[EM] Arrow's theorem

[S Sosnick]

On May 2, commenting on the criterion of Independence from Irrelevant Alternatives, Forest 
Simmons wrote, "IIAC is a totally unreasonable requirement."  On May 3, Kevin Venzke added, 
"IIA isn't compatible with Condorcet.  It's not compatible with much of anything.  I take that to be 
the point of Arrow:  If you want IIA you have to do some drastic things."

While I agree with those comments, I think that one can--generously but usefully--equate 
Arrow's theorem with a broader point, namely, no election system in which voters rank 
candidates can have all properties that seem democratic and appropriate.  For example, no 
election system in which voters rank candidates can guarantee both Condorcet compliance and 
Later-no-harm.

The reason is that "democratic" embraces majority rule, and--when 3 or more voters rank 3 or 
more candidates--each candidate may be ranked below at least one of the other candidates by a 
majority of the voters.  Voting cycles can result, and they make trouble for any democratic 
system.

--Stephen H. Sosnick (3-Apr-2011)