[EM] Description of "Median," my Approval variant

[Forest Simmons]

On Thu, 6 Mar 2003, [iso-8859-1] Venzke Kevin wrote:

>
> Looking at some of your proposals for picking the
> winner:

These were not really intended as proposals so much as examples to
establish a context for understanding your method relative to commonly
understood methods.


>
> >(1) Take the team that gave up the fewest points per
> game on
> >average (i.e. had the fewest points scored against
> them per
> >game on average). This might be considered the team
> with the
> >best defense.
> >(5) Take the team that scored the highest point
> average per game.
> >(6) Take the team with the maximal minimum number of
> points per game.
> >In other words, if team A scored at least 25 points
> in every game, and
> >every other team scored fewer than 25 points in at
> least one of their
> >games, then A should be the winner according to this
> criterion. etc.
>
> Using these would influence the number of candidates.

True, that's why I used the sports context, where that problem wouldn't
arise.

> Under (1), it's best for candidates to run alongside
> many clones.  Under (5) or (6), candidates are
> punished for having similar support bases, like under
> Plurality.
>
> >(3) Take the team for which the maximum margin
> against them was
> >minimal. This is analogous to MinMax (margins). If
> there is a beats
> >all team, this method will pick it.
> >(4) Take the team for which the maximum score against
> them was
> >minimal. This is analogous to MinMax (winning votes),
> and also will
> >detect a beats all winner. All of these methods pick
> teams based on
> >measurements of defensive prowess. But what about
> offensive prowess?
>
> I'm a little confused.  Will these pick different
> winners from Approval?
>

Well, approval votes cannot be inferred from the pairwise matrix or its
transpose, so the question has no meaning in the sports context nor in the
context of ranked ballots without approval information.

But in the context of approval ballots processed to get the pairwise
information, yes, the two MinMax methods do give the same result as
Approval, but the others don't necessarily agree.


(more later)