[EM] Condorcet incompatibility proofs
Steve Eppley
seppley at alumni.caltech.edu
Sun Sep 19 16:10:05 PDT 2004
Hi,
James G-A wrote:
> Steve E writes:
>> I assume James is using the name "consistency" to
>> refer to the criterion also called "reinforcement."
>
> Um, yeah. I meant that if one group of ballots,
> processed by the given method, gives A as the winner,
> and another group of ballots gives A as the winner too,
> then if all of the ballots are combined and processed,
> you should still get A. Is that "reinforcement"?
Yup, that's it. (Assuming both groups voted on the
same set of candidates, which James surely intended.)
Peyton Young used the name reinforcement for a weaker
reinforcement criterion that's satisfied by Kemeny-Young:
If the votes of group 1 produce the same social ordering
of the candidates as the votes of group 2, then the
combined votes must also produce that social ordering.
When Moulin wrote about reinforcement and participation
in his book, he called them "very strong arguments" for
using a scoring rule (such as plurality rule and Borda)
instead of a Condorcet-consistent rule. In my webpages,
I argue that they are very weak arguments. Reinforcement
failures cannot be manipulated by a minority if the power
to partition the voters requires a majority. Participation
failures may engender some regrets and may depress voter
turnout, but it seems very doubtful that either of those
effects would be as bad as the regrets and reduced turnout
caused by more serious flaws.
--Steve
More information about the Election-Methods
mailing list