[EM] Condorcet incompatibility proofs

[Steve Eppley]

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