[EM] two more variations of MMPO

Kevin Venzke stepjak at yahoo.fr
Fri Jun 10 12:09:28 PDT 2005

Hi Russ,

--- Russ Paielli <6049awj02 at sneakemail.com> a écrit :
> Russ Paielli 6049awj02-at-sneakemail.com |EMlist| wrote:
> > I'd like to throw out a couple more ideas I've had for variations of 
> > MMPO. I'm not certain, but I think they might retain the key properties 
> > of MMPO.
> > 
> > Suggestion 1: MMPO top-two pairwise runoff
> > 
> > Find the top two MMPO candidates and select the one who wins the 
> > pairwise race between them. This method uses no Approval cutoff.

I'll pass on considering this due to the Clone-Loser failure.

> > Suggestion 2: MMPO/Approval runoff
> > 
> > This method uses an Approval cutoff and is similar to the one I 
> > suggested a few days ago but a bit simpler. The Approval winner and the 
> > MMPO winner have a pairwise runoff to select the final winner.

At first glance I thought this looked promising, since MMPO and Approval
both satisfy FBC. But I think the pairwise runoff breaks it: If your preference
order is A>B>C>D, it could be that sincerely putting A at the top could
put A in the runoff, and then lose to D, whereas if you had left A off your
ranking, B would have made it to the runoff and beat D.

> What's with all the pairwise runoffs, you ask? Well, one thing that 
> bothers me about MMPO is that it uses no direct information about who 
> wins or loses any particular pairwise contest. Could the Condorcet loser 
> actually win? I don't know off hand, but if so, that would be a serious 
> blemish.

It is possible.

What do you think of Minmax(wv) combined with the "T matrix" tie rule?
That method regards pairwise contests. (It doesn't satisfy LNHarm, though.)

> But even if the Condorcet Loser can't win, I am still bothered by the 
> lack of direct head-to-head win/lose competition. It's almost like 
> having a football season but not keeping track of who wins or loses any 
> particular game, and simply giving the championship to the team that 
> scores the most overall points (or allows the least overall). It just 
> doesn't seem right.

Actually, this doesn't sound that bad to me. The main problem is that some
games will count more than others.

>I'm not trying to spam the list, but I just thought of a more accurate 
>analogy. As I said, MMPO is a bit like having a football season but not 
>keeping track of who wins or loses any particular game. The championship 
>then goes to the team whose maximum points against in any particular 
>"game" is the lowest.

There are some advantages, though:

Suppose teams A and B are "friendly," and B is not expected to "win" many
games. There is no incentive here for B to let A have an easy win, whereas 
there would be if we were picking a Copeland winner.

Also, fans of team A never have to hope that team B will "lose" a game to
an enemy team, to ensure that B won't jeopardize A's overall win. Using 
Copeland, team A fans might hope that team B will suffer "just enough" losses 
to enemy teams.

Kevin Venzke


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