[EM] I think Bishop's deconstruction algorithm fails
wds at math.temple.edu
Sun Nov 27 17:25:36 PST 2005
no, I meant Bishop's alg would fail to fid ANY deconstruction even when one
existed. The problem was not, as Kislanko worries, that there might be
a non-unique solution. That is a valid worry, but I do not care about that
Also, to reply some more to Kislanko, he argued that "a condorcet matrix"
is one arising from ballots, therefore he fails to understand how
a matirx could exist which does not arise from ballots.
Well, one reply to that is "duh." Another reply is, there are matrices
which do not arise from ballots. It is an interesting question which
matrices are achievable and which are not.
Bishop's algoorithm if it works (which I doubt) would answer that question.
I have a method involving solving an integer program which does answer the
question, but only at heavy computational cost. Bishop's method
if it works would have mild computational cost.
My method works and I doubt Bishop's works, but it would be nice
to produce an explicit counterexample to Bishop's algorithm.
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