Discussion:
Voting Criteria 101, Four Criteria
Benjamin Grant
2013-06-16 16:55:26 UTC
Permalink
With your kind indulgence, I would like some assistance in understanding and
hopefully mastering the various voting criteria, so that I can more
intelligently and accurately understanding the strengths and weaknesses of
different voting systems.



So, if it's alright, I would like to explain what I understand about some of
these voting criteria, a few at a time, perhaps, and perhaps the group would
be willing to "check my math" as it were and see if I actually understand
these, one by one?



I'll start with what seem to be the simpler ones. (For what it's worth, my
understanding comes from various websites that do not always agree with each
other. Also, I have the fundamental belief that one cannot consider oneself
to have mastered something until and unless one has the ability to
understand it well enough to explain it to someone else - which is what I
will try to do below, re-explain these criteria as a test to see if I really
get them.)



Name: Plurality

Description: If A gets more "first preference" ballots than B, A must not
lose to B.

Thoughts: If I understand this correctly, this is not a critical criteria to
my way of thinking. Consider an election with 10 candidates. A gets 13% of
the first place votes, more than any other single candidate. And yet B gets
8% of the first place votes, and 46% of the second place votes. It seems
obvious to me that B "ought" to win. And yet, in this circumstance, this
violates the above Plurality Criterion. Therefor is seems to be that the
Plurality Criterion is not useful, to my way of thinking.



Name: Majority

Description: If one candidate is preferred by an absolute majority of
voters, then that candidate must win.

Thoughts: I might be missing something here, but this seems like a
no-brainer. If over 50% of the voters want someone, they should get him, any
other approach would seem to create minority rule? I guess a challenge to
this criteria might be the following: using Range Voting, A gets a 90 range
vote from 60 out of 100 voters, while B gets an 80 from 80 out of 100
voters. A's net is 5400, but B's net is 6400, so B would win (everyone else
got less). Does this fail the Majority Criterion, because A got a higher
vote from over half, or does it fulfill Majority because B's net was greater
than A's net??



Name: Participation

Description: If a ballot is added which prefers A to B, the addition of the
ballot must not change the winner from A to B

Thoughts: This seems to make sense. If we do not require this, then we
permit voting systems where trying to vote sincerely harms your interests.
Also, any voting system that would fail Participation would be I think
fragile and react in not always predictable ways - like IRV. SO this seems
to me to be a solid requirement, that I can't imagine a system that failed
this Criterion to have some other benefit so wonderful to make failing
Participation worth overlooking - I cannot imagine it.



Name: Independence of Irrelevant Alternatives (IIA)

Description: Adding a new candidate B to an election that previously A would
have won must not cause anyone apart from A or B to win. That is, If A
would have won before B was added to the ballot, C must not win now.

Thoughts: This also seems fairly non-controversial. This I think is the
repudiation of the spoiler effect - that just because Nader enters the race
shouldn't disadvantage the candidate that would have won before that
happened. This would seem (to me) to also be a good Criterion to hold to in
order to encourage more than just two Candidates/Parties always dominating
the scene. I wonder what the downside would be to strongly embracing this
criteria?



Question: It seems to me that another criterion I have heard of -
Independence of Clones(IoC) - is a subset of IIA, that if a system satisfies
IIA, it would have to satisfy the Independence of Clones criterion as well -
is that correct? If not, what system what satisfy IoC but *not* satisfy IIA?



Question: it seems like the two above criteria - Participation and IIA -
would be related. Is it possible to fail one and not the other? Or does
either wind up mandate the other - for example, a system with IIA must also
fulfill Participation, or vice versa?



So let me stop there for now - I know there are other Criteria, but let me
pause so you guys can tell me what I am getting right and what I am getting
wrong.



Thanks.



-Benn Grant

eFix Computer Consulting

<mailto:***@4efix.com> ***@4efix.com

603.283.6601
Jameson Quinn
2013-06-16 20:43:43 UTC
Permalink
...I would like to explain what I understand about some of these voting
criteria, a few at a time...
Thanks for doing this, and again, welcome.

*Name*: *Plurality*
*Description*: If A gets more “first preference” ballots than B, A must
not lose to B.****
*Thoughts*: If I understand this correctly, this is not a critical
criteria to my way of thinking. Consider an election with 10 candidates. A
gets 13% of the first place votes, more than any other single candidate.
And yet B gets 8% of the first place votes, and 46% of the second place
votes. It seems obvious to me that B “ought” to win. And yet, in this
circumstance, this violates the above Plurality Criterion. Therefor is
seems to be that the Plurality Criterion is not useful, to my way of
thinking.
I think that most here would agree with what you've said.
****
** **
*Name: Majority*
*Description*: If one candidate is preferred by an absolute majority of
voters, then that candidate must win.
Presumably, by "preferred", you mean "preferred over all others". This
definition is actually a bit controversial. I'll explain, but I have to go
back a bit. Note that all that follows is my personal opinion; it's far too
opinionated to pass muster at Wikipedia, and though I suspect that some
here would agree with most of it, I'm also sure that others will chime in
to debate me on some points.

The modern science of voting theory begins with Kenneth Arrow in the 1950s.
I happen to be reading Kuhn (*The Structure of Scientific Revolutions*) at
the moment, so I'll use his terms. Before Arrow, the study of single-winner
voting systems was disorganized and unscientific; though figures such as
Maurice Duverger and Duncan Black had important insights into the
incentives of plurality on parties and voters, they could offer little
guidance as to how to improve the situation. Arrow offered the first
paradigm for the field. The Arrovian paradigm is essentially preferential,
and it tends to lead toward Condorcet systems as being "best".
From its very beginning, Arrow's own theorem marked sharp limits to how far
you could go within his paradigm. Nonetheless, as Kuhn quotes from Bacon,
"error leads to truth more quickly than confusion"; that is, even a flawed
paradigm is immensely more productive than prescientific disorganization.
For instance, the important Gibbard-Satterthwaite theorem on strategy
followed close on the heels of Arrow's result.

Since Arrow, there have been other paradigms advanced. Around 1980, Steven
Brams suggested Approval Voting, a simple idea which prior to that had been
used but never theorized. This was clearly a step out of the Arrovian
paradigm, but it didn't quite yet offer an alternative basis for further
research and refinement. Donald Saari then reacted against approval by
advancing a paradigm based on ordinal ballots and mathematical symmetry
(and thus, Borda voting); in my opinion, his willful ignorance of strategic
issues makes his way of thinking ultimately counterproductive, though some
of the tools he created are useful.

So the first person to offer a truly fertile alternative to the Arrovian
paradigm was, in my opinion, Warren Smith (active on this list), with his
1999 paper on Range Voting. This system, now mostly called Score Voting,
goes beyond approval to allow fractional ratings. The division between
Arrovian, preferential systems, and Score-like systems has been expressed
using multiple terms: ranked versus rated (with rated systems sometimes
further subdivided into rated or graded); ordinal versus cardinal;
preferential versus ???; and my own favorite terms, comparative versus
evaluative.

Since Smith, there has also been work in yet another paradigm, that of
delegation. The DemoEx party in Sweden, the study of Asset voting, liquid
democracy, delegable proxy, delegated yes-no (DYN), the revival of interest
in Dodgson's 19th-century proposal for delegated proportional
representation, and most recently my own proposal Simple
Optionally-delegated Approval (SODA) all lie in this line of inquiry.

Still, as always, there are some who continue to mine the vein of the old
Arrovian paradigm, and it can't be said that that vein is entirely played
out. The new paradigms also remain much less well-established academically;
for instance, Smith's seminal paper has never been published in a
peer-reviewed journal.

....

So all of that history is a backdrop for the debate over how to apply the
definitions of such criteria as Majority and Mutual Majority to evaluative
systems. Your definition of Majority uses the word "preferred", which
inevitably biases it towards ranked thinking. An advocate for evaluative
systems, like myself, would argue that it would be better to say "voted as
favorably as possible". This distinction makes no difference at all for a
comparative system — a candidate who is preferred over all others is, by
definition, at the very top of any purely comparative ballot — but it
allows a level playing field on which evaluative systems can aspire to pass
this criterion as well. Of course, partisans of the comparative Arrovian
paradigm argue back with what seem to me to be unproductive semantic
arguments: the criteria were originally defined in an earlier era, with
reference to comparative systems, so any extension of them to cover
evaluative ones is argued as illegitimate.
****
*Thoughts*: I might be missing something here, but this seems like a
no-brainer. If over 50% of the voters want someone, they should get him,
any other approach would seem to create minority rule? I guess a challenge
to this criteria might be the following: using Range Voting,
(Note: these days the term Score Voting is preferred.)
A gets a 90 range vote from 60 out of 100 voters, while B gets an 80 from
80 out of 100 voters. A’s net is 5400, but B’s net is 6400, so B would win
(everyone else got less). Does this fail the Majority Criterion, because A
got a higher vote from over half, or does it fulfill Majority because B’s
net was greater than A’s net??
Your example uses the ranked definition of the majority criterion. In the
rated definition I'd favor, neither group of voters is rating their
candidate at the top rating, so the majority criterion simply does not
apply. But simply change the the rating of A proponents from 90 to 100, and
the rated definition applies, so you've shown that Score voting doesn't
pass majority under any definition. A score proponent would argue that a
win by B would be the best result in this situation, because it would
(probably) maximize total social utility; the large extra utility for the
minority who prefer B is more than the small loss of utility for the
majority who prefer A.

****
** **
*Name: Participation*
*Description*: If a ballot is added which prefers A to B, the addition of
the ballot must not change the winner from A to B****
*Thoughts*: This seems to make sense. If we do not require this, then we
permit voting systems where trying to vote sincerely harms your interests.
Also, any voting system that would fail Participation would be I think
fragile and react in not always predictable ways – like IRV. SO this seems
to me to be a solid requirement, that I can’t imagine a system that failed
this Criterion to have some other benefit so wonderful to make failing
Participation worth overlooking – I cannot imagine it.
You have fairly described the participation criterion. I would ask you to
consider that this criterion focuses only on the direction of preference,
not its strength; and so it is inevitably biased towards preferential
systems, and dooms you to live within the limits set by Arrow's theorem. My
two favorite systems — SODA voting and the as-yet-unnamed version of
Bucklin — both fail this criterion, though I would argue they do so in
relatively rare and minor ways, and both satisfy some weakened version of
the criterion.
****
** **
*Name: Independence of Irrelevant Alternatives (IIA)*
*Description*: Adding a new candidate B to an election that previously A
would have won must not cause anyone apart from A or B to win. That is, If
A would have won before B was added to the ballot, C must not win now.****
*Thoughts*: This also seems fairly non-controversial. This I think is
the repudiation of the spoiler effect – that just because Nader enters the
race shouldn’t disadvantage the candidate that would have won before that
happened. This would seem (to me) to also be a good Criterion to hold to
in order to encourage more than just two Candidates/Parties always
dominating the scene. I wonder what the downside would be to strongly
embracing this criteria?
IIA, on the other hand, strongly favors evaluative systems, because in
comparative systems the entry of a new candidate can inevitably change the
absolute ranking levels of existing candidates. I think that IIA is
certainly a nice thing to pass, but I'd hesitate to make it a sine qua non.
****
** **
*Question*: It seems to me that another criterion I have heard of –
Independence of Clones(IoC) – is a subset of IIA, that if a system
satisfies IIA, it would have to satisfy the Independence of Clones
criterion as well – is that correct? If not, what system what satisfy IoC
but **not** satisfy IIA?
Not quite. A system which satisfied IoC could, in theory, shift from clone
X1 to X2 when another candidate (either an X3 or a Y3) entered the race,
which would violate IIA. And a system which satisfied IIA could, in
principle, shift from clone X1 to a newly-entering clone Y2, even though a
clone Y1 had already been in the race. I'm not offhand aware of which
systems would fall into these corners of the Venn diagram, but you are
mostly right: the large majority of systems which pass IoC also pass IIA.
****
** **
*Question*: it seems like the two above criteria – Participation and IIA
– would be related. Is it possible to fail one and not the other? Or does
either wind up mandate the other – for example, a system with IIA must also
fulfill Participation, or vice versa?****
** **
So let me stop there for now – I know there are other Criteria, but let me
pause so you guys can tell me what I am getting right and what I am getting
wrong.
Looking forward to your further posts. I encourage you to look next at some
strategic criteria: favorite betrayal, later-no-harm, and later-no-help. I
have strong opinions about which of those are important or not, but I'll
let you take your own look first.

Cheers,
Jameson
****
** **
Thanks.****
** **
-Benn Grant****
eFix Computer Consulting****
603.283.6601****
----
Election-Methods mailing list - see http://electorama.com/em for list info
Benjamin Grant
2013-06-16 21:36:14 UTC
Permalink
Re: Majority Criteria:



To be honest, I am worried that some (or all) of your history lesson
regarding Arrow might not have landed as well as it should in my brain. I
can say that one of the things I may need help on is the wording of the
criteria, so if "preferred" is not the right word, then we should use
something else.



However, I *think* the base idea is the idea that if over 50% of a group
want a candidate to win, they should get that candidate. What is more murky
to me - and perhaps more than me - is how you decide whether or not that is
being violated in systems that are more complex.



I guess I would say at a minimum, that if one is using Range Voting (which I
think you are saying is called Score Voting by the list; freely assign a
score of 0 to the maximum amount to each candidate (say 100), the candidate
with the greatest aggregate score wins) let me see how this might fail.
Let's say out of 1000 people 550 give candidate A scores of "100". Then
let's say that 700 people give candidate B scores of "80" each. Let's also
say that everyone else falls short of either of those totals. A gets 55,000
total, B gets 56,000. B wins.



On the one hand, one could say in one sense this violates Majority, but in
another sense one could perhaps with even more justification claim that B
actually has the larger majority. Or maybe to put another way, Majority
criteria only applies to voters when the system is one person, 1 vote -
others perhaps Majority criteria applies to *votes*, not voters.



In other words, maybe Majority criteria should be worded thusly: If one
candidate is preferred by an absolute majority of *votes*, then that
candidate must win.



In which case it (I think) becomes even more obvious and pointless as a
criteria (as any system that gave the victory to people who get less votes,
however we are counting and measuring votes, would make no sense, I think.)
Post by Jameson Quinn
Post by Benjamin Grant
Name: Participation
Description: If a ballot is added which prefers A to B, the addition of
the ballot must not change the winner from A to B
Post by Jameson Quinn
Post by Benjamin Grant
Thoughts: This seems to make sense. If we do not require this, then we
permit voting systems where trying to vote sincerely
Post by Jameson Quinn
Post by Benjamin Grant
harms your interests. Also, any voting system that would fail
Participation would be I think fragile and react in not always
Post by Jameson Quinn
Post by Benjamin Grant
predictable ways - like IRV. SO this seems to me to be a solid
requirement, that I can't imagine a system that failed this
Post by Jameson Quinn
Post by Benjamin Grant
Criterion to have some other benefit so wonderful to make failing
Participation worth overlooking - I cannot imagine it.
Post by Jameson Quinn
You have fairly described the participation criterion. I would ask you to
consider that this criterion focuses only on the
Post by Jameson Quinn
direction of preference, not its strength; and so it is inevitably biased
towards preferential systems, and dooms you to live
Post by Jameson Quinn
within the limits set by Arrow's theorem. My two favorite systems - SODA
voting and the as-yet-unnamed version of
Post by Jameson Quinn
Bucklin - both fail this criterion, though I would argue they do so in
relatively rare and minor ways, and both satisfy some
Post by Jameson Quinn
weakened version of the criterion.
I don't understand how a bias exists here. In every case I can currently
imagine, if an election as it stands has A winning, and one more ballot is
added which still prefers A to B, why should that ever cause the winner to
change to B?



Range/Score Voting: If A is winning, and the following ballot was added
(A:90, B:89) A would still be winning. If IRV is being used and the
following ballot is added (D first place, A second place, B third place) we
wouldn't want B to suddenly be beating A. (Although in IRV I guess it could
happen, but the point is that we wouldn't want it to, right?)



This seems to be a serious issue. Whatever the voting method, if A is
currently winning, and one more ballot gets added that happens to favor A
with relation to B, how could it EVER be a good thing if B somehow becomes
the winner through the addition of that ballot?



I don't understand what bias has to do with the answer to that question?



Also, how could Bucklin (as I understand it) *ever* fail this one? Because a
ballot added that favors A to B under Bucklin would at minimum increase A by
the same amount as B, possibly more, but would *never* increase B more than
A, else the ballot could not be said to prefer A over B, right?
Post by Jameson Quinn
Post by Benjamin Grant
IIA, on the other hand, strongly favors evaluative systems, because in
comparative systems the entry of a new candidate
Post by Jameson Quinn
Post by Benjamin Grant
can inevitably change the absolute ranking levels of existing candidates.
I think that IIA is certainly a nice thing to pass, \
Post by Jameson Quinn
Post by Benjamin Grant
but I'd hesitate to make it a sine qua non.
Independence of Irrelevant Alternative (IIA): Adding a new candidate B to an
election that previously A would have won must not cause anyone apart from A
or B to win. That is, if A would have won before B was added to the ballot,
C must not win now.



Again, I seem to be missing something here. If you are running an election
with whatever method, and A would win, but then B enters the race, I can get
A still winning. I can get B leaping ahead somehow and winning. What I
cannot understand is how a candidate that A was beating before B's entry,
somehow A now loses to. At least I cannot understand how any system that
fails this criteria could still be worth considering - how the outcome of A
beating C *until* B enters the race, after which C wins, is desirable. Is
there some example that explain how this turn of events could be somehow
fair or sensible?



Independence of Clones: since you are saying that IoC is not equivalent with
IIA, I will take up IoC independently along the way in a later set of
criteria.



I still am curious about this question:

Question: it seems like the two above criteria - Participation and IIA -
would be related. Is it possible to fail one and not the other? Or does
either wind up mandating the other - for example, a system with IIA must
also fulfill Participation, or vice versa?

Thanks for your time and help - and please, anyone who wants to chime in,
please do so, this is not just a conversation between myself and Jameson,
but between me and the community her.



Thanks! :)



-Benn Grant

eFix Computer Consulting

<mailto:***@4efix.com> ***@4efix.com

603.283.6601



From: Jameson Quinn [mailto:***@gmail.com]
Sent: Sunday, June 16, 2013 4:44 PM
To: Benjamin Grant
Cc: election-***@lists.electorama.com
Subject: Re: [EM] Voting Criteria 101, Four Criteria





2013/6/16 Benjamin Grant <***@4efix.com <mailto:***@4efix.com> >

...I would like to explain what I understand about some of these voting
criteria, a few at a time...



Thanks for doing this, and again, welcome.



Name: Plurality

Description: If A gets more "first preference" ballots than B, A must not
lose to B.

Thoughts: If I understand this correctly, this is not a critical criteria to
my way of thinking. Consider an election with 10 candidates. A gets 13% of
the first place votes, more than any other single candidate. And yet B gets
8% of the first place votes, and 46% of the second place votes. It seems
obvious to me that B "ought" to win. And yet, in this circumstance, this
violates the above Plurality Criterion. Therefor is seems to be that the
Plurality Criterion is not useful, to my way of thinking.



I think that most here would agree with what you've said.





Name: Majority

Description: If one candidate is preferred by an absolute majority of
voters, then that candidate must win.



Presumably, by "preferred", you mean "preferred over all others". This
definition is actually a bit controversial. I'll explain, but I have to go
back a bit. Note that all that follows is my personal opinion; it's far too
opinionated to pass muster at Wikipedia, and though I suspect that some here
would agree with most of it, I'm also sure that others will chime in to
debate me on some points.



The modern science of voting theory begins with Kenneth Arrow in the 1950s.
I happen to be reading Kuhn (The Structure of Scientific Revolutions) at the
moment, so I'll use his terms. Before Arrow, the study of single-winner
voting systems was disorganized and unscientific; though figures such as
Maurice Duverger and Duncan Black had important insights into the incentives
of plurality on parties and voters, they could offer little guidance as to
how to improve the situation. Arrow offered the first paradigm for the
field. The Arrovian paradigm is essentially preferential, and it tends to
lead toward Condorcet systems as being "best".
Post by Jameson Quinn
From its very beginning, Arrow's own theorem marked sharp limits to how far
you could go within his paradigm. Nonetheless, as Kuhn quotes from Bacon,
"error leads to truth more quickly than confusion"; that is, even a flawed
paradigm is immensely more productive than prescientific disorganization.
For instance, the important Gibbard-Satterthwaite theorem on strategy
followed close on the heels of Arrow's result.



Since Arrow, there have been other paradigms advanced. Around 1980, Steven
Brams suggested Approval Voting, a simple idea which prior to that had been
used but never theorized. This was clearly a step out of the Arrovian
paradigm, but it didn't quite yet offer an alternative basis for further
research and refinement. Donald Saari then reacted against approval by
advancing a paradigm based on ordinal ballots and mathematical symmetry (and
thus, Borda voting); in my opinion, his willful ignorance of strategic
issues makes his way of thinking ultimately counterproductive, though some
of the tools he created are useful.



So the first person to offer a truly fertile alternative to the Arrovian
paradigm was, in my opinion, Warren Smith (active on this list), with his
1999 paper on Range Voting. This system, now mostly called Score Voting,
goes beyond approval to allow fractional ratings. The division between
Arrovian, preferential systems, and Score-like systems has been expressed
using multiple terms: ranked versus rated (with rated systems sometimes
further subdivided into rated or graded); ordinal versus cardinal;
preferential versus ???; and my own favorite terms, comparative versus
evaluative.



Since Smith, there has also been work in yet another paradigm, that of
delegation. The DemoEx party in Sweden, the study of Asset voting, liquid
democracy, delegable proxy, delegated yes-no (DYN), the revival of interest
in Dodgson's 19th-century proposal for delegated proportional
representation, and most recently my own proposal Simple
Optionally-delegated Approval (SODA) all lie in this line of inquiry.



Still, as always, there are some who continue to mine the vein of the old
Arrovian paradigm, and it can't be said that that vein is entirely played
out. The new paradigms also remain much less well-established academically;
for instance, Smith's seminal paper has never been published in a
peer-reviewed journal.



....



So all of that history is a backdrop for the debate over how to apply the
definitions of such criteria as Majority and Mutual Majority to evaluative
systems. Your definition of Majority uses the word "preferred", which
inevitably biases it towards ranked thinking. An advocate for evaluative
systems, like myself, would argue that it would be better to say "voted as
favorably as possible". This distinction makes no difference at all for a
comparative system - a candidate who is preferred over all others is, by
definition, at the very top of any purely comparative ballot - but it allows
a level playing field on which evaluative systems can aspire to pass this
criterion as well. Of course, partisans of the comparative Arrovian paradigm
argue back with what seem to me to be unproductive semantic arguments: the
criteria were originally defined in an earlier era, with reference to
comparative systems, so any extension of them to cover evaluative ones is
argued as illegitimate.



Thoughts: I might be missing something here, but this seems like a
no-brainer. If over 50% of the voters want someone, they should get him, any
other approach would seem to create minority rule? I guess a challenge to
this criteria might be the following: using Range Voting,



(Note: these days the term Score Voting is preferred.)



A gets a 90 range vote from 60 out of 100 voters, while B gets an 80 from 80
out of 100 voters. A's net is 5400, but B's net is 6400, so B would win
(everyone else got less). Does this fail the Majority Criterion, because A
got a higher vote from over half, or does it fulfill Majority because B's
net was greater than A's net??



Your example uses the ranked definition of the majority criterion. In the
rated definition I'd favor, neither group of voters is rating their
candidate at the top rating, so the majority criterion simply does not
apply. But simply change the the rating of A proponents from 90 to 100, and
the rated definition applies, so you've shown that Score voting doesn't pass
majority under any definition. A score proponent would argue that a win by B
would be the best result in this situation, because it would (probably)
maximize total social utility; the large extra utility for the minority who
prefer B is more than the small loss of utility for the majority who prefer
A.





Name: Participation

Description: If a ballot is added which prefers A to B, the addition of the
ballot must not change the winner from A to B

Thoughts: This seems to make sense. If we do not require this, then we
permit voting systems where trying to vote sincerely harms your interests.
Also, any voting system that would fail Participation would be I think
fragile and react in not always predictable ways - like IRV. SO this seems
to me to be a solid requirement, that I can't imagine a system that failed
this Criterion to have some other benefit so wonderful to make failing
Participation worth overlooking - I cannot imagine it.



You have fairly described the participation criterion. I would ask you to
consider that this criterion focuses only on the direction of preference,
not its strength; and so it is inevitably biased towards preferential
systems, and dooms you to live within the limits set by Arrow's theorem. My
two favorite systems - SODA voting and the as-yet-unnamed version of Bucklin
- both fail this criterion, though I would argue they do so in relatively
rare and minor ways, and both satisfy some weakened version of the
criterion.





Name: Independence of Irrelevant Alternatives (IIA)

Description: Adding a new candidate B to an election that previously A would
have won must not cause anyone apart from A or B to win. That is, If A
would have won before B was added to the ballot, C must not win now.

Thoughts: This also seems fairly non-controversial. This I think is the
repudiation of the spoiler effect - that just because Nader enters the race
shouldn't disadvantage the candidate that would have won before that
happened. This would seem (to me) to also be a good Criterion to hold to in
order to encourage more than just two Candidates/Parties always dominating
the scene. I wonder what the downside would be to strongly embracing this
criteria?



IIA, on the other hand, strongly favors evaluative systems, because in
comparative systems the entry of a new candidate can inevitably change the
absolute ranking levels of existing candidates. I think that IIA is
certainly a nice thing to pass, but I'd hesitate to make it a sine qua non.



Question: It seems to me that another criterion I have heard of -
Independence of Clones(IoC) - is a subset of IIA, that if a system satisfies
IIA, it would have to satisfy the Independence of Clones criterion as well -
is that correct? If not, what system what satisfy IoC but *not* satisfy IIA?



Not quite. A system which satisfied IoC could, in theory, shift from clone
X1 to X2 when another candidate (either an X3 or a Y3) entered the race,
which would violate IIA. And a system which satisfied IIA could, in
principle, shift from clone X1 to a newly-entering clone Y2, even though a
clone Y1 had already been in the race. I'm not offhand aware of which
systems would fall into these corners of the Venn diagram, but you are
mostly right: the large majority of systems which pass IoC also pass IIA.



Question: it seems like the two above criteria - Participation and IIA -
would be related. Is it possible to fail one and not the other? Or does
either wind up mandate the other - for example, a system with IIA must also
fulfill Participation, or vice versa?



So let me stop there for now - I know there are other Criteria, but let me
pause so you guys can tell me what I am getting right and what I am getting
wrong.



Looking forward to your further posts. I encourage you to look next at some
strategic criteria: favorite betrayal, later-no-harm, and later-no-help. I
have strong opinions about which of those are important or not, but I'll let
you take your own look first.



Cheers,

Jameson



Thanks.



-Benn Grant

eFix Computer Consulting

<mailto:***@4efix.com> ***@4efix.com

603.283.6601


----
Election-Methods mailing list - see http://electorama.com/em for list info
Jameson Quinn
2013-06-17 02:35:31 UTC
Permalink
Re: Majority Criteria:****
** **
To be honest, I am worried that some (or all) of your history lesson
regarding Arrow might not have landed as well as it should in my brain.
Sorry. Sometimes I tend to try to say things too succinctly, and end up
leaving my meaning a bit locked up in jargon or terminology. If you have
any specific questions about the "history lesson" I'd be happy to expand.
I can say that one of the things I may need help on is the wording of the
criteria, so if “preferred” is not the right word, then we should use
something else.
For a rated majority criterion: "top-rated". For a rated mutual majority
criterion: "rated above a given threshold".
****
** **
However, I **think** the base idea is the idea that if over 50% of a
group want a candidate to win, they should get that candidate. What is
more murky to me – and perhaps more than me – is how you decide whether or
not that is being violated in systems that are more complex.
The point is that if I can use any score from 0-100, and yet the majority
gives candidate X only (say) 20, or even 99; even if they give all other
candidates even lower scores, the majority criterion shouldn't apply.

For Score Voting, it doesn't matter, because as you showed, score voting
doesn't satisfy the majority criterion anyway. But for rated Bucklin, it
could matter.
****
** **
I guess I would say at a minimum, that if one is using Range Voting (which
I think you are saying is called Score Voting by the list);
Right. Both "Score" and "Range" are understood, but these days, most prefer
"Score".

freely assign a score of 0 to the maximum amount to each candidate (say
100), the candidate with the greatest aggregate score wins) let me see how
this might fail. Let’s say out of 1000 people 550 give candidate A scores
of “100”. Then let’s say that 700 people give candidate B scores of “80”
each. Let’s also say that everyone else falls short of either of those
totals. A gets 55,000 total, B gets 56,000. B wins.
Right.
****
** **
On the one hand, one could say in one sense this violates Majority, but in
another sense one could perhaps with even more justification claim that B
actually has the larger majority. Or maybe to put another way, Majority
criteria only applies to voters when the system is one person, 1 vote –
others perhaps Majority criteria applies to **votes**, not voters.****
** **
In other words, maybe Majority criteria should be worded thusly: *If one
candidate is preferred by an absolute majority of *votes*, then that
candidate must win.*
That would be stretching the criterion to the point of meaninglessness. The
majority criterion speaks of voters, and Range doesn't pass, but Bucklin
systems do.

The more controversial case for this criterion is approval. Some try to
define the criterion so that an internal preference which doesn't fit on
the ballot is enough to constitute a "majority"; others prefer to define it
so that a "majority" only means anything in terms of the ballots
themselves. I tend to side with the latter as a matter of definition, but I
certainly understand that as a practical matter approval's passing of the
majority criterion leaves much to be desired.
**
** **
In which case it (I think) becomes even more obvious and pointless as a
criteria (as any system that gave the victory to people who get less votes,
however we are counting and measuring votes, would make no sense, I think.)
****
** **
Post by Jameson Quinn
Name: Participation****
Description: If a ballot is added which prefers A to B, the addition of
the ballot must not change the winner from A to B****
Post by Jameson Quinn
Thoughts: This seems to make sense. If we do not require this, then we
permit voting systems where trying to vote sincerely****
Post by Jameson Quinn
harms your interests. Also, any voting system that would fail
Participation would be I think fragile and react in not always ****
Post by Jameson Quinn
predictable ways – like IRV. SO this seems to me to be a solid
requirement, that I can’t imagine a system that failed this ****
Post by Jameson Quinn
Criterion to have some other benefit so wonderful to make failing
Participation worth overlooking – I cannot imagine it.****
** **
Post by Jameson Quinn
You have fairly described the participation criterion. I would ask you to
consider that this criterion focuses only on the ****
Post by Jameson Quinn
direction of preference, not its strength; and so it is inevitably biased
towards preferential systems, and dooms you to live ****
Post by Jameson Quinn
within the limits set by Arrow's theorem. My two favorite systems — SODA
voting and the as-yet-unnamed version of ****
Post by Jameson Quinn
Bucklin — both fail this criterion, though I would argue they do so in
relatively rare and minor ways, and both satisfy some ****
Post by Jameson Quinn
weakened version of the criterion.****
** **
I don’t understand how a bias exists here. In every case I can currently
imagine, if an election as it stands has A winning, and one more ballot is
added which still prefers A to B, why should that ever cause the winner to
change to B?****
** **
Range/Score Voting: If A is winning, and the following ballot was added
(A:90, B:89) A would still be winning. If IRV is being used and the
following ballot is added (D first place, A second place, B third place) we
wouldn’t want B to suddenly be beating A. (Although in IRV I guess it could
happen, but the point is that we wouldn’t want it to, right?)****
** **
This seems to be a serious issue. Whatever the voting method, if A is
currently winning, and one more ballot gets added that happens to favor A
with relation to B, how could it EVER be a good thing if B somehow becomes
the winner through the addition of that ballot?****
** **
I don’t understand what bias has to do with the answer to that question?**
**
** **
Also, how could Bucklin (as I understand it) **ever** fail this one?
Because a ballot added that favors A to B under Bucklin would at minimum
increase A by the same amount as B, possibly more, but would **never**
increase B more than A, else the ballot could not be said to prefer A over
B, right?
OK, that's several questions.

When would participation failure ever be a good thing? It wouldn't. But in
voting theory, tradeoffs are common. A system which had other desirable
features could fail a reasonable-sounding criterion, and if that failure is
minor and/or rare enough, that could still be a good system. I'd argue that
that's the case for Bucklin systems and the participation criterion. Though
there are certainly many people here who would argue with me on that
specific point, the fact is that choosing any system involves making
tradeoffs.

So, how does Bucklin fail participation? Imagine you had the following
votes, giving candidates X and Y grades A-F

49: X:A Y:D
50: X:F Y:D

The bloc of 50 voters is a majority, so they set the median. Or in Bucklin
terms, Y reaches a majority at grade D, while X doesn't until grade F, so Y
wins.

Now add 2 votes with X:C Y:B. Now, X reaches a majority at grade B, while Y
still doesn't until grade D. So now X wins, even though those votes favored
the prior winner Y.

I find this specific example implausible for multiple reasons, and think
that actual cases of participation failure would be very rare. For
instance, those last two voters could have voted X:F Y:B, and honestly
expressed their preference without changing the result.

****
** **
Post by Jameson Quinn
IIA, on the other hand, strongly favors evaluative systems, because in
comparative systems the entry of a new candidate ****
Post by Jameson Quinn
can inevitably change the absolute ranking levels of existing
candidates. I think that IIA is certainly a nice thing to pass, \****
Post by Jameson Quinn
but I'd hesitate to make it a sine qua non.****
** **
Independence of Irrelevant Alternative (IIA): Adding a new candidate B to
an election that previously A would have won must not cause anyone apart
from A or B to win. That is, if A would have won before B was added to the
ballot, C must not win now.****
** **
Again, I seem to be missing something here. If you are running an
election with whatever method, and A would win, but then B enters the race,
I can get A still winning. I can get B leaping ahead somehow and winning.
What I cannot understand is how a candidate that A was beating before B’s
entry, somehow A now loses to. At least I cannot understand how any system
that fails this criteria could still be worth considering – how the outcome
of A beating C **until** B enters the race, after which C wins, is
desirable. Is there some example that explain how this turn of events could
be somehow fair or sensible?
Again, it's a matter of tradeoffs. The systems I favor happen to meet IIA,
but some people here think the Condorcet criterion, which is incompatible
with IIA, is more important than it.
****
** **
Independence of Clones: since you are saying that IoC is not equivalent
with IIA, I will take up IoC independently along the way in a later set of
criteria.****
** **
I still am curious about this question:****
*Question*: it seems like the two above criteria – Participation and IIA
– would be related. Is it possible to fail one and not the other? Or does
either wind up mandating the other – for example, a system with IIA must
also fulfill Participation, or vice versa?
They are independent criteria.
****
Thanks for your time and help – and please, anyone who wants to chime in,
please do so, this is not just a conversation between myself and Jameson,
but between me and the community her.****
** **
Thanks! J****
** **
-Benn Grant****
eFix Computer Consulting****
603.283.6601****
** **
*Sent:* Sunday, June 16, 2013 4:44 PM
*To:* Benjamin Grant
*Subject:* Re: [EM] Voting Criteria 101, Four Criteria****
** **
** **
...I would like to explain what I understand about some of these voting
criteria, a few at a time...****
** **
Thanks for doing this, and again, welcome. ****
** **
*Name*: *Plurality*****
*Description*: If A gets more “first preference” ballots than B, A must
not lose to B.****
*Thoughts*: If I understand this correctly, this is not a critical
criteria to my way of thinking. Consider an election with 10 candidates. A
gets 13% of the first place votes, more than any other single candidate.
And yet B gets 8% of the first place votes, and 46% of the second place
votes. It seems obvious to me that B “ought” to win. And yet, in this
circumstance, this violates the above Plurality Criterion. Therefor is
seems to be that the Plurality Criterion is not useful, to my way of
thinking.****
** **
I think that most here would agree with what you've said.****
****
****
*Name: Majority*****
*Description*: If one candidate is preferred by an absolute majority of
voters, then that candidate must win.****
** **
Presumably, by "preferred", you mean "preferred over all others". This
definition is actually a bit controversial. I'll explain, but I have to go
back a bit. Note that all that follows is my personal opinion; it's far too
opinionated to pass muster at Wikipedia, and though I suspect that some
here would agree with most of it, I'm also sure that others will chime in
to debate me on some points.****
** **
The modern science of voting theory begins with Kenneth Arrow in the
1950s. I happen to be reading Kuhn (*The Structure of Scientific
Revolutions*) at the moment, so I'll use his terms. Before Arrow, the
study of single-winner voting systems was disorganized and unscientific;
though figures such as Maurice Duverger and Duncan Black had important
insights into the incentives of plurality on parties and voters, they could
offer little guidance as to how to improve the situation. Arrow offered the
first paradigm for the field. The Arrovian paradigm is essentially
preferential, and it tends to lead toward Condorcet systems as being
"best". ****
** **
From its very beginning, Arrow's own theorem marked sharp limits to how
far you could go within his paradigm. Nonetheless, as Kuhn quotes from
Bacon, "error leads to truth more quickly than confusion"; that is, even a
flawed paradigm is immensely more productive than prescientific
disorganization. For instance, the important Gibbard-Satterthwaite theorem
on strategy followed close on the heels of Arrow's result.****
** **
Since Arrow, there have been other paradigms advanced. Around 1980, Steven
Brams suggested Approval Voting, a simple idea which prior to that had been
used but never theorized. This was clearly a step out of the Arrovian
paradigm, but it didn't quite yet offer an alternative basis for further
research and refinement. Donald Saari then reacted against approval by
advancing a paradigm based on ordinal ballots and mathematical symmetry
(and thus, Borda voting); in my opinion, his willful ignorance of strategic
issues makes his way of thinking ultimately counterproductive, though some
of the tools he created are useful.****
** **
So the first person to offer a truly fertile alternative to the Arrovian
paradigm was, in my opinion, Warren Smith (active on this list), with his
1999 paper on Range Voting. This system, now mostly called Score Voting,
goes beyond approval to allow fractional ratings. The division between
Arrovian, preferential systems, and Score-like systems has been expressed
using multiple terms: ranked versus rated (with rated systems sometimes
further subdivided into rated or graded); ordinal versus cardinal;
preferential versus ???; and my own favorite terms, comparative versus
evaluative.****
** **
Since Smith, there has also been work in yet another paradigm, that of
delegation. The DemoEx party in Sweden, the study of Asset voting, liquid
democracy, delegable proxy, delegated yes-no (DYN), the revival of interest
in Dodgson's 19th-century proposal for delegated proportional
representation, and most recently my own proposal Simple
Optionally-delegated Approval (SODA) all lie in this line of inquiry.****
** **
Still, as always, there are some who continue to mine the vein of the old
Arrovian paradigm, and it can't be said that that vein is entirely played
out. The new paradigms also remain much less well-established academically;
for instance, Smith's seminal paper has never been published in a
peer-reviewed journal.****
** **
....****
** **
So all of that history is a backdrop for the debate over how to apply the
definitions of such criteria as Majority and Mutual Majority to evaluative
systems. Your definition of Majority uses the word "preferred", which
inevitably biases it towards ranked thinking. An advocate for evaluative
systems, like myself, would argue that it would be better to say "voted as
favorably as possible". This distinction makes no difference at all for a
comparative system — a candidate who is preferred over all others is, by
definition, at the very top of any purely comparative ballot — but it
allows a level playing field on which evaluative systems can aspire to pass
this criterion as well. Of course, partisans of the comparative Arrovian
paradigm argue back with what seem to me to be unproductive semantic
arguments: the criteria were originally defined in an earlier era, with
reference to comparative systems, so any extension of them to cover
evaluative ones is argued as illegitimate.****
****
*Thoughts*: I might be missing something here, but this seems like a
no-brainer. If over 50% of the voters want someone, they should get him,
any other approach would seem to create minority rule? I guess a challenge
to this criteria might be the following: using Range Voting,****
** **
(Note: these days the term Score Voting is preferred.)****
****
A gets a 90 range vote from 60 out of 100 voters, while B gets an 80 from
80 out of 100 voters. A’s net is 5400, but B’s net is 6400, so B would win
(everyone else got less). Does this fail the Majority Criterion, because A
got a higher vote from over half, or does it fulfill Majority because B’s
net was greater than A’s net??****
** **
Your example uses the ranked definition of the majority criterion. In the
rated definition I'd favor, neither group of voters is rating their
candidate at the top rating, so the majority criterion simply does not
apply. But simply change the the rating of A proponents from 90 to 100, and
the rated definition applies, so you've shown that Score voting doesn't
pass majority under any definition. A score proponent would argue that a
win by B would be the best result in this situation, because it would
(probably) maximize total social utility; the large extra utility for the
minority who prefer B is more than the small loss of utility for the
majority who prefer A.****
** **
****
*Name: Participation*****
*Description*: If a ballot is added which prefers A to B, the addition of
the ballot must not change the winner from A to B****
*Thoughts*: This seems to make sense. If we do not require this, then we
permit voting systems where trying to vote sincerely harms your interests.
Also, any voting system that would fail Participation would be I think
fragile and react in not always predictable ways – like IRV. SO this seems
to me to be a solid requirement, that I can’t imagine a system that failed
this Criterion to have some other benefit so wonderful to make failing
Participation worth overlooking – I cannot imagine it.****
** **
You have fairly described the participation criterion. I would ask you to
consider that this criterion focuses only on the direction of preference,
not its strength; and so it is inevitably biased towards preferential
systems, and dooms you to live within the limits set by Arrow's theorem. My
two favorite systems — SODA voting and the as-yet-unnamed version of
Bucklin — both fail this criterion, though I would argue they do so in
relatively rare and minor ways, and both satisfy some weakened version of
the criterion.****
****
****
*Name: Independence of Irrelevant Alternatives (IIA)*****
*Description*: Adding a new candidate B to an election that previously A
would have won must not cause anyone apart from A or B to win. That is, If
A would have won before B was added to the ballot, C must not win now.****
*Thoughts*: This also seems fairly non-controversial. This I think is
the repudiation of the spoiler effect – that just because Nader enters the
race shouldn’t disadvantage the candidate that would have won before that
happened. This would seem (to me) to also be a good Criterion to hold to
in order to encourage more than just two Candidates/Parties always
dominating the scene. I wonder what the downside would be to strongly
embracing this criteria?****
** **
IIA, on the other hand, strongly favors evaluative systems, because in
comparative systems the entry of a new candidate can inevitably change the
absolute ranking levels of existing candidates. I think that IIA is
certainly a nice thing to pass, but I'd hesitate to make it a sine qua non.
****
****
*Question*: It seems to me that another criterion I have heard of –
Independence of Clones(IoC) – is a subset of IIA, that if a system
satisfies IIA, it would have to satisfy the Independence of Clones
criterion as well – is that correct? If not, what system what satisfy IoC
but **not** satisfy IIA?****
** **
Not quite. A system which satisfied IoC could, in theory, shift from clone
X1 to X2 when another candidate (either an X3 or a Y3) entered the race,
which would violate IIA. And a system which satisfied IIA could, in
principle, shift from clone X1 to a newly-entering clone Y2, even though a
clone Y1 had already been in the race. I'm not offhand aware of which
systems would fall into these corners of the Venn diagram, but you are
mostly right: the large majority of systems which pass IoC also pass IIA.*
***
****
*Question*: it seems like the two above criteria – Participation and IIA
– would be related. Is it possible to fail one and not the other? Or does
either wind up mandate the other – for example, a system with IIA must also
fulfill Participation, or vice versa?****
****
So let me stop there for now – I know there are other Criteria, but let me
pause so you guys can tell me what I am getting right and what I am getting
wrong.****
** **
Looking forward to your further posts. I encourage you to look next at
some strategic criteria: favorite betrayal, later-no-harm, and
later-no-help. I have strong opinions about which of those are important or
not, but I'll let you take your own look first.****
** **
Cheers,****
Jameson ****
****
Thanks.****
****
-Benn Grant****
eFix Computer Consulting****
603.283.6601****
----
Election-Methods mailing list - see http://electorama.com/em for list info
****
** **
Benjamin Grant
2013-06-17 16:07:34 UTC
Permalink
OK, now on to the questions and responses on the other Criteria:





From: Jameson Quinn [mailto:***@gmail.com]
Sent: Sunday, June 16, 2013 10:36 PM
Subject: Re: [EM] Voting Criteria 101, Four Criteria

In which case it (I think) becomes even more obvious and pointless as a
criteria (as any system that gave the victory to people who get less votes,
however we are counting and measuring votes, would make no sense, I think.)
Post by Jameson Quinn
Post by Benjamin Grant
Name: Participation
Description: If a ballot is added which prefers A to B, the addition of
the ballot must not change the winner from A to B
Post by Jameson Quinn
Post by Benjamin Grant
Thoughts: This seems to make sense. If we do not require this, then we
permit voting systems where trying to vote sincerely
Post by Jameson Quinn
Post by Benjamin Grant
harms your interests. Also, any voting system that would fail
Participation would be I think fragile and react in not always
Post by Jameson Quinn
Post by Benjamin Grant
predictable ways - like IRV. SO this seems to me to be a solid
requirement, that I can't imagine a system that failed this
Post by Jameson Quinn
Post by Benjamin Grant
Criterion to have some other benefit so wonderful to make failing
Participation worth overlooking - I cannot imagine it.
Post by Jameson Quinn
You have fairly described the participation criterion. I would ask you to
consider that this criterion focuses only on the
Post by Jameson Quinn
direction of preference, not its strength; and so it is inevitably biased
towards preferential systems, and dooms you to live
Post by Jameson Quinn
within the limits set by Arrow's theorem. My two favorite systems - SODA
voting and the as-yet-unnamed version of
Post by Jameson Quinn
Bucklin - both fail this criterion, though I would argue they do so in
relatively rare and minor ways, and both satisfy some
Post by Jameson Quinn
weakened version of the criterion.
I don't understand how a bias exists here. In every case I can currently
imagine, if an election as it stands has A winning, and one more ballot is
added which still prefers A to B, why should that ever cause the winner to
change to B?

Range/Score Voting: If A is winning, and the following ballot was added
(A:90, B:89) A would still be winning. If IRV is being used and the
following ballot is added (D first place, A second place, B third place) we
wouldn't want B to suddenly be beating A. (Although in IRV I guess it could
happen, but the point is that we wouldn't want it to, right?)

This seems to be a serious issue. Whatever the voting method, if A is
currently winning, and one more ballot gets added that happens to favor A
with relation to B, how could it EVER be a good thing if B somehow becomes
the winner through the addition of that ballot?

I don't understand what bias has to do with the answer to that question?

Also, how could Bucklin (as I understand it) *ever* fail this one? Because a
ballot added that favors A to B under Bucklin would at minimum increase A by
the same amount as B, possibly more, but would *never* increase B more than
A, else the ballot could not be said to prefer A over B, right?



OK, that's several questions.



When would participation failure ever be a good thing? It wouldn't. But in
voting theory, tradeoffs are common. A system which had other desirable
features could fail a reasonable-sounding criterion, and if that failure is
minor and/or rare enough, that could still be a good system. I'd argue that
that's the case for Bucklin systems and the participation criterion. Though
there are certainly many people here who would argue with me on that
specific point, the fact is that choosing any system involves making
tradeoffs.



So, how does Bucklin fail participation? Imagine you had the following
votes, giving candidates X and Y grades A-F



49: X:A Y:D

50: X:F Y:D



The bloc of 50 voters is a majority, so they set the median. Or in Bucklin
terms, Y reaches a majority at grade D, while X doesn't until grade F, so Y
wins.



Now add 2 votes with X:C Y:B. Now, X reaches a majority at grade B, while Y
still doesn't until grade D. So now X wins, even though those votes favored
the prior winner Y.



I find this specific example implausible for multiple reasons, and think
that actual cases of participation failure would be very rare. For instance,
those last two voters could have voted X:F Y:B, and honestly expressed their
preference without changing the result.



OK, first of all, my brain does not seem to be able to handle letters on
both sides of the colon (":"), so with your permission, let me alter the
typography of your example, hopefully functionally changing nothing:



49: X:1st Y:4th

50: X:5th Y:4th



So if I understand this right, under Bucklin, we look at all 1st place votes
(we need at least 50), and see if we have over half - we don't, so now we
look at all 2nd, still no, all 3rd, still no, and only when we consider 4th
place do we finally have enough votes for candidate Y to have enough to win.



Now we add two votes:



2: X:3rd Y:2nd



Now we repeat the process, not enough 1st place votes (we need at least 51),
not enough 2nd place votes, and adding in 3rd place we now have 51,
precisely what we need for X to win.



OK I think I see what you mean. That does show that with this system,
adding in more ballots, even if those ballots prefer Y to X, can still
change the outcome that would have been Y to X. I don't like that at all.



It's moments like these that make me want to give up on even trying to
pursue fair voting systems. Grrr..



I will think about this more, I really hate the idea that even theoretically
it might be possible to add a ballot that prefers a candidate, and have that
hurt the candidate. A lot.



Also, as much as possible, for the sake of my brain, if you can avoid using
letter grades in these examples, it will help me. Or I can simply try to
translate like I did above to the best of my ability.
Post by Jameson Quinn
Post by Benjamin Grant
IIA, on the other hand, strongly favors evaluative systems, because in
comparative systems the entry of a new candidate
Post by Jameson Quinn
Post by Benjamin Grant
can inevitably change the absolute ranking levels of existing candidates.
I think that IIA is certainly a nice thing to pass, \
Post by Jameson Quinn
Post by Benjamin Grant
but I'd hesitate to make it a sine qua non.
Independence of Irrelevant Alternative (IIA): Adding a new candidate B to an
election that previously A would have won must not cause anyone apart from A
or B to win. That is, if A would have won before B was added to the ballot,
C must not win now.

Again, I seem to be missing something here. If you are running an election
with whatever method, and A would win, but then B enters the race, I can get
A still winning. I can get B leaping ahead somehow and winning. What I
cannot understand is how a candidate that A was beating before B's entry,
somehow A now loses to. At least I cannot understand how any system that
fails this criteria could still be worth considering - how the outcome of A
beating C *until* B enters the race, after which C wins, is desirable. Is
there some example that explain how this turn of events could be somehow
fair or sensible?

Again, it's a matter of tradeoffs. The systems I favor happen to meet IIA,
but some people here think the Condorcet criterion, which is incompatible
with IIA, is more important than it.



Is it a well-established fact that Condorcet is incompatible with IIA? That
you cannot have both?



Independence of Clones: since you are saying that IoC is not equivalent with
IIA, I will take up IoC independently along the way in a later set of
criteria.

I still am curious about this question:

Question: it seems like the two above criteria - Participation and IIA -
would be related. Is it possible to fail one and not the other? Or does
either wind up mandating the other - for example, a system with IIA must
also fulfill Participation, or vice versa?



They are independent criteria.



OK, then I will take up IoC separately and later.



-Benn Grant

eFix Computer Consulting

<mailto:***@4efix.com> ***@4efix.com

603.283.6601
Kristofer Munsterhjelm
2013-06-17 16:09:02 UTC
Permalink
Post by Benjamin Grant
With your kind indulgence, I would like some assistance in understanding
and hopefully mastering the various voting criteria, so that I can more
intelligently and accurately understanding the strengths and weaknesses
of different voting systems.
So, if it’s alright, I would like to explain what I understand about
some of these voting criteria, a few at a time, perhaps, and perhaps the
group would be willing to “check my math” as it were and see if I
actually understand these, one by one?
No problem :-)
Post by Benjamin Grant
*Name*: *_Plurality_*
*Description*: If A gets more “first preference” ballots than B, A must
not lose to B.
Be careful not to mistake Plurality, the criterion, from Plurality the
method. Plurality, the criterion, says: "If there are two candidates X
and Y so that X has more first place votes than Y has any place votes,
then Y shouldn't win".

The Plurality criterion is only relevant when the voters may truncate
their ballots. In it, there's an assumption that listed candidates are
ranked higher than non-listed ones - a sort of Approval assumption, if
you will.

To show a concrete example: say a voter votes A first, B second, and
leaves C off the ballot. Furthermore say nobody actually ranks C. Then C
shouldn't win, because A has more first-place votes than C has any-place
votes.
Post by Benjamin Grant
*Name: _Majority_*
*Description*: If one candidate is preferred by an absolute majority of
voters, then that candidate must win.
That's right. More specifically, if a candidate has a majority of the
first place votes, he should win. There's also a setwise version (mutual
majority) where the criterion goes "if a group of candidates is listed
ahead of candidates not in that group, on a majority of the ballots,
then a candidate in that group should win".
Post by Benjamin Grant
*Thoughts*: I might be missing something here, but this seems like a
no-brainer. If over 50% of the voters want someone, they should get him,
any other approach would seem to create minority rule? I guess a
challenge to this criteria might be the following: using Range Voting, A
gets a 90 range vote from 60 out of 100 voters, while B gets an 80 from
80 out of 100 voters. A’s net is 5400, but B’s net is 6400, so B would
win (everyone else got less). Does this fail the Majority Criterion,
because A got a higher vote from over half, or does it fulfill Majority
because B’s net was greater than A’s net??
There are usually two arguments against the Majority criterion from
those that like cardinal methods.

First, there's the "pizza example": say three people are deciding on
what piza to get. Two of them prefer pepperoni to everything else, but
the last person absolutely can't have pepperoni. Then, the argument
goes, it would be unreasonable and unflexible to pick the pepperoni
pizza just because a majority wanted it.

Second, there's the redistribution argument. Consider a public election
where a candidate wants to confiscate everything a certain minority owns
and then distribute the loot to the majority. If the electorate is
simple enough, a majority might vote for that candidate, but the choice
would not be a good one.

Briefly: the argument against Majority is "tyranny of majority". But
ranked methods can't know whether any given election is a
tyranny-of-majority one, and between erring in favor of the majority and
in favor of a minority (which might not be a good minority at all), the
former's better. Condorcet's jury theorem is one way of formalizing that.

Rated methods could distinguish between tyranny-of-majority cases, were
all the voters honest, but being subject to Gibbard and Satterthwaite
just like ranked methods, they too can be gamed. There's usually a way
for a majority to force a win if they absolutely want to, too[1].
Post by Benjamin Grant
*Name: _Participation_*
*Description*: If a ballot is added which prefers A to B, the addition
of the ballot must not change the winner from A to B
*Thoughts*: This seems to make sense. If we do not require this, then
we permit voting systems where trying to vote sincerely harms your
interests. Also, any voting system that would fail Participation would
be I think fragile and react in not always predictable ways – like IRV.
SO this seems to me to be a solid requirement, that I can’t imagine a
system that failed this Criterion to have some other benefit so
wonderful to make failing Participation worth overlooking – I cannot
imagine it.
Welcome to the unintuitive world of voting methods :-) Arrow's theorem
says you can't have unanimity (if everybody agrees that A>B, B does not
win), IIA (as you mention below) and non-dictatorship. Since one can't
give up the latter two and have anything like a good ranked voting
method, that means every method must fail IIA.

The trade-off with Participation is similar. It is impossible, for
instance, to have a method that passes both Participation and Condorcet,
so one has to choose which is more important. Similarly, it's impossible
to have a method that passes Later-no-harm, later-no-help, mutual
majority and monotonicity. (IRV passes them all except monotonicity; DAC
and DSC pass them all except one of the Later-no criteria; and Plurality
pass them all except mutual majority.)
Post by Benjamin Grant
*Name: _Independence of Irrelevant Alternatives (IIA)_*
*Description*: Adding a new candidate B to an election that previously A
would have won must not cause anyone apart from A or B to win. That is,
If A would have won before B was added to the ballot, C must not win now.
*Thoughts*: This also seems fairly non-controversial. This I think is
the repudiation of the spoiler effect – that just because Nader enters
the race shouldn’t disadvantage the candidate that would have won before
that happened. This would seem (to me) to also be a good Criterion to
hold to in order to encourage more than just two Candidates/Parties
always dominating the scene. I wonder what the downside would be to
strongly embracing this criteria?
From the ranked-ballot side of things, one usually says "okay, so IIA
is impossible, but how far can we get?". This leads to things like local
IIA (removing the winner or loser of an election shouldn't change the
output ranking for the other candidates), independence of clones (which
I'll get to later), and independence of Smith-dominated alternatives (if
X is not in the Smith set, removing X shouldn't make the winner change).

There's also a heuristic argument that IIA is too strong. It goes that
the introduction of additional candidates may tell you that things
aren't the same before and after the introduction of the same
candidates. See
https://en.wikipedia.org/wiki/Independence_of_irrelevant_alternatives#Criticism_of_IIA
for more information.

Also note that IIA and majority is incompatible. The same link shows why.
Post by Benjamin Grant
*Question*: It seems to me that another criterion I have heard of –
Independence of Clones(IoC) – is a subset of IIA, that if a system
satisfies IIA, it would have to satisfy the Independence of Clones
criterion as well – is that correct? If not, what system what satisfy
IoC but **not** satisfy IIA?
Methods that pass IIA also pass IoC, yes, but not all methods that pass
IoC pass IIA. Schulze and Tideman are simple examples of rules that are
cloneproof (pass IoC) yet, being deterministic ranked ballot methods
reducing to majority when there are only two candidates, must fail IIA
itself.
Post by Benjamin Grant
*Question*: it seems like the two above criteria – Participation and IIA
– would be related. Is it possible to fail one and not the other? Or
does either wind up mandate the other – for example, a system with IIA
must also fulfill Participation, or vice versa?
Trying to come up with counterexamples usually is a simple task, because
one can design an obviously outrageous system. As long as the system
provides a counterexample, it doesn't matter how unsuitable it otherwise is.

So for Participation and IIA, consider a method that works like Range as
long as there are fewer than 100 voters, but reverses the order of the
winners if there are more than 100 voters - i.e. the Range loser becomes
the new winner.

This method passes IIA since both Range and Anti-Range (as it were) does
so. Yet it obviously fails Participation. Say you're voter number 100,
and you prefer the Range winner. Then submitting your ballot will make
the Range loser win instead, so you're better off not doing so.
Post by Benjamin Grant
So let me stop there for now – I know there are other Criteria, but let
me pause so you guys can tell me what I am getting right and what I am
getting wrong.
Thanks.
-Benn Grant
[1] I'm kind of seeing a strategy-stealing argument here, which if
right, would mean a majority could force a win in any anonymous rated
system that fails Majority. But I could be wrong and I don't want to
clutter the text proper with it.

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Benjamin Grant
2013-06-17 16:36:21 UTC
Permalink
-----Original Message-----
Sent: Monday, June 17, 2013 12:09 PM
Subject: Re: [EM] Voting Criteria 101, Four Criteria
Post by Benjamin Grant
*Name*: *_Plurality_*
*Description*: If A gets more "first preference" ballots than B, A
must not lose to B.
Be careful not to mistake Plurality, the criterion, from Plurality the
method.
Plurality, the criterion, says: "If there are two candidates X and Y so
that X has
more first place votes than Y has any place votes, then Y shouldn't win".
The Plurality criterion is only relevant when the voters may truncate
their
ballots. In it, there's an assumption that listed candidates are ranked
higher
than non-listed ones - a sort of Approval assumption, if you will.
To show a concrete example: say a voter votes A first, B second, and
leaves C
off the ballot. Furthermore say nobody actually ranks C. Then C shouldn't
win, because A has more first-place votes than C has any-place votes.
OK, that makes sense.
Post by Benjamin Grant
*Name: _Majority_*
*Thoughts*: I might be missing something here, but this seems like a
no-brainer. If over 50% of the voters want someone, they should get
him, any other approach would seem to create minority rule? I guess a
challenge to this criteria might be the following: using Range Voting,
A gets a 90 range vote from 60 out of 100 voters, while B gets an 80
from
80 out of 100 voters. A's net is 5400, but B's net is 6400, so B would
win (everyone else got less). Does this fail the Majority Criterion,
because A got a higher vote from over half, or does it fulfill
Majority because B's net was greater than A's net??
There are usually two arguments against the Majority criterion from those
that like cardinal methods.
First, there's the "pizza example": say three people are deciding on what
piza
to get. Two of them prefer pepperoni to everything else, but the last
person
absolutely can't have pepperoni. Then, the argument goes, it would be
unreasonable and unflexible to pick the pepperoni pizza just because a
majority wanted it.
Second, there's the redistribution argument. Consider a public election
where a candidate wants to confiscate everything a certain minority owns
and then distribute the loot to the majority. If the electorate is simple
enough, a majority might vote for that candidate, but the choice would not
be a good one.
Briefly: the argument against Majority is "tyranny of majority". But
ranked
methods can't know whether any given election is a tyranny-of-majority
one,
and between erring in favor of the majority and in favor of a minority
(which
might not be a good minority at all), the former's better. Condorcet's
jury
theorem is one way of formalizing that.
In my (limited) experience, every instance where there has been an
allegation of tyranny of the majority, the reverse choice is something even
worse, tyranny of the minority. While ultimately certain things, like human
rights, shouldn't be a matter for voting at all, if something deserves a
vote it probably deserves to serve the greatest good for the greatest
number.

To take your pizza analogy, if the two people *only* want pepperoni, it
would be selfish of the third to expect the majority to bend to his desires.
On the other hand, if the two people are already fine with *either*
pepperoni or plain, then they will say so.

Ultimately, the only time I find when people complain about the tyranny of
the majority is when they are in a minority that doesn't want what the
majority truly does - and that's just the downside of not being a dictator.

So I guess I would say this - whenever you hear the phrase tyranny of the
majority, you can probably indentify the speaker is *usually* someone who
wants more power over the selection process than they ought to have.
Post by Benjamin Grant
*Name: _Participation_*
*Description*: If a ballot is added which prefers A to B, the addition
of the ballot must not change the winner from A to B
*Thoughts*: This seems to make sense. If we do not require this, then
we permit voting systems where trying to vote sincerely harms your
interests. Also, any voting system that would fail Participation would
be I think fragile and react in not always predictable ways - like IRV.
SO this seems to me to be a solid requirement, that I can't imagine a
system that failed this Criterion to have some other benefit so
wonderful to make failing Participation worth overlooking - I cannot
imagine it.
Welcome to the unintuitive world of voting methods :-) Arrow's theorem
says you can't have unanimity (if everybody agrees that A>B, B does not
win), IIA (as you mention below) and non-dictatorship. Since one can't
give
up the latter two and have anything like a good ranked voting method, that
means every method must fail IIA.
Wow. I am just starting to get exposed to this stuff, but it is being a
bitter pill to swallow that it is mathematically impossible to have one
voting system fulfill several desirable criteria - that these criteria might
be incompatible. Ultimately, I guess I will have to figure out which
criteria are incompatible with which, and determine among my choices which I
need and which I don't. Taking notes here.
There's also a heuristic argument that IIA is too strong. It goes that the
introduction of additional candidates may tell you that things aren't the
same
before and after the introduction of the same candidates. See
https://en.wikipedia.org/wiki/Independence_of_irrelevant_alternatives#Critic
ism_of_IIA
for more information.
Also note that IIA and majority is incompatible. The same link shows why.
I "deconstructed" Majority in another post, I wonder if this address IIA
compatibility with what I was left with?

Thanks for your thoughts, they help! :)

-Benn Grant
eFix Computer Consulting
***@4efix.com
603.283.6601


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Jameson Quinn
2013-06-17 16:38:17 UTC
Permalink
Post by Kristofer Munsterhjelm
Post by Benjamin Grant
With your kind indulgence, I would like some assistance in understanding
and hopefully mastering the various voting criteria, so that I can more
intelligently and accurately understanding the strengths and weaknesses
of different voting systems.
So, if it’s alright, I would like to explain what I understand about
some of these voting criteria, a few at a time, perhaps, and perhaps the
group would be willing to “check my math” as it were and see if I
actually understand these, one by one?
No problem :-)
*Name*: *_Plurality_*
Post by Benjamin Grant
*Description*: If A gets more “first preference” ballots than B, A must
not lose to B.
Be careful not to mistake Plurality, the criterion, from Plurality the
method. Plurality, the criterion, says: "If there are two candidates X and
Y so that X has more first place votes than Y has any place votes, then Y
shouldn't win".
The Plurality criterion is only relevant when the voters may truncate
their ballots. In it, there's an assumption that listed candidates are
ranked higher than non-listed ones - a sort of Approval assumption, if you
will.
To show a concrete example: say a voter votes A first, B second, and
leaves C off the ballot. Furthermore say nobody actually ranks C. Then C
shouldn't win, because A has more first-place votes than C has any-place
votes.
Right. Kristofer's response here is better than mine was.
Post by Kristofer Munsterhjelm
*Name: _Majority_*
Post by Benjamin Grant
*Description*: If one candidate is preferred by an absolute majority of
voters, then that candidate must win.
That's right. More specifically, if a candidate has a majority of the
first place votes, he should win. There's also a setwise version (mutual
majority) where the criterion goes "if a group of candidates is listed
ahead of candidates not in that group, on a majority of the ballots, then a
candidate in that group should win".
Kristofer gives the ranked version of Mutual Majority. The rated version
is: "If a group of candidates is listed at or above a certain rating, and
those not in the group below that rating, on a majority of ballots, then a
candidate in that group should win". This criterion, in at least one of its
versions, is a prerequisite for IoC. I prefer the rated version, but those
like Kristofer who are working within the Arrovian paradigm prefer the
ranked one.

(Note that the mere fact that the rated paradigm is newer than the Arrovian
one does not necessarily make it better. Saari's ranked-symmetry paradigm
is newer than Arrow's, and also in my opinion worse. So in this debate
between people like me and people like Kristofer, there is no short cut to
evaluating each side's arguments on their merits. I of course think I'm
right, but Kristofer is a very smart guy, and you would be unwise to ignore
his side.)
Post by Kristofer Munsterhjelm
Post by Benjamin Grant
*Thoughts*: I might be missing something here, but this seems like a
no-brainer. If over 50% of the voters want someone, they should get him,
any other approach would seem to create minority rule? I guess a
challenge to this criteria might be the following: using Range Voting, A
gets a 90 range vote from 60 out of 100 voters, while B gets an 80 from
80 out of 100 voters. A’s net is 5400, but B’s net is 6400, so B would
win (everyone else got less). Does this fail the Majority Criterion,
because A got a higher vote from over half, or does it fulfill Majority
because B’s net was greater than A’s net??
There are usually two arguments against the Majority criterion from those
that like cardinal methods.
First, there's the "pizza example": say three people are deciding on what
piza to get. Two of them prefer pepperoni to everything else, but the last
person absolutely can't have pepperoni. Then, the argument goes, it would
be unreasonable and unflexible to pick the pepperoni pizza just because a
majority wanted it.
Second, there's the redistribution argument. Consider a public election
where a candidate wants to confiscate everything a certain minority owns
and then distribute the loot to the majority. If the electorate is simple
enough, a majority might vote for that candidate, but the choice would not
be a good one.
Briefly: the argument against Majority is "tyranny of majority". But
ranked methods can't know whether any given election is a
tyranny-of-majority one, and between erring in favor of the majority and in
favor of a minority (which might not be a good minority at all), the
former's better. Condorcet's jury theorem is one way of formalizing that.
Rated methods could distinguish between tyranny-of-majority cases, were
all the voters honest, but being subject to Gibbard and Satterthwaite just
like ranked methods, they too can be gamed. There's usually a way for a
majority to force a win if they absolutely want to, too[1].
I agree 100% with what Kristofer has said here.
Post by Kristofer Munsterhjelm
*Name: _Participation_*
Post by Benjamin Grant
*Description*: If a ballot is added which prefers A to B, the addition
of the ballot must not change the winner from A to B
*Thoughts*: This seems to make sense. If we do not require this, then
we permit voting systems where trying to vote sincerely harms your
interests. Also, any voting system that would fail Participation would
be I think fragile and react in not always predictable ways – like IRV.
SO this seems to me to be a solid requirement, that I can’t imagine a
system that failed this Criterion to have some other benefit so
wonderful to make failing Participation worth overlooking – I cannot
imagine it.
Welcome to the unintuitive world of voting methods :-) Arrow's theorem
says you can't have unanimity (if everybody agrees that A>B, B does not
win), IIA (as you mention below) and non-dictatorship. Since one can't give
up the latter two and have anything like a good ranked voting method, that
means every method must fail IIA.
This is the fundamental bone of contention between ranked thinkers like
Kristofer and rated ones like me. I say that Arrow's theorem says you can't
have those things and a ranked system; and I'd far rather choose a rated
system than give up IIA. The downside of choosing a rated system is that
the problem of strategic ambiguity gets worse; for a given set of
preferences, there are many possible "honest" votes, which complicates the
analysis. Most rated voting advocates would say that this problem is
manageable if you assume voters have some knowable underlying cardinal
utilities for each candidate; and that, though that assumption is not
perfectly realistic, it is close enough for meaningful results.
Post by Kristofer Munsterhjelm
The trade-off with Participation is similar. It is impossible, for
instance, to have a method that passes both Participation and Condorcet, so
one has to choose which is more important. Similarly, it's impossible to
have a method that passes Later-no-harm, later-no-help, mutual majority and
monotonicity. (IRV passes them all except monotonicity; DAC and DSC pass
them all except one of the Later-no criteria; and Plurality pass them all
except mutual majority.)
Here I agree with Kristofer.
Post by Kristofer Munsterhjelm
*Name: _Independence of Irrelevant Alternatives (IIA)_*
Post by Benjamin Grant
*Description*: Adding a new candidate B to an election that previously A
would have won must not cause anyone apart from A or B to win. That is,
If A would have won before B was added to the ballot, C must not win now.
*Thoughts*: This also seems fairly non-controversial. This I think is
the repudiation of the spoiler effect – that just because Nader enters
the race shouldn’t disadvantage the candidate that would have won before
that happened. This would seem (to me) to also be a good Criterion to
hold to in order to encourage more than just two Candidates/Parties
always dominating the scene. I wonder what the downside would be to
strongly embracing this criteria?
From the ranked-ballot side of things, one usually says "okay, so IIA is
impossible, but how far can we get?". This leads to things like local IIA
(removing the winner or loser of an election shouldn't change the output
ranking for the other candidates), independence of clones (which I'll get
to later), and independence of Smith-dominated alternatives (if X is not in
the Smith set, removing X shouldn't make the winner change).
There's also a heuristic argument that IIA is too strong. It goes that the
introduction of additional candidates may tell you that things aren't the
same before and after the introduction of the same candidates. See
https://en.wikipedia.org/wiki/**Independence_of_irrelevant_**
alternatives#Criticism_of_IIA<https://en.wikipedia.org/wiki/Independence_of_irrelevant_alternatives#Criticism_of_IIA>for more information.
Also note that IIA and majority is incompatible. The same link shows why.
*Question*: It seems to me that another criterion I have heard of –
Post by Benjamin Grant
Independence of Clones(IoC) – is a subset of IIA, that if a system
satisfies IIA, it would have to satisfy the Independence of Clones
criterion as well – is that correct? If not, what system what satisfy
IoC but **not** satisfy IIA?
Methods that pass IIA also pass IoC, yes,
Wait... I think you're right. I thought I had a counterexample in my
earlier response, but now I realize there was a problem with it. Do you
know of a proof of this statement? Because right now it seems right to me,
but I can't obviously see how I would prove it.
Post by Kristofer Munsterhjelm
but not all methods that pass IoC pass IIA. Schulze and Tideman are simple
examples of rules that are cloneproof (pass IoC) yet, being deterministic
ranked ballot methods reducing to majority when there are only two
candidates, must fail IIA itself.
*Question*: it seems like the two above criteria – Participation and IIA
Post by Benjamin Grant
– would be related. Is it possible to fail one and not the other? Or
does either wind up mandate the other – for example, a system with IIA
must also fulfill Participation, or vice versa?
Trying to come up with counterexamples usually is a simple task, because
one can design an obviously outrageous system. As long as the system
provides a counterexample, it doesn't matter how unsuitable it otherwise is.
So for Participation and IIA, consider a method that works like Range as
long as there are fewer than 100 voters, but reverses the order of the
winners if there are more than 100 voters - i.e. the Range loser becomes
the new winner.
This method passes IIA since both Range and Anti-Range (as it were) does
so. Yet it obviously fails Participation. Say you're voter number 100, and
you prefer the Range winner. Then submitting your ballot will make the
Range loser win instead, so you're better off not doing so.
Post by Benjamin Grant
So let me stop there for now – I know there are other Criteria, but let
me pause so you guys can tell me what I am getting right and what I am
getting wrong.
Thanks.
-Benn Grant
[1] I'm kind of seeing a strategy-stealing argument here, which if right,
would mean a majority could force a win in any anonymous rated system that
fails Majority. But I could be wrong and I don't want to clutter the text
proper with it.
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