieving the
opposite of the purpose becomes more interesting.

Here is an example:

Election 1: Papers = S1, Winners = {A}
<-->
Election 2: Papers = S1 + (CDAB), Winners = {B}


Mr Schulze made just about the same mistake years ago, in this
mailing list, when replying to me. The mistake being to have the
preceding preference list not be the same in the two elections,
when commenting on candidate that didn't have the 1st preference.
to remind Mr Schulze, the topic was

'should voters be punished for arriving at the election booths'.

The example below shows that they (i.e. papers) would be punished
with remarkable severity.


--------

Consider this (irv-wrong-winners, yet another wrong Mayor in office)
See that there is a large support rise for A and that causes
A to lose. This is nearly showing that the Alternative Vote
violates the Participation Axiom (unless I remember it incorrectly).
Post by Markus Schulze
----------------------------
A 19999 80004
B 1 5
BA 19997 19997
CB 40002 40002
DBA 20001 20001
----------------------------
Total: 100000 160009
AV Winner: A B
1:1:elim B: 19997+19999=39996(A)
1:2:elim D: 39996+20001=59997(A)
1:3:test 40002(C)<59997(A)-->A wins
2:1:elim D: 20001+19997=39998(BA)
2:2:elim C: 40002+5+39998=80005
2:3:test 80004(A)<80005(B)-->B wins
Recapitulation: a huge 37% of the vote vanishes and they are all
FPTP votes too.

--------------

That looks like a "classical participation axiom" problem (but it
is not since B got 4 votes).

Shulze wrote Yes but meant "No". A slip up of that sort is always
possible when the aim is to withhold the definition from
mathematicians while trying to lead others to believe that it
is indeed held.

Some things slip through the CVD cracks in wooden-floored building.

The META-RULE:

When that rule considers 2 or more election examples, then it will
impose that which is implied by the adding of the same preceding
preference list to all the papers that change in the examples.

A restriction of course is that the not-changing papers are
not considered by the rule but they could be considered by the
method being tested. Maybe the method has to be a fair method or
one that is all about restrictions on winners when altering papers.

This is about where the messages start to go downhill.

Shulze had a long military commander's stick and waved it and said
no factions shall form when over 50 million ballot papers. I
forget the name of the principle is and maybe Mr Schulze would
give it a name, for us.







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Markus Schulze
2003-03-02 12:22:18 UTC
Permalink
Dear Craig,
Post by Craig Carey
Consider this (irv-wrong-winners, yet another wrong Mayor in
office) See that there is a large support rise for A and that
causes A to lose.
Post by Craig Carey
----------------------------
A 19999 80004
B 1 5
BA 19997 19997
CB 40002 40002
DBA 20001 20001
----------------------------
Total: 100000 160009
AV Winner: A B
That looks like a "classical participation axiom" problem (but
it is not since B got 4 votes).
In your example, the fact that the winner is changed from candidate A
to candidate B is caused only by the addition of the 4 B voters. Your
conclusion that "the large support rise for A causes A to lose" is
false.

Actually, when IRV is being used and candidate A is the unique winner,
then a set of additional voters who strictly prefer candidate A to
every other candidate can never make candidate A lose.

Markus Schulze

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Craig Carey
2003-03-02 16:55:18 UTC
Permalink
I replied privately to Mr Jan Kok who was being misled by the
electionmethods,org website. Subscribers that could criticise
the site are likely to drop out. I assume that Mr Forest Simmons
(who has to wait for me to unsubscribe and then a delay or
week or so (unless he has an arrangement with the owner to find
out if I had unsubscribed ), won't be dropping out. Simmons
did not seem to want the site removed.
...
Post by Markus Schulze
Post by Craig Carey
Post by Craig Carey
----------------------------
A 19999 80004
B 1 5
BA 19997 19997
CB 40002 40002
DBA 20001 20001
----------------------------
Total: 100000 160009
AV Winner: A B
That looks like a "classical participation axiom" problem (but
it is not since B got 4 votes).
In your example, the fact that the winner is changed from candidate A
to candidate B is caused only by the addition of the 4 B voters. Your
conclusion that "the large support rise for A causes A to lose" is
false.
Where is the "participation" word ?.

Also it is unsafe to say that A started to lose because there were
extra 4 votes against A. The Alternative Vote negates votes (etc.)
so pure support rises can harm the candidate supported.

I recall that the B votes are rising because that was a consequence
of requiring that all of the altering be done with FPTP-style papers.

The fraction, 60,005/16,009 gets big fast:


Num Candidates : Fraction that arrived late to harm their candidate
4 3.0000812454 / 8
5 7/16 = 0.4375 % the next are extrapolations only
6 15/32 = 0.46875
7 31/64 = 0.484375
8 63/128 = 0.4921875
9 127/256 = 0.49609375
10 255/512 = 0.498046875
11 511/1024 = 0.4990234375
12 1023/2048 = 0.4995117188 = 1/2 - 10**(-3.3113299523)
13 2047/4096 = 0.4997558594 = 1/2 - 10**(-3.612359948)
14 4095/8192 = 0.4998779297 = 1/2 - 10**(-3.9133899436)
etc.

Mr Shulze can say if he had an IRV passing rule that stops
exactly that type of problem.

--

This next text mismatches with text of the text you in reply to a
message of Mr Rouillon. Here are the two.

_________________________________________________________________
Post by Markus Schulze
Actually, when IRV is being used and candidate A is the unique winner,
then a set of additional voters who strictly prefer candidate A to
every other candidate can never make candidate A lose.
_________________________________________________________________

_________________________________________________________________
Post by Markus Schulze
Dear Steph,
Post by Craig Carey
Suppose that candidate A is the winner. Suppose that
a set of voters, where each voter strictly prefers
candidate A to candidate B, is added to the original
profile. Then candidate B must not become the new winner.
Yes. You're right.
_________________________________________________________________


I comment on the two texts.

(1) Statement S2 talks about the win-lose state of candidate B while
S1 talks about the win-lose status of candidate A. But both have
candidate A be the preference of the two (if two) that is nearer
the first preference. So the two are totally different. They word
participation is switch and Mr Schulze doesn't want admit that he
can see that problem, I assume.

(2) Also the bad wording "[caged kangaroos] who prefer candidate A
to every other candidate..." in S2 presumably is referring
to all candidates, rather than only the candidates named on the
added papers. So it must mean something like 'A is the 1st preference'.

In S1 (underneath S2), symbol A only has to be before symbol B in the
list. So the rule S1 is garbage when there are many candidates

(3) S1 has a consideration of 2 candidates and S2 (above S1) hasn't.

(4)

The words "strictly prefer ... to every other candidate"
Post by Markus Schulze
then a set of additional voters who strictly prefer candidate A to
every other candidate can never make candidate A lose.
What if the ballot paper is this ?: (CA). Also candidate B's
preference is off the RHS edge of the ballot paper

No one knows whether A is strictly preferred by the breathing
Australian kangaroos of the Mr Schulze's mathematical, over candidate
B or not.

That is same mistake again because it means that with 3 lines
Mr Schulze struggled to get out, has plopped him back into the
dogs breakfast kitchen floor mess of brandishing the stick for
many. I.e. my P2 rule, a rule good enough for me to use, since
great stuff and not something from Mr Schulze, and its is also a rule
that passes the Alternative Vote, has candidate A hold a
greater influence than B in this paper (CA), than happens with
this paper: (CAB).

E.g. if there are 4 candidates: then (CA) has maybe around 1/2 the
power of (CAB), at promoting B.
I.e. (CA) = (1/2)( (CAB) + (CAD)) by rule P2.
Candidate B is out of the back of the paper, and the voters may
jump to conclusions but not have sharp and strict views on what
they like.

____

Apologies on the nuclear waste disposal operation. I was going to
run an experiment proving that American members would copy the
"IRV" term, but not speak up for Mr Ritchie. So the sensitive
amongst us would know that missed Mr Ritchies view of 'Why IRV'
and so on. The latter is hidden.

Another wording mistake was the argument on calling "rules"
"criteria". Mr Schulze was calling it a criterion. I don't need to
correct my bad sentence wording if the name was abandonded.

I might quit soon if Mr Schulze doesn't transfer a fraction of the
emphasis on materiality of descriptions out to the idea with an
reality that something to describe arises. It is all done with
English and I am really doubt that extending a plank of common
understanding that English is material, is going to be helpful
to the exposition when the others are in the Commonwealth (I
am thinking of New Zealand and African countries. Persons in
Africa can't remain confused forever, though it seems possible
for Nth Americans).




Craig Carey



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Markus Schulze
2003-03-03 09:31:57 UTC
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Dear Craig,

fortunately, "incompleteness" is not an issue since nobody
suggests to use a Condorcet method without a tie-breaker.

Markus Schulze

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Craig Carey
2003-03-04 01:53:43 UTC
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Post by Markus Schulze
Dear Craig,
fortunately, "incompleteness" is not an issue since nobody
suggests to use a Condorcet method without a tie-breaker.
Perhaps you did not read this.
It limits your freedom to alter the interpretation of the
word Condorcet. A tiebreaker would not be considered by a good
rule since no peeking into the internals (but an exception would
easily occur when the output is unpredictable).


------------------------------------------------------------------------
Date: Sun, 02 Mar 2003 09:58:47 +1300
To: election-methods-***@eskimo.com
From: Craig Carey <***@ijs.co.nz>
Subject: 3-valued Booleans inside rules, passing Condorcet (Re: [EM]
"More often" (was: IRV and Condorcet operating identically)
Post by Markus Schulze
...
Post by Stephane Rouillon
what is the participation criterion?
Steph
Post by Markus Schulze
FBC is the only criteria that favors Approval
over Condorcet.
Condorcet violates the participation criterion.
Approval Voting meets the participation criterion.
And the missing third sentence is: both statements are so
unimportant as to be best ignored.
There is no clue there on the weightiness of the claims. I am
sure that they are not important. Certainly that view can locked
down if the definition of the "criterion" is not available.
To the extent possible, please regard the following comments being
about an election having only the papers (AB), (B), and (C). For
that election, the Condorcet method has an undefined region of
quite a big size.
It is controversial to create a weak rule and see that it passes
some methods and not others. Instead a plausible rule that fails
all the methods that need to pass can be used, but it is length
(or bigness) of the worst failure is measured. It looked
------------------------------------------------------------------------

The 3 paper limitation continues until the end of this thread.

What was the argument that you are replying to?.

That above is the first message in this thread according to its
Subject header information.

AB a
B. b
C. c

a+b+c=1

B beaten by A = (b<a) % passes through (C) vertex
C beaten by B = (c<a+b) = (1/2<c)
A beaten by C = (a<c) % passes through (B) vertex

Failure region = (b<a)(c<a+b)(a<c) [or could indifferently use "<="]

The formula does not contain a "tiebreaker".


Recall that I sent to you (5 minutes after the date of the message
I reply to) some lengthy good arguments indicating that the Condorcet
method is not a variant of itself. The mailing list did not receive
a copy.

Did Mr Schulze try to alter the meaning of the word "Condorcet" ?.





Craig Carey



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