[EM] Smith, Ext-Minmax(margins) appears to meet mono-add-top - possible proof?

[Kevin Venzke]

Hi Kristofer,

--- En date de : Sam 26.6.10, Kristofer Munsterhjelm <km-elmet at broadpark.no> a écrit :
> For instance, I don't know why Margins works and WV
> doesn't, except that WV implies Plurality and that Woodall
> has shown you can't have all three of Smith, Plurality, and
> Mono-add-top.

I would say this is because as you add A-top ballots, in margins this
steadily weakens A's losses, so no one can "outrace" the previous winner
to a superior score. By the time anyone with a worse defeat reverses it,
the previous winner has become CW.

> So, what *is* Ext-Minmax? It is, as I have explained in an
> earlier post, a variant of Minmax that breaks ties by
> next-to-maximal defeat, and then by next to next to maximal
> defeat and so on. More formally:

So if I'm not mistaken, Ext-Minmax will never differ from Minmax if no
two pairwise contests are of the same strength?

What do you make of this scenario:

There are four candidates, ABCD. There is a cycle A>B>C>A. D is the
Condorcet loser. The margins among A>B>C>A are 25, 30, 20, so that A has
the weakest defeat among the Smith set. D's loss margins are 3 to A, 4
to B, 5 to C.

Add 6 A>D ballots. Now D is in the Smith set and C's worst loss is only
1 vote, which is strictly the weakest, so the new ballots change the
winner from A to C.

My numbers may not be possible but I suppose something similar must be.

Kevin