Condorcet(x( ))

[Mike Ossipoff]

Lucien Saumur writes:
> 
> In an article, seppley at alumni.caltech.edu ("Steve Eppley") writes:
> 
> >Lucien wrote:
> >[snip]
> >>          This winter, I have modified my computer voting
> >>and tallying system to incorporate two features:
> >[snip]
> >>          When tallying the ballots, the program adds half
> >>a vote to each candidate of the tied pairs.
> >[snip]
> >
> >That's not Condorcet's method according to Mike Ossipoff's proposal,
> >and based on the discussion in EM in recent days I think he's right
> >not to tally .5 against each of the tied pairs.  
> >
>           I have difficulty identifying what constitutes
> "the Condorcet method" beyond ranking the candidates and
> performing a pairwise comparison of the results. I am aware
> that Condorcet imagined the possibility of circular ties
> but I am not aware that he has proposed a solution. Nor am

Well, consider yourself aware of it now: Condorcet did propose
a circular tie solution. It's called "Condorcet's method". It
scores candidates according to their worst defeats. My Condorcet's
method proposal is consistent with Condorcet's proposal.

I refer you to _The Theory of Committees & Elections_, by
Duncan Black. I believe it was published in 1958. It's in
most university libraries, I would expect.

> I aware that he has imagined equal ranking and truncated
> voting much less am I aware how he proposed to deal with
> these ballot refinements.

Condorcet's proposal only speaks of counting preferences that the
voters actually voted. He didn't say anything about making up
preferences that weren't voted. 
If you don't solve circular ties according to scores based on a
candidate's worse defeat, that isn't Condorcet's method. If
you invent preferences that the voter didn't vote, you're
adding something that Condorcet never mentioned. Call it
"Saumur's method", but not Condorcet's method.

> 
> >You may or may not have implemented Condorcet(.5), depending on how
> >you resolve circular ties.  How do you calculate the size of each
> >candidate's worst defeat?  By "margin of difference" (not Condorcet)
> >or by "votes for the pairwinner" (Condorcet)?
> >
>           As I have said before, I am not sure what to make
> of circular ties. My feel is that they represent a weak
> preference on the part of the voters so that the voters
> would not be adverse to drawing lots to determine the
> winner. But I could be wrong which is why that I think that
> we need practical experience on this matter but I think
> that to use the size of the worst defeat is an artificial
> way to determine the winner.

Circular ties, as I've showed you several times, can be caused
by some voters voting short rankigs (truncation). Truncation is
common in rank-balloting elections, and, with your method, would
often defeat the "Condorcet winner", the candidate who, when compared
separately to each of the others, is preferred to him/her by more
voters than vice-versa.

You say that Condorcet doesn't value majority rule? But you've
just proposed drawing lots, where Condorcet would defeat a
candidate with a majority against him, unless everyone has
a majority against him.

> 
> >Would you consider implementing Condorcet(0), where nothing is
> >tallied against the tied pairs, in your webpage? 
> 
>           My system could be changed in this way but I do
> not see why this would be necessary.

Of course it isn't: Anyone can propose anything they want to propose
on their web page, regardless of its merit.

> 
>           I do not understand why we have so much problem
> with truncated ballots. I think that a truncated ballot may
> not be interpreted otherwise than to mean that the voter
> has no preference between the unranked candidates and that
> no preference logically means equal preference. My system

Condorcet's method, and every rank-balloting method ever proposed
on EM or ER, also lets voters truncate ballots if they so wish.


> lets a voter truncate the whole ballot which is to show no
> preference for any of the candidates. Because my system
> also lets the voters indicate whether some or all of the
> candidates are unacceptable independently of the ranking, a
> completely truncated ballot is not the same as a failure to
> vote because a truncated ballot may affect the result of
> the election by serving to declare that a winning candidate
> is unacceptable or else by preventing that a winning
> candidate be declared unacceptable.

Truncation would indeed cause problems with your methods, but
not with Condorcet's method.

You say that truncation means indifference between the unranked
candidates, but few people are completely indifferent between
a particular pair of candidates. I've observed offensively-intended
truncation. I've observed lazy truncation in an election between
50 or more candidates.

> 
> __________________________________________
>           aa447 at FreeNet.Carleton.CA
>           http://www.igs.net/~lsaumur/
> .-
> 


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