[EM] simpler proof of "no conflict theorem" now trivial

[Jonathan Lundell]

At 4:58 PM -0700 8/16/06, David Cary wrote:
>Without knowing the exact wording of the criterion, it can be very
>difficult to judge whether or not an election method meets the
>criterion, or whether the criterion makes sense or contains
>ambiguities. 
>
>As stated on Wikipedia (
>http://en.wikipedia.org/wiki/Condorcet_criterion ), there is
>certainly some ambiguity, as mentioned on the discussion page:
>
>"The Condorcet criterion for a voting system is that it chooses the
>Condorcet winner when one exists."
>
>"The Condorcet candidate or Condorcet winner of an election is the
>candidate who, when compared in turn with each of the other
>candidates, is preferred over the other candidate."
>
>The ambiguity is about exactly how candidates are compared with each
>other and what preferences are to be used.  The balloted preferences
>of the voting system in question? The sincere preferences of the
>voters? Is there a hidden presumption that voters cast ballots that
>are sincere, or are at least consistent with their sincere
>preferences?  Is the Condorcet criterion only applicable to certain
>kinds of election methods?

Good point. The previously cited paper "In Praise of Manipulation" is 
problematical in this regard, in that the authors get way too literal 
about the meaning of "sincere".

I take the meaning of "preferred" above to equivalent to asking the 
voter in question to break a tie between the two candidates. If your 
vote will swing the outcome, which of these two candidates would you 
choose for the seat to be filled?

The problem is, of course, that this is seldom if ever the context in 
which the voter actually marks a ballot, often for strategic reasons 
(fear of wasting a vote, wanting to bury a close competitor, etc).

Hence the desirability of an election method that encourages a 
rational voter to cast a sincere ballot.

>The more these ambiguities are resolved to make the Condorcet winner
>dependent on the election method under consideration, the easier it
>may be for an election method to satisfy the Condorcet criterion.
>
>The Wikipedia article is notably lacking any references.

Many of the election-methods Wikipedia articles leave a lot to be 
desired (the Droop quota article is a good (bad) example).
-- 
/Jonathan Lundell.