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

[Dave Ketchum]

On Wed, 16 Aug 2006 00:44:53 -0400 Abd ul-Rahman Lomax 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.

Really?

A criterion that would tolerate Plurality does not seem worth having.
What would such usefully reject?

Approval is better, but still not worth bragging.

Seems like the minimum that should be acceptable is three ranks, doable
also with range.  Get this far and adding more ranks requires little in
additional support - but adds little in value.
 >
 > (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. Obviously, such a method requires equal ranking. Note also
 > that a voter might prefer to add more than one write-in candidate.
 > Should this too be allowed? If not, why not? -- the answer, ballot
 > complexity, would similarly apply to reducing the number of
 > expressible ranks when there are many candidates.)
 >
 > Sometimes we forget that Approval and Plurality are ranked methods
 > with only two ranks. The problem with Plurality, of course, is that
 > equal ranking is generally prohibited. If overvoting were allowed,
 > with one stroke of the deletion pen in the election code, Plurality
 > would become Approval, which has got to be the simplest of the
 > proposed election reforms.
 >
I remember our debating asset voting.  Agreed the idea  has merit, but we 
disagreed as to details.

 > (But Asset voting, using plurality counting, i.e., no overvoting
 > allowed, is just as simple to count and uses the same ballot. If
 > overvoting is allowed, the counting gets more complex because in this
 > case the votes must become fractional votes, i.e., the method becomes
 > Fractional Approval Asset Voting, my current favorite. But what I'll
 > now call Standard Asset Voting -- i.e., vote for one only -- is
 > really almost as good without the counting complexity. Pick the
 > candidate you most trust and vote for him or her, no worry about wasted 
votes.)
-- 
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   Dave Ketchum   108 Halstead Ave, Owego, NY  13827-1708   607-687-5026
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