[EM] Simple Acceptable Ranked Choice Voting

[Forest Simmons]

Kevin,

The funny thing is that in the Round Robin sports tournament context the
MMPS method for picking the winning team seems to be monotone ... one team
can get more points against another without affecting any other pairwise
scores ... in the pairwise matrix only one entry changes.

Maybe we could call that Tournament Monotonicity.
a
How about the Chicken Defense and MMPS?

Thanks,

Forest

On Sun, Jan 15, 2023, 5:42 AM Kevin Venzke <stepjak at yahoo.fr> wrote:

> Hi Forest,
>
> > Perhaps we need to use the entire finish order of the seed method to get
> an appropriate
> > uncovered winner:
> >
> > Unc(Finish Order)
> >
> > Initialize the variable X as the candidate highest in Finish Order.
> >
> > Then ...
> >
> > While X is covered, replace it with the highest Finish Order candidate
> that covers it. EndWhile.
> >
> > Elect the updated X.
> >
> > I would like to suggest as the seed method the following version of
> MaxMinPairwise Support:
> >  [...]
>
> Unfortunately I don't find this to be monotone with "MMPS." The issue is
> that a winning
> candidate B may wish for a candidate they defeat, A, to have a certain
> number of votes
> against B, so that A is the initial chain head that B then defeats. So
> when B gains some
> votes at the expense of A, a different candidate D becomes initial chain
> head and wins:
>
> 0.328: D>B
> 0.253: A>C
> 0.204: A>B  <-- changes to B>A
> 0.140: C>D>B>A
> 0.074: B
>
> I calculate in the "before" scenario the MMPS order is ADBC, B alone
> covers A, no one covers
> B. Then in the "after" scenario the order is DBAC, and no one covers D.
>
> > If I'm not mistaken, the following variant of the FBC is satisfied by
> this version of
> > MaxMinPairwise Support (before the uncovering modification):
> >
> > If the winner W of this method is ranked top on ballot B, and the winner
> changes when F is
> > moved to equal top with W on ballot B, then the new winner must be F.
>
> Yes, MMPS does seem to satisfy the weak FBC. But the *strong* FBC
> compliance (i.e. what I
> normally just refer to as "compromise incentive") is worse than Bucklin or
> C//A. So I guess
> if the legislature enacts MMPS it should make sure not to forget to allow
> equal ranking.
>
> I am thinking you got lucky with the first draft of MGAscent being
> monotone. (To be honest
> it makes me question my own result there. Why should the max gross score
> version work and
> nothing else? Not sure.)
>
> Kevin
> votingmethods.net
>
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