[EM] Problem solved (for pure ranked ballot)
Abd ul-Rahman Lomax
abd at lomaxdesign.com
Thu Jan 25 19:54:50 PST 2007
At 08:54 PM 1/25/2007, Forest W Simmons wrote:
>[...]
>8. ICC. The probabilities assigned by the method to members of a clone
>set must add up to the probability that the method would give to a
>single alternative replacing the clone set on each ballot.
>[...]
>Suppose that we have three voters with ranked preferences of
>
>1 A>B>>C
>1 B>>C>A
>1 C>>A>B
>
>Their nearest expression in the pure ordinal ballots of our method
>would be
>
>1 A>B>C
>1 B>C>A
>1 C>A>B .
>[...]
>
>A sure win by B would be an improvement for the first two voters.
>
>The first voter can accomplish this unilaterally by burying favorite:
>
>1 B>C>A
>1 B>C>A
>1 C>A>B
>
>Properties 6, 7, and 8 (applied to the clone set {C, A}) make B the
>winner with 100 percent probability under our method with this ballot
>set.
Had Warren not posted his proof, I wouldn't be on guard against the
problem of the definition of "clone set." The problem is not that C,A
isn't a clone set -- it is, as expressed in the votes with FB -- but
that the clone set relates to the "prior" election
1 B>CA
2 B>CA
3 CA>B
CA being the candidate who is cloned into C and A.
B wins in this election and also in the "FB" election shown. ICC is
not violated.
What has happened -- it's clear to me with Warren's proof, but I'm
not so certain that I've followed Mr. Simmon's proof as well -- is
that the ICC property is incorrectly being tested by comparing the
wrong elections.
I've suffered from brain faults so many times in the EM world that I
wouldn't be surprised if I've done it again, but I'll still say that
this is quite clear to me....
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