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

[David Cary]

--- Abd ul-Rahman Lomax <abd at lomaxdesign.com> wrote:

> Approval Voting satisfies the Condorcet criterion (as does 
> Plurality). The idea that it does not is based on the imputation of
> unexpressed preferences. That is, *if* there were more expressible 
> ranks, and the voters used them, the outcome could change.
> 
> (But if the Condorcet criterion *requires* that all preferences be 
> expressible, i.e., that the number of ranks equals the number of 
> candidates, then, of course, any method which does not allow that 
> does not satisfy the criterion. I don't know the exact wording. But
> I've never seen anyone objecting that a method which only allows N 
> ranks in the presence of more than N candidates does not satisfy
> the Criterion. 

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?

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.

-- David Cary

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