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

Allen Smith easmith at beatrice.rutgers.edu
Sat Nov 5 07:53:17 PST 2005

In message <mid+200511050903.jA593eRa054127 at dogberry.rutgers.edu> (on 5
November 2005 04:03:39 -0500), easmith at beatrice.rutgers.edu (Allen Smith)
>Hi. I am attempting to get my head around the participation/no-show paradox
>with regard to Condorcet-satisfying methods, and would greatly appreciate
>an example of a set of voters and candidates in which there is a (single,
>strong (no ties)) Condorcet winner, x, but said winner changes (to another
>single, strong Condorcet winner, y) upon the addition of one voter (with said
>voter favoring x to y). (Perez's "The Strong No Show Paradoxes are a common
>flaw in Condorcet voting correspondences" has what he claims to be a
>counterexample to Condorcet and no-show being compatible, but it doesn't
>appear to me to actually be such a counterexample.) Note that I am _not_
>asking for an example for a Condorcet _extension_ method - only for a pure
>Condorcet winner change.

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)?



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.

Allen Smith                       http://cesario.rutgers.edu/easmith/
February 1, 2003                               Space Shuttle Columbia
Ad Astra Per Aspera                     To The Stars Through Asperity

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