# 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?

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

```