[EM] Example of participation/no-show paradox with Condorcet?

[Allen Smith]

In message <20051105165721.79470.qmail at web26808.mail.ukl.yahoo.com> (on 5
November 2005 17:57:21 +0100), stepjak at yahoo.fr (Kevin Venzke) wrote:
>
>--- Allen Smith <easmith at beatrice.rutgers.edu>:
>> Chris Benham (thanks!) has pointed out that the above is not quite doable
>>for Condorcet itself, with a single voter being added (so _strong_ no-show
>>paradoxes are for Condorcet _completion_ methods?). (Chris has also
>>emailed me a copy of the "Condorcet and Participation" post by Markus
>>Schulze from the archives, which I had missed in my searches; also thanks!
>>That one appears to be for a Condorcet completion method, however, since
>>the original ballots generate a cycle.) So how about with the addition of
>>one _or more_ voter(s) (with said voter(s) favoring x to y)?
>
>It's not possible that if X is the CW, and some ballots are added which favor
>X over Y, then the new CW is Y. Y will still have a pairwise loss to X.

That's about what I was thinking, but the articles I have been able to
locate regarding the No Show Paradox did not make that at all clear, so I
was wondering if my logic was screwy someplace; thank you.

>But this doesn't matter, since there's no such thing as a Condorcet method
>which isn't a Condorcet completion method.

I agree that in most cases some method of solving (top) cycles is
necessary. (But not in all - there are some purposes for which a full-scale
Condorcet winner is what is desirable, and if there isn't one, no winner
should be selected; for instance, election to a collegium with life
terms.)

>> P.S. Incidentally, is there any known means of telling whether, with a given
>> set of ballots, the Participation/No-Show paradox has taken place, besides
>> the brute force method of checking by seeing if eliminating one or more
>> ballots changed the result in an unexpected manner? If so, then a usable
>> method that would be Condorcet except when this would result in a
>> Participation/No-Show paradox could be created.
>
>I don't think there is any method other than brute force. You could design
>the method from scratch using principles that ensure that it satisfies
>Participation, I guess.

I'll leave that to the logicians/mathematicians...

>There are very few methods which satisfy Participation: FPP, Approval,
>range, Borda, and Woodall's DAC/DSC methods. These methods all assign
>points in a very simple way to candidates (or sets of candidates) and then
>use a very simple method of interpreting the ranking of candidates (or
>sets).

True. I suspect what is more practical is to try to make occurences of the
paradox both rare and risky (by which I mean maximizing the potential of, if
one decided that one's vote was likely to result in one's first-place candidate
losing and therefore failed to vote, one would get an even worse candidate
winning than the candidate that would _actually_ win if one failed to vote -
make the amount of information needed to plan a successful no-show strategy
as high as possible), by using an appropriate completion system. (I am
currently contemplating a Schwartz/Approval combo.)

	  -Allen

-- 
Allen Smith			http://cesario.rutgers.edu/easmith/
September 11, 2001		A Day That Shall Live In Infamy II
"They that can give up essential liberty to obtain a little temporary
safety deserve neither liberty nor safety." - Benjamin Franklin