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

[Kevin Venzke]

Allen,

--- Allen Smith <easmith at beatrice.rutgers.edu> a écrit :
> 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.

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

> 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.

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).

Kevin Venzke



	

	
		
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