[EM] MinMax variant

[Markus Schulze]

Dear Steve,

you wrote (7 March 2003):
> Minimax(pairwise opposition) even satisfies a criterion promoted by
> some advocates of Instant Runoff, which I call "Uncompromising":
>
>    Let w denote the winning alternative given some set
>    of ballots.  If one or more ballots that had only w
>    higher than bottom are  changed so some other
>    "compromise" alternative x is raised to second
>    place (still below w but raised over all the other
>    alternatives) then w must still win.
>
> The proof that Minimax(pairwise opposition) satisfies Uncompromising
> is simple:  Raising x increases the pairwise opposition for all
> candidates except w and x, and does not decrease the pairwise
> opposition for any candidate, so w must still have the smallest
> maximum pairwise opposition.
>
> That criterion can be strengthened somewhat and still be satisfied:
> Changing pairwise indifferences to strict preferences in ballots that
> ranked w top cannot increase w's pairwise opposition or decrease any
> other alternatives' pairwise opposition.

That sounds like Woodall's later-no-harm + later-no-help.
(Douglas R. Woodall, "Monotonicity of single-seat preferential election
rules," Discrete Applied Mathematics, vol. 77, pp. 81-98, 1997.)

In another paper, Woodall proves that no election method can
simultaneously meet later-no-harm, later-no-help, monotonicity,
and mutual majority. Therefore, the fact that Minimax(pairwise
opposition) violates mutual majority in such a drastic manner
can be considered a consequence of the fact that it meets
later-no-harm, later-no-help, and monotonicity.

Example:

   20 ABCD
   20 BCAD
   20 CABD
   13 DABC
   13 DBCA
   13 DCAB

You wrote (7 March 2003):
> That's why I think the best method is a variation of Ranked Pairs
> which I call Maximize Affirmed Majorities, or MAM.

In so far as you have always considered Mike Ossipoff to be
authoritative, I would like to know what you think about the
fact that he doesn't promote Ranked Pairs anymore at his
web pages.

Markus Schulze