[EM] I think Bishop's deconstruction algorithm fails

[Paul Kislanko]

Mr Smith obviously doesn't understand English any more than he does math.

Mis-quoting me and mis-charactizing my arguments is proof of that.

What I said, in plain English, is that since there are multiple
decompositions of a pairwise matrix that would lead to the same pairwise
matrix, it would be more logical to begin vote-counting from ballots instead
of from the pairwise matrix.

I don't expect him to understand, but let us not allow his
mis-understandings to characterize my post. 

> -----Original Message-----
> From: Warren Smith [mailto:wds at math.temple.edu] 
> Sent: Sunday, November 27, 2005 7:26 PM
> To: wds at math.temple.edu; kislanko at airmail.net; 
> election-methods at electorama.com
> Subject: Re: [EM] I think Bishop's deconstruction algorithm fails
> 
> 
> 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
> worry.
> 
> 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.
> wds
>