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
information.
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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