# Elimination by largest votes-against? (was Re: Fairness,

Steve Eppley seppley at alumni.caltech.edu
Sat Apr 20 16:56:13 PDT 1996

```Mike Ossipoff wrote [in "Brief reply..."]:
>procedures, including an elimination method, would do well by the
>lesser-of-2-evils standard. The elimination procedure Steve
>suggested was something that I checked out early on, along with
>votes-for & margins of defeat. No, nothing else does the job but
>votes-against. But I'll demonstrate that in subsequent letters.

The elimination procedure I suggested *does* use "largest votes
against in pairwise defeats" to identify which candidate to eliminate.
Then that candidate is eliminated from the ballots, and new pairings
are calculated.  And so on until there's one winner.

This is vague, though, since I'm unsure what to do about the Smith
criterion.  Should all the candidates not in the Smith set be
presume that if those candidates are disqualified by Smith, it won't
make a difference whether or not they're eliminated from the
ballots.  (This is because if {a,b,c} each beat {d,e,f,g}, then {a,b}
will still each beat {d,e,f,g}, and none of {a,b,c} has a worst
defeat outside Smith.)  In which case it will be faster to recalc the
new pairings if the non-Smith candidates are all eliminated at the
same time as the Smith candidate with the largest votes-against, in
the first round.

Is this clear enough so your demonstration of lesser-of-evils will be
for the right method?

--Steve

```