At 08:37 PM 4/10/2010, Kevin Venzke wrote:
--- En date de : Sam 10.4.10, Kevin Venzke <[email protected]> a écrit :
> I can't study the underlying utilities because I don't have
> them. If I
> did I could make them say anything I wanted. I would have
> to come up
> with a general rule anyway, or else give up and say all
> methods are the
> same.
This should rather say, if I proposed utilities behind the scenario, I
could make those utilities say anything I wanted.
I pointed out some extremes, which reveal as the
ideal winner A, B, or C. In other words, you are
apparently agreeing with me. However, I believe
that I showed that a middle-of-the road
assumption about underlying utilities, with
stated assumptions that were not designed to make
it turn out some particular way, A could indeed be the best winner.
(I did not set out to "prove" that A was the best
winner, but rather just to attempt to infer
utilities from the voting patterns, which didn't
allow me to assume equal ranking except at the bottom).
The matter hinges on the A voters, who are, after
all, almost a majority. Why did none of them rank
B or C? The only reasonable assumption is that
they have strong preference, and that's what ices
it. This is the classic reason to violate the
Condorcet or Majority criteria: a strong
preference of a minority, particularly when the margin is thin.
If, in fact, B and C were true clones, with only
minor preference between them, the assumption of
a significant reduction of utility between them
(which is the other factor that lowers the rating for B and C) would fail.
If the method allowed equal ranking, we'd see
that in the votes, and B might win. The A votes
would be the same, the B bullet voters would be
the same, but the other B and C voters would
equal rank B and C. Because of the B bullet
voters, B would win by a small majority.
So my result for A could be an artifact of the
voting system not allowing equal ranking. I used
Range 2, which doesn't give a lot of room for
"creative interpretation." That was much easier
with Range 10, as I showed. With Range 2, there
wasn't any other reasonable way to interpret the votes.
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