[EM] Discounting ties, how can MinMax differ from Ranked Pairs? ooops!

Kristofer Munsterhjelm km_elmet at t-online.de
Wed Jun 12 09:37:56 PDT 2019

On 12/06/2019 09.27, robert bristow-johnson wrote:

> While I think that ties of votes will be rare (but i was once at a Dem
> caucus for mayor in Burlington in 2012 where the caucus was tied with
> ca. 830 voters), i wonder if Margins might be tied more often.
> If we're doing RP or MinMax using Margins, how might we order it if the
> Margins are tied between two pairwise races?  I can kinda conceive how
> it would make a difference in a weird case.  Which is better?  A higher
> Winning Votes or a lower Losing Votes?  With a fixed Margin, a lower
> Losing Votes (which makes the total votes lower) means that the Margin
> corresponds to a higher percent margin.  Maybe that's better than
> Winning Votes.  What do you guys think?

For breaking ties in Minmax, I like what I've called "Ext-Minmax". In
ordinary Minmax, the winner has the best worst defeat against him (i.e.
it's the A so that the greatest value of X>A is the least, for some X).
In Ext-Minmax, just break ties by the next-to-greatest defeat. If there
are still any ties, break by third greatest defeat, and so on.

I wonder if there's anything that's to Schulze what Ext-Minmax is to
Minmax, but I haven't yet found any equally intuitive extensions. (That
said, I haven't been looking hard either.)

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