[EM] thoughts on the pairwise matrix

Paul Kislanko kislanko at airmail.net
Mon Nov 28 14:44:09 PST 2005

I'll try again to make clear what I mean by not being convinced that methods
that use the PM to count votes can accurately reflect voters' preferences.
The basic claim is that the pairwise matrix accurately reflects pairwise
preferences by the voters. I do not believe this claim, because it it is not
based upon collecting votes via ballots that collect that kind of
The "is it raw data or an intermediate value?" question is critical. 
A process that translates a ranked ballot into the pairwise matrix form is
normally what is used to construct the intermediate value. But I (along with
Jobst Heitzig) have argued that if you want the voters' pairwise
preferences, the BALLOTS have to be in that format.
If you ask me to rank 5 alternatives, I might vote A>B>C>D>E. But if you ask
me to pick one of A and C, I might chose C. To ASSUME that my ranked ballot
reflects my pairwise votes has not been (and probably can't be) justified. 
Academics suggest that voting C>A in a two-way race but A>C in a five-way
race is not rational. All I offer in response to that is "PROVE that the PM
reflects the voters preferences". (Hint: Arrow got a Nobel prize for proving
they can't do that).
I think the only pairwise-matrix that is defensible is one constructed by
ballots. If the Ballot says "Choose one, choose both, choose neither" for
each pair of alternatives then there's a clear path from voters' choices to
the resulting PM. Otherwise, it's a matter of how the ballots were processed
to get the PM.
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