Definition of Pairwise (to Bruce)
Mike Ossipoff
dfb at bbs.cruzio.com
Sat Apr 20 12:49:21 PDT 1996
Bruce Anderson writes:
>
> Define the Unanimity voting method as follows. Let v be the number of voters
> and let c be the number of candidates on the ballot. If there is a candidate,
> say i, such that the sum/j of p(i,j) = v(c-1), then Unanimity chooses that
> candidate as its unique winner; otherwise (i.e., if there is no such candidate),
> then Unanimity chooses every candidate on the ballot as being tied as its
> winners.
When Bruce says that sum/j of p(i,j) = v(c-1), this is his way of saying
that i is everyone's 1st choice, if I interpret the formulese correctly.
But, in letters to Bruce, I've defined a "Unanimity" count method
that is different from the one he defines in the message quoted
here.
>
> If pairwise//nonpairwise methods are called pairwise, then wouldn't
> "Unanimity//Plurality" and "Unanimity//Hare" also be pairwise? Is this what you
> want? I sure would not want to have to explain to anyone why
> Unanimity//Plurality and Unanimity//Hare are considered as being "pairwise
> methods," since they are virtually identical to Plurality and Hare,
> respectively.
Yes, so maybe that means that we have to either say that Hare is
a Pairwise method, or that Smith//Condorcete//Pluralitty &
Copeland//Plurality aren't Pairwise methods.
But there's something quite bogus about Bruce's Unanimity/Hare
& Unanimity//Plurality, since their results would be identical
to Hare & Plurality. Maybe we'd have to specify, in our definition
of a Pairwise method, then, that its results must not be identical
to those of non-Pairwise tie-breakers that it uses.
Can we add that clause to our definitions of Pairwise methdods
& be done with it?
>
> Again, let me emphasize that it's not at all important to me either way. I
> really don't care that much how "pairwise method" is defined. What I do care
> about is that each and every definition is precisely stated.
Ok, so can we please add the above clause to the definitions & dispense
with the subject?
>
> Bruce
> .-
>
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