Re: [EM] Eric Maskin promotes the Black method (fsimm...@pcc.edu)

[robert bristow-johnson]

On Jun 24, 2011, at 4:40 PM, fsimm...@pcc.edu wrote:




The first time I heard the phrase "True Majority Winner" was in
the Scientific American article six or eight
years ago on Condorcet Voting. The point of the article was
that if you believe in majority rule, you
should prefer electing the CW over any other alternative. But at
the end of the article (in order to give a
definite example of a decisive Condorcet method) they proposed a
method that turned out to be
Copeland with a Borda tie breaker, i.e. just slightly different
(and almost as bad as) Black.

Note that Copeland with a Borda tie breaker is not quite as bad
as Black for the same reason that
Beatpath(covering, wv) is slightly better than Beatpath(wv).


The Scientific American article I was thinking of was actually seven  
years ago, and ironically, one of the

authors was Eric Maskin!

The title was "The Fairest Vote of All."


i coulda told you that (that's what motivated me to comment).  but you  
were able to remember much more about it than me.


--

r b-j  r...@audioimagination.com

"Imagination is more important than knowledge."





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Re: [EM] Eric Maskin promotes the Black method (fsimm...@pcc.edu)

[Warren Smith]

I already emitted various criticisms of Eric Maskin...
   http://www.rangevoting.org/MaskinArrow.html
   http://www.rangevoting.org/Maskin.html
   http://www.rangevoting.org/NewSciMcKenna.html
Maskin sometimes has favored Black's method (e.g. in a Scientific
American piece he wrote which actually refused to specify the voting
method he was "advocating" but by reading between the lines I think he
meant Black, see middle URL above); but he also has been quoted as
instead advocating Copeland's method, e.g. see the last URL above.

As far as I can tell, Maskin thinks (and/or others think) he is
incredibly wise in the ways of voting, since he got a Nobel Prize in
Economics and was a student of Arrow's.  But actually, he knows very
little about voting and the few things he has written on the topic are
(a) unimportant and (b) rife with errors and massive omissions.
Furthermore, whenever somebody actually expert on the topic tries to
correspond with him, i.e. me, he never replies.  Your mileage may
vary, but I've been highly disappointed in Maskin so far.

Range voting produces more Condorcet winners than Condorcet methods
produce (in simulations involving strategic voters).  This is a
refutation of Maskin's argument, or at least highly impactful on it
(anyhow at the very least, it needs to be discussed).  Maskin, of
course, ignores it, as he has ignored essentially every communication
from me.   I just have a hard time taking him seriously as a voting
scientist when he behaves in that fashion.

The "Nobel Prize" in Economics has caused a lot of damage (certainly
amounting to the
equivalent of killing thousands of people).

[And it actually is not a Nobel prize, although it commonly is claimed
to be.  I have a sneaking suspicion if Nobel could be reincarnated
he'd be furious they created a "Nobel Prize in Economics."]


-- 
Warren D. Smith
http://RangeVoting.org  <-- add your endorsement (by clicking
"endorse" as 1st step)
and
math.temple.edu/~wds/homepage/works.html

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[EM] Eric Maskin promotes the Black method (fsimm...@pcc.edu)

[fsimmons]

> The first time I heard the phrase "True Majority Winner" was in 
> the Scientific American article six or eight 
> years ago on Condorcet Voting. The point of the article was 
> that if you believe in majority rule, you 
> should prefer electing the CW over any other alternative. But at 
> the end of the article (in order to give a 
> definite example of a decisive Condorcet method) they proposed a 
> method that turned out to be 
> Copeland with a Borda tie breaker, i.e. just slightly different 
> (and almost as bad as) Black.
> 
> Note that Copeland with a Borda tie breaker is not quite as bad 
> as Black for the same reason that 
> Beatpath(covering, wv) is slightly better than Beatpath(wv).

The Scientific American article I was thinking of was actually seven years ago, 
and ironically, one of the 
authors was Eric Maskin!

The title was "The Fairest Vote of All."

It was in the March 2004 issue.

The authors were Partha Dasgupta and Eric Maskin.

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Re: [EM] Eric Maskin promotes the Black method

[Juho Laatu]

On 24.6.2011, at 3.47, Paul Kislanko wrote:

> Marcus wrote:
> Maskin's argumentation doesn't work because
> of the following reason: Whether an election
> method is good or bad depends on which criteria
> it satisfies. 
> 
> 
> 
> Now, if "good" and "bad" are defined by which criteria methods satisfy, it
> seems to me that having introduced "judgement" we need "judges" to define
> the "goodness" of each criterion. And if there are more than 2 "judges" to
> decide the "goodness" of more than two criteria, there is no unambiguous way
> to consolidate the opinions of the "judges."

In addition to defining how important each criterion is we must also estimate 
how much each method violates some criterion. Since we can not meet all 
criteria (e.g. being strategy free) and not all interesting criteria at the 
same time it often makes sense to violate some criteria just a little, so that 
from practical point of view the method is about as good as if it meth that 
criterion fully. One bad violation of some key criterion may thus be worse than 
violating multiple criteria just a little. The number of criteria that some 
method meets of course has no meaning, only the importance of those criteria 
has, and maybe also other factors that have no named criterion representing 
them.

> 
> I think Maskin's "arguent" is actually a really old one - if there's a CW
> nobody really has a complaint (though there are pathological cases where the
> CW is disliked by a majority of the voters...)

This expression s a bit confusing. Majority of the voters may have some other 
candidates that they prefer to the CW but there is no majority that would 
prefer one single candidate x to the CW.

> and if there's not a CW use
> Borda (or Bucklin or ...) considering only the smallest Smith Set.

There can be many opinions on if one should always pick the winner from the 
Smith Set.

> 
> Logically, all we're talking about here is how to order alternatives in
> pairwise A>B>C>A loops, right?

Well, yes but, in principle there is no need to order the candidates but just 
pick one winner, and if that loop does not contain all the candidates, then 
there is also the option to elect the winner from the other candidate.

> If we don't like Y=Borda we can start talking
> about what "Y" should be if there's a need to have a "Y". 

Yes, there are also better options. (although Borda may not be too terrible 
here if we assume that usually we have a CW and people don't care too much who 
will be elected if there is a tie (=top loop))

Juho









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Re: [EM] Eric Maskin promotes the Black method

[Kristofer Munsterhjelm]

Paul Kislanko wrote:

Marcus wrote:
Maskin's argumentation doesn't work because
of the following reason: Whether an election
method is good or bad depends on which criteria
it satisfies. 




Now, if "good" and "bad" are defined by which criteria methods satisfy, it
seems to me that having introduced "judgement" we need "judges" to define
the "goodness" of each criterion. And if there are more than 2 "judges" to
decide the "goodness" of more than two criteria, there is no unambiguous way
to consolidate the opinions of the "judges."

I think Maskin's "arguent" is actually a really old one - if there's a CW
nobody really has a complaint (though there are pathological cases where the
CW is disliked by a majority of the voters...) and if there's not a CW use
Borda (or Bucklin or ...) considering only the smallest Smith Set.


Condorcet//Borda isn't Smith, though. As I pointed out, if we like 
Condorcet, why not also like Smith; and if we like Smith, why not also 
like Landau, etc?



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Re: [EM] Eric Maskin promotes the Black method

[Paul Kislanko]

Marcus wrote:
Maskin's argumentation doesn't work because
of the following reason: Whether an election
method is good or bad depends on which criteria
it satisfies. 



Now, if "good" and "bad" are defined by which criteria methods satisfy, it
seems to me that having introduced "judgement" we need "judges" to define
the "goodness" of each criterion. And if there are more than 2 "judges" to
decide the "goodness" of more than two criteria, there is no unambiguous way
to consolidate the opinions of the "judges."

I think Maskin's "arguent" is actually a really old one - if there's a CW
nobody really has a complaint (though there are pathological cases where the
CW is disliked by a majority of the voters...) and if there's not a CW use
Borda (or Bucklin or ...) considering only the smallest Smith Set.

Logically, all we're talking about here is how to order alternatives in
pairwise A>B>C>A loops, right? If we don't like Y=Borda we can start talking
about what "Y" should be if there's a need to have a "Y". 





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[EM] Eric Maskin promotes the Black method

[fsimmons]

> From: Jameson Quinn 
> To: robert bristow-johnson 
> Cc: Markus Schulze ,
> election-meth...@electorama.com
> Subject: Re: [EM] Eric Maskin promotes the Black method
> 
> >
> >
> > and we've all been groping for a name for this primary voting 
> criteria that
> > is not this non-American, Frenchie, probably sorta pinko-
> socialist secular
> > humanist "intellectual" (did i mention *not* American?) whose 
> heresy is
> > leading us away from the One True Faith of the Single 
> Affirmative Vote. we
> > have sects in the One True Faith, some of us believe in the 
> sanctity of the
> > Two Party System: "if yer ain't fer us, you agin' us. and 
> pass da
> > ammunition, Ma."
> >
> > i don't have a better idea than "true majority rule". but 
> there must be a
> > better one than that. Warren, i remember you like "beats-all 
> winner" for
> > the CW. i wonder if the "beats-all method" is a good label.
> >
> > At one point I ran a poll to try to decide on good names for 
> Condorcetvoting (as well as for Range/Score and for MCA/ER-
> Bucklin/median-based
> systems). You can see the results here 
> .Ironically, there was a 
> Condorcet cycle on what to call Condorcet; the smith
> set was [Instant?] Round Robin Voting; Pairwise Champion Voting; and
> Beats-All Voting.

The trouoble with "beats all voting" is that it lends itself to editorial 
ridicule too easily: "Well don't that 
beat all!"

> 
> Since then, I've tried to use the term "pairwise champion" for 
> the CW,
> except occasionally when I'm writing about mathematical issues 
> to a
> highly-savvy audience. In my opinion, that terminology works 
> well. I do not,
> therefore, think that PCV is necessarily the best "brand" for 
> Condorcetsystems; I think that probably IRRV is good for that 
> (despite the fact that
> it suggests Copeland as the tiebreaker, whereas I support C//A 
> as the best
> simply-explainable tiebreaker). The similarity with IRV is a 
> good thing, to
> my mind, though I understand that some may disagree.
> 
> Note that if you google "True Majority Voting", you'll find that 
> there was a
> recent (but now-defunct??) attempt by IRV advocates to 
> appropriate this
> term. I think that "true majority" is less explanatory than 
> IRRV, PCV, or
> BAV.

The first time I heard the phrase "True Majority Winner" was in the Scientific 
American article six or eight 
years ago on Condorcet Voting.  The point of the article was that if you 
believe in majority rule, you 
should prefer electing the CW over any other alternative. But at the end of the 
article (in order to give a 
definite example of a decisive Condorcet method) they proposed a method that 
turned out to be 
Copeland with a Borda tie breaker, i.e. just slightly different (and almost as 
bad as) Black.

Note that Copeland with a Borda tie breaker is not quite as bad as Black for 
the same reason that 
Beatpath(covering, wv) is slightly better than Beatpath(wv).

Forest

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Re: [EM] Eric Maskin promotes the Black method

[Jameson Quinn]

>
>
> and we've all been groping for a name for this primary voting criteria that
> is not this non-American, Frenchie, probably sorta pinko-socialist secular
> humanist "intellectual" (did i mention *not* American?) whose heresy is
> leading us away from the One True Faith of the Single Affirmative Vote.  we
> have sects in the One True Faith, some of us believe in the sanctity of the
> Two Party System: "if yer ain't fer us, you agin' us.  and pass da
> ammunition, Ma."
>
> i don't have a better idea than "true majority rule".  but there must be a
> better one than that.  Warren, i remember you like "beats-all winner" for
> the CW.  i wonder if the "beats-all method" is a good label.
>
> At one point I ran a poll to try to decide on good names for Condorcet
voting (as well as for Range/Score and for  MCA/ER-Bucklin/median-based
systems). You can see the results here .
Ironically, there was a Condorcet cycle on what to call Condorcet; the smith
set was [Instant?] Round Robin Voting; Pairwise Champion Voting; and
Beats-All Voting.

Since then, I've tried to use the term "pairwise champion" for the CW,
except occasionally when I'm writing about mathematical issues to a
highly-savvy audience. In my opinion, that terminology works well. I do not,
therefore, think that PCV is necessarily the best "brand" for Condorcet
systems; I think that probably IRRV is good for that (despite the fact that
it suggests Copeland as the tiebreaker, whereas I support C//A as the best
simply-explainable tiebreaker). The similarity with IRV is a good thing, to
my mind, though I understand that some may disagree.

Note that if you google "True Majority Voting", you'll find that there was a
recent (but now-defunct??) attempt by IRV advocates to appropriate this
term. I think that "true majority" is less explanatory than IRRV, PCV, or
BAV.

JQ

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Re: [EM] Eric Maskin promotes the Black method

[robert bristow-johnson]

On Jun 21, 2011, at 7:56 AM, Markus Schulze wrote:


Hallo,

Eric Maskin, a Nobel laureate, is currently very
active in promoting the Black method.


i have to confess, even though i had heard of ranked-choice voting  
before and had myself thought that what would later to be learned is  
called "Condorcet compliant" was the only logical and consistent (with  
a simple majority binary vote in all binary cases) manner to decide  
it.  and i thought of the possible problem that there was no single  
candidate who wins every pair they're in, didn't know what to call it,  
and didn't even know if there were any theorems that spoke to it, and  
decided not to worry about it.


anyway, because i'm a real neophyte to this, it wasn't until sometime  
last decade that i read anything about it until i read a Scientific  
American article of his titled "The fairest vote of all" that promoted  
Condorcet, but didn't really call it that.  Maskin labeled the method  
"true majority rule" and only obliquely raised the issue that a cycle  
could happen and mentioned Condorcet in that context.  soon after i  
learned the terms from the Wikipedia articles and at about the same  
time, we voted in IRV by about 65% (which was repealed in 2010 in a  
dramatic but really stupid slugfest between the one true faith "One  
person, one vote" crowd and those who denied anything went wrong in  
the 2009 election).


anyway, especially after reviewing his bio again, i can't help by  
admire the guy and it was an article of his that first got me thinking  
analytically about the voting systems issue.  but i wonder if he was  
using terminology that was more neology, even pre-neology.  i think he  
was trying to coin a term that would end up getting attached to his  
name.


and we've all been groping for a name for this primary voting criteria  
that is not this non-American, Frenchie, probably sorta pinko- 
socialist secular humanist "intellectual" (did i mention *not*  
American?) whose heresy is leading us away from the One True Faith of  
the Single Affirmative Vote.  we have sects in the One True Faith,  
some of us believe in the sanctity of the Two Party System: "if yer  
ain't fer us, you agin' us.  and pass da ammunition, Ma."


i don't have a better idea than "true majority rule".  but there must  
be a better one than that.  Warren, i remember you like "beats-all  
winner" for the CW.  i wonder if the "beats-all method" is a good label.




The Black
method says: If there is a Condorcet winner, then
the Condorcet winner should win; if there is no
Condorcet winner, then the Borda winner should win.



i hadn't heard of the Black method before, but just reading this shows  
pretty superficially a problem.  above is one way to say something...



See e.g.:

1 Sep 2009: http://research.microsoft.com/apps/video/default.aspx?id=143268
8 Apr 2011: http://www.youtube.com/watch?v=Bx_lt06W9Ww

Maskin argues as follows:

  If election method X is the best possible
  election method in domain X and if election
  method Y is the best possible election method
  in domain Y and if domain X and domain Y are
  disjoint and if domain X and domain Y together
  cover all possible situations, then the best
  possible election method is to use election
  method X in domain X and election method Y in
  domain Y.

Maskin argues: "domain X" = "situations with a
Condorcet winner"; "election method X" = "any
Condorcet method"; "domain Y" = "situations
without a Condorcet winner"; "election method Y"
= "Borda method".



... and this is another way to say the same thing.  so, right away,  
Maskin is just restating an assertion as some sort of argument  
supportive of the assertion, but it is nothing new.  just a re- 
assertion.  (is that what is "begging the question" is?)


at the core, let's assume that we are already disciples of Condorcet,  
we all agree that method X is best for domain X, he doesn't say squat  
about why method Y is preferred in domain Y.  if we're nowhere near to  
a conclusion that Borda is good for anything (he might have been a  
good general, i dunno), then how do we conclude that it is preferable  
to everything else when there is no CW?  sorry, i haven't even got  
past this block.




Maskin's argumentation doesn't work because
of the following reason: Whether an election
method is good or bad depends on which criteria
it satisfies. Most criteria say how the result
should change when the profile changes. Now it
can happen that the original profile and the
new profile are in different domains. This
means that, to satisfy some criterion, election
method X for domain X and election method Y for
domain Y must not be chosen independent from
each other.



but, this is the fundamental argument of those who claim that it is  
natural for an election to be spoiled, to be dependent upon irrelevant  
alternatives.  isn't that what the fundamental issue is about for why  
Condorcet (assuming a CW exists) is consistent with any simp

Re: [EM] Eric Maskin promotes the Black method

[Markus Schulze]

Hallo,

here are more videos by Eric Maskin:

11 Jun 2009: http://www.carloalberto.unito.it/videos/maskin/maskin3.flv
11 Dec 2009: http://vimeo.com/820
19 May 2010: http://www.youtube.com/watch?v=Un135dexx_Y

In one of his lectures, Maskin claims that the
"American Economic Association" (AEA) has adopted
the Black method for the election of Distinguished
Fellows. I have checked the AEA website. It says
(http://www.aeaweb.org/minutes/09Apr24minExec.pdf):

> The first position is filled by the candidate who
> beats the most other candidates in head-to-head
> match-ups (according to the voters' rankings).
> The next position is filled by the candidate who
> beats the second-most other candidates, and so on.
> A tie can be broken in favor of the candidate who
> gets the most first place votes.

In my opinion, this doesn't sound like the Black
method. This rather sounds like the Copeland method
with plurality voting as tie-breaker.

Markus Schulze


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Re: [EM] Eric Maskin promotes the Black method

[Peter Zbornik]

Dear all,

Why not write an open letter to him (i.e. publish the letter on this
list) and invite him to further discuss on this list?
I found Maskin's email: mas...@ias.edu in his CV, which is online.
If hybrid methods is the way to go, then the forthcoming paper in
Voting matters which Kristofer linked to seems to be better than his
Condorcet-Borda:
http://www.votingmatters.org.uk/FORTHCOMING/I29P1f.pdf

Peter

On Tue, Jun 21, 2011 at 1:56 PM, Markus Schulze
 wrote:
>
> Hallo,
>
> Eric Maskin, a Nobel laureate, is currently very
> active in promoting the Black method. The Black
> method says: If there is a Condorcet winner, then
> the Condorcet winner should win; if there is no
> Condorcet winner, then the Borda winner should win.
>
> See e.g.:
>
> 1 Sep 2009: http://research.microsoft.com/apps/video/default.aspx?id=143268
> 8 Apr 2011: http://www.youtube.com/watch?v=Bx_lt06W9Ww
>
> Maskin argues as follows:
>
>   If election method X is the best possible
>   election method in domain X and if election
>   method Y is the best possible election method
>   in domain Y and if domain X and domain Y are
>   disjoint and if domain X and domain Y together
>   cover all possible situations, then the best
>   possible election method is to use election
>   method X in domain X and election method Y in
>   domain Y.
>
> Maskin argues: "domain X" = "situations with a
> Condorcet winner"; "election method X" = "any
> Condorcet method"; "domain Y" = "situations
> without a Condorcet winner"; "election method Y"
> = "Borda method".
>
> ***
>
> That method, that uses election method X in
> domain X and election method Y in domain Y,
> will be called "election method Z".
>
> ***
>
> Maskin's argumentation doesn't work because
> of the following reason: Whether an election
> method is good or bad depends on which criteria
> it satisfies. Most criteria say how the result
> should change when the profile changes. Now it
> can happen that the original profile and the
> new profile are in different domains. This
> means that, to satisfy some criterion, election
> method X for domain X and election method Y for
> domain Y must not be chosen independent from
> each other.
>
> Example:
>
> The participation criterion says that adding
> some ballots, that rank candidate A above
> candidate B, must not change the winner from
> candidate A to candidate B.
>
> Election method X satisfies the participation
> criterion in domain X. Reason: If candidate A
> was the winner in the original profile and if
> the original profile was in domain X, then this
> means that candidate A was the Condorcet winner
> and, therefore, that candidate A pairwise beat
> candidate B. If candidate B is the winner in
> the new profile and if the new profile is in
> domain X, then this means that candidate B
> is the Condorcet winner and, therefore, that
> candidate B pairwise beats candidate A. If
> candidate A pairwise beat candidate B in the
> original profile and if candidate B pairwise
> beats candidate A in the new profile, then
> this means that the added ballots rank
> candidate B above candidate A.
>
> Election method Y satisfies the participation
> criterion in domain Y, because the Borda method
> satisfies the participation criterion in general.
>
> However, election method Z doesn't satisfy the
> participation criterion since the Condorcet
> criterion and the participation criterion are
> incompatible.
>
> In short: Even if election method X satisfies
> criterion A in domain X and election method Y
> satisfies criterion A in domain Y, it doesn't
> mean that election method Z satisfies
> criterion A. Therefore, Maskin's argumentation
> doesn't work.
>
> ***
>
> I also question the claim that the Borda
> method is the best possible election method
> in situations without a Condorcet winner.
>
> Markus Schulze
>
> 
> Election-Methods mailing list - see http://electorama.com/em for list info

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Re: [EM] Eric Maskin promotes the Black method

[Kristofer Munsterhjelm]

Markus Schulze wrote:

Hallo,

Eric Maskin, a Nobel laureate, is currently very
active in promoting the Black method. The Black
method says: If there is a Condorcet winner, then
the Condorcet winner should win; if there is no
Condorcet winner, then the Borda winner should win.


(...)


Maskin's argumentation doesn't work because
of the following reason: Whether an election
method is good or bad depends on which criteria
it satisfies. Most criteria say how the result
should change when the profile changes. Now it
can happen that the original profile and the
new profile are in different domains. This
means that, to satisfy some criterion, election
method X for domain X and election method Y for
domain Y must not be chosen independent from
each other.


I find it strange for a Nobel laureate (and within mechanism design at 
that!) to not notice this. I've mentioned my concept of "discontinuity" 
before, and it seems quite obvious that if you stitch together two 
methods, you can't just look at how one method behaves and how the other 
does, but also the boundary between the two. To my knowledge the 
Participation and LNH incompatibility proofs against Condorcet work this 
way: they show that no matter how you smooth the transition between the 
Condorcet domain and the non-Condorcet domain, there will be sudden 
transitions ("discontinuities") and you can't line them all up at the 
same time.


Moreover, I agree with you that Borda doesn't seem to be very good. 
Well, it works when there's no strategy (and it gets respectable regret 
in such cases), but strategy is very obvious and can backfire horribly 
(as by Warren's NEC example where the mediocre candidates win because of 
massive burial).
The burial strategy may be obvious enough that voters would engage in it 
even if they thought there would be a CW. They would think that "perhaps 
there won't be a CW and in that case I should maximize the effect of my 
vote", similar to how FPC could encourage compromising in a 
Nader/Bush/Gore scenario.


Finally, if one accepts that the Condorcet criterion makes sense, and to 
comply with it is best when there is a CW, why not expand? Why not limit 
oneself to the Smith set, or to uncovered candidates? The decision to be 
Condorcet compliant but to go no further in the Condorcet direction 
seems rather arbitrary.



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[EM] Eric Maskin promotes the Black method

[Markus Schulze]

Hallo,

Eric Maskin, a Nobel laureate, is currently very
active in promoting the Black method. The Black
method says: If there is a Condorcet winner, then
the Condorcet winner should win; if there is no
Condorcet winner, then the Borda winner should win.

See e.g.:

1 Sep 2009: http://research.microsoft.com/apps/video/default.aspx?id=143268
8 Apr 2011: http://www.youtube.com/watch?v=Bx_lt06W9Ww

Maskin argues as follows:

   If election method X is the best possible
   election method in domain X and if election
   method Y is the best possible election method
   in domain Y and if domain X and domain Y are
   disjoint and if domain X and domain Y together
   cover all possible situations, then the best
   possible election method is to use election
   method X in domain X and election method Y in
   domain Y.

Maskin argues: "domain X" = "situations with a
Condorcet winner"; "election method X" = "any
Condorcet method"; "domain Y" = "situations
without a Condorcet winner"; "election method Y"
= "Borda method".

***

That method, that uses election method X in
domain X and election method Y in domain Y,
will be called "election method Z".

***

Maskin's argumentation doesn't work because
of the following reason: Whether an election
method is good or bad depends on which criteria
it satisfies. Most criteria say how the result
should change when the profile changes. Now it
can happen that the original profile and the
new profile are in different domains. This
means that, to satisfy some criterion, election
method X for domain X and election method Y for
domain Y must not be chosen independent from
each other.

Example:

The participation criterion says that adding
some ballots, that rank candidate A above
candidate B, must not change the winner from
candidate A to candidate B.

Election method X satisfies the participation
criterion in domain X. Reason: If candidate A
was the winner in the original profile and if
the original profile was in domain X, then this
means that candidate A was the Condorcet winner
and, therefore, that candidate A pairwise beat
candidate B. If candidate B is the winner in
the new profile and if the new profile is in
domain X, then this means that candidate B
is the Condorcet winner and, therefore, that
candidate B pairwise beats candidate A. If
candidate A pairwise beat candidate B in the
original profile and if candidate B pairwise
beats candidate A in the new profile, then
this means that the added ballots rank
candidate B above candidate A.

Election method Y satisfies the participation
criterion in domain Y, because the Borda method
satisfies the participation criterion in general.

However, election method Z doesn't satisfy the
participation criterion since the Condorcet
criterion and the participation criterion are
incompatible.

In short: Even if election method X satisfies
criterion A in domain X and election method Y
satisfies criterion A in domain Y, it doesn't
mean that election method Z satisfies
criterion A. Therefore, Maskin's argumentation
doesn't work.

***

I also question the claim that the Borda
method is the best possible election method
in situations without a Condorcet winner.

Markus Schulze


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