Definition of "Pairwise Method"
Steve Eppley
seppley at alumni.caltech.edu
Tue Apr 16 00:08:49 PDT 1996
Bruce Anderson wrote:
[snip]
>To address Steve's objection concerning ambiguity in my
>definition-1 above, let me make it even more explicit as follows.
>
>DEFINITION 1: Let p(x,y) be the sum number of voters who
>explicitly rank x over y plus the number of voters who explicitly
>rank x do not explicitly rank y, and let q(x,y) be the sum of the
>number of voters who explicitly rank X as tied with y plus the
>number of voters who do not explicitly rank either x or y, and let
>p and q be the corresponding arrays of values of p(x,y) and q(x,y).
>Then a ranked-ballot single-winner voting method is a "pairwise
>method" if and only if its set of winners can be calculated using
>only the number of candidates, the number of voters, and the values
>in p and q.
>
>Steve: Is this precise enough?
The "either..or" is still ambiguous. How about this, nearly the same:
DEFINITION 1: Let p(x,y) be the sum of the number of voters who
explicitly rank x over y plus the number of voters who rank x and
leave y unranked. Let q(x,y) be the sum of the number of voters who
explicitly rank x as tied with y plus the number of voters who leave
both x and y unranked. Let p and q be the corresponding arrays of
values of p(x,y) and q(x,y). Then a ranked-ballot single-winner
voting method is a "pairwise method" if and only if its set of
winners can be calculated using only the number of candidates, the
number of voters, and the values in p and q.
Why include the number of voters there at the end? Why disallow
other info?
I'd like to be able to refer to pairwise//nonpairwise methods as
pairwise. Would that be tabooed by a "strict constructionist"
interpretation of Definition 1?
--Steve
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