[EM] Condorcet incompatibility proofs

Steve Eppley seppley at alumni.caltech.edu
Sun Sep 19 08:54:58 PDT 2004


James G-A requested:
> 	Looking for help again! Does anyone know where I can 
> find the earliest proof that Condorcet efficiency is
> incompatible with consistency?

I assume James is using the name "consistency" to refer
to the criterion also called "reinforcement."  There are 
so many criteria that can reasonably be classified as 
"aesthetic consistency" criteria (e.g., monotonicity) 
that I don't think we should cater to the Borda advocates 
like Saari who would love to have hegemony over that name.  
Why not instead use the name consistency to refer to 
independence from "exact clone" alternatives, so Borda 
advocates can be the ones bonked by it instead?

In Herve Moulin's book "Axioms Of Cooperative Decision
Making" he cites the proof by H. Peyton Young that
no Condorcet-consistent method satisfies reinforcement:

   Young HP (1975): Social Choice Scoring Functions.
   SIAM Journal of Applied Mathematics, 28, 824-38.

> I'm also not sure who to cite for Condorcet being 
> incompatible with later-no-help and later-no-harm. 
> Is it Woodall in Voting Matters, May 1996?

That looks right, but I skimmed it very fast just now
and may have failed to notice if Woodall cited one of 
his own earlier papers.  However, I did notice while 
skimming that his proof relies on Moulin's proof 
that Condorcet-consistency is incompatible with 
the participation criterion if there can be 4 or more 
candidates.  Woodall cites a 1988 paper by Moulin, 
but Moulin's book mentioned above cites an older 
paper about participation:

   Moulin H (1986): Choosing from a tournament.
   Social Choice and Welfare, 3, 271-91.


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