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<DIV><SPAN class=529031922-28112005><FONT face=Arial color=#0000ff size=2>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.</FONT></SPAN></DIV>
<DIV><SPAN class=529031922-28112005><FONT face=Arial color=#0000ff
size=2></FONT></SPAN> </DIV>
<DIV><SPAN class=529031922-28112005><FONT face=Arial color=#0000ff size=2>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.</FONT></SPAN></DIV>
<DIV><SPAN class=529031922-28112005><FONT face=Arial color=#0000ff
size=2></FONT></SPAN> </DIV>
<DIV><SPAN class=529031922-28112005><FONT face=Arial color=#0000ff size=2>The
"is it raw data or an intermediate value?" question is critical.
</FONT></SPAN></DIV>
<DIV><SPAN class=529031922-28112005><FONT face=Arial color=#0000ff
size=2></FONT></SPAN> </DIV>
<DIV><SPAN class=529031922-28112005><FONT face=Arial color=#0000ff size=2>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.</FONT></SPAN></DIV>
<DIV><SPAN class=529031922-28112005><FONT face=Arial color=#0000ff
size=2></FONT></SPAN> </DIV>
<DIV><SPAN class=529031922-28112005><FONT face=Arial color=#0000ff size=2>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.
</FONT></SPAN></DIV>
<DIV><SPAN class=529031922-28112005><FONT face=Arial color=#0000ff
size=2></FONT></SPAN> </DIV>
<DIV><SPAN class=529031922-28112005><FONT face=Arial color=#0000ff
size=2>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).</FONT></SPAN></DIV>
<DIV><SPAN class=529031922-28112005><FONT face=Arial color=#0000ff
size=2></FONT></SPAN> </DIV>
<DIV><SPAN class=529031922-28112005><FONT face=Arial color=#0000ff size=2>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.</FONT></SPAN></DIV></BODY></HTML>