On May 3, 2011, at 7:55 PM, S Sosnick wrote:
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.
"Majority" clearly makes sense in Plurality elections. If we get 49A,
48B, and 3C, C is a clear loser, voters could not indicate their
preference among A and B while voting for C, and we clearly need a
Runoff between A and B. Of course, if we get 33A, 33B, and 33C, it is
time to wish for something different.
Given 49A, 48B, and 35C in Approval, there is less value in a Runoff.
Most C voters could, and presumably did, indicate their choice between
A and B. Some unhappy voters could have noticed that they could not
both vote for two vs one disliked and for one of the two as liked
most. These last could promote such as Score or Condorcet.
Voting cycles can result, and they make trouble for any democratic
system.
But the cycles are simply information - that there are voters who
like, most, each of A, B, or C - information that methods such as
Plurality never know. While properly responding is a challenge, the
having of the information is useful if we wish to, ACTUALLY, respond
to the voters true desires.
--Stephen H. Sosnick (3-Apr-2011)
Clearly you meant May, not Apr.
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