Markus' Econometrica reference on RB & IIAC

[Blake Cretney]

MIKE OSSIPOFF wrote:

>
> 1. No one, that I'm aware of, says that Plurality passes CC.
>
> 2. Blake Cretney says that his CC applies only to rank methods.
>   He does that in order to keep Plurality from passing. I don't
>   claim that anyone other than Blake uses that way of preventing
>   Plurality from passing CC. I didn't say
>   that there's an article that does that. I don't claim that there's
>   an article that does that. I said that Blake, in his website,
>   does that.
>
The Condorcet Criterion is most naturally expressed with regard to 
ranked ballots.  Plurality is most naturally expressed with regard to 
lone-mark ballots.  If you want to talk about whether Plurality passes 
CC, you either have to define Plurality so that it applies to ranked 
ballots, or define CC in such a way that it refers to Plurality ballots.

Its pretty easy to define CC to apply to plurality ballots, because you 
can think of the voted for candidate as ranked above all the others, and 
all the others as being ranked equally.  Defined this way, plurality 
passes CC.  However, we have a sense that it has cheated, that it has 
passed only by greatly limiting the expressivity of the ballot.

Another way out is to redefine plurality so that it applies to ranked 
ballots.  The winner is the candidate who gets the most first-place 
votes.  Now, plurality fails.  I suspect that this is the approach most 
academics would take.  However, it clearly involves a redefinition of 
plurality.

For my web site, I avoid the problem by using a definition of CC that 
only applies to ranked ballots, and a definition of plurality that only 
applies to lone-mark.  So, CC doesn't apply to plurality.  In other 
words, I avoid the question.  Personally, I think that it is obvious 
that the goals of the Condorcet advocates are not achieved by plurality. 
 But I am not interested in redefining plurality because then someone 
could legitimately question what my plurality has to do with the 
traditional kind.  I think I could answer this question, but the defense 
would be complicated and perhaps subjective.

Another solution to the problem would be to redefine CC to involve the 
idea of voting sincerely.  Presumably, sincere votes in a Condorcet 
completion method should result in the sincere Condorcet winner winning. 
 But they would not in plurality.  So, if we define CC on sincere votes, 
perhaps this would be the best solution.

In fact, as this list has proven, that solution is far more complicated 
that one might naively imagine.  Remember that the previously suggested 
approaches only considered ballots, with methods and criteria based on 
them.  The sincerity-based CC involves a theory involving voters having 
mental states that correspond to particular ballots.  But it isn't 
always clear in what sense these mental states exist, and how they 
correspond to "sincere" votes is not obvious either.  

I am amazed by all the competing interpretations of sincere votes.  Mike 
believes that a voter implies acceptance of any candidates she ranks. 
 I, for one, believe no such acceptance is implied.  Some people believe 
that they "approve" only of a fixed number of candidates, and that a 
sincere approval vote is for exactly these candidates.  So for them, a 
particular approval ballot corresponds to a particular judgment about 
the candidates, a particular mental state.  Personally, I do not 
normally make this kind of judgment about the candidates in an election.

So although the purpose of the sincerity-based CC was to make it easier 
to explain why a Condorcet advocate would reject plurality.  In fact, it 
makes the explanation much more complicated.  

Having said all that, I'll get to how I interpret P&P.  P&P talk about 
ballots, and criteria and methods based on those ballots.  By ballots I 
could just as easily say preference orders.  I don't think P&P intend to 
propose a theory in which the preference orders are mental states, but 
the method works on actual ballots, so the ballots must be "sincere", 
whatever that might mean.  They ignore the sincerity issue.  They just 
have methods and criteria that refer to preference orders.  But where 
those preference orders come from isn't their concern.  For you, 
preference order implies sincere preferences, and you recognize that a 
real-world method can only work on cast votes.  But for P&P, a method is 
just a function from a hypothetical set of preference orders to a set of 
winners.

Of course, the current dispute is not really over this issue.  It is 
about who was wrong countless emails ago.  I honestly don't know the 
answer, and since I have no interest in the question, I suspect I'll 
never know.

------
Blake Cretney

See my Election Method Resource
http://www.fortunecity.com/meltingpot/harrow/124/