[EM] MAM vs Schulze

[Kristofer Munsterhjelm]

On 10/08/2016 03:06 PM, C.Benham wrote:
> Mike,
> 
> As far as I can tell, for all intents and purposes  MAM,  Schulze, River
> and  Smith//MinMax (wv)  are all just different wordings
> of the same method.
> 
> If you think that MAM  is better than Shulze, then what criterion (that
> we might care about) is met by MAM and not Shulze?
> 
> Or perhaps you have some example in mind where you think the MAM winner
> is much prettier than the Schulze  winner?

I'm not Mike (and I don't see his posts), but I would probably say LIIA
for MAM and IPDA/ISDA for River. Those criteria probably only become
relevant (that is, failed by Schulze) when the Smith set size is large,
however, so whether you consider them important would depend in part on
whether you think large Smith sets may occur in real elections. On the
one hand, they haven't so far; on the other, adoption of a Condorcet
method might lead to a richer political landscape where they could.

MAM and River may also be simpler to explain than Schulze, since a brief
description of beatpaths require recursion, and recursion is a tricky
concept to get if you haven't already been exposed to it.

>> MAM's brief definition just says:
>>
>> A defeat is affirmed if it isn't the weakest defeat in a cycle whose
>> other defeats are affirmed.

How about, for MAM:

Sort defeats in order from strongest to weakest. Going from strongest to
weakest, affirm a defeat unless it forms a cycle with earlier affirmed
defeats. The candidate who isn't beaten in any affirmed defeat wins.

Schulze:

A has a beatpath to B if A beats B or A beats someone who has a beatpath
to B. The strength of a beatpath is defined by the strength of its
weakest defeat. The candidate who, for every other candidate has a
stronger beatpath to that candidate than that candidate has to him, wins.

Neither definition goes into the subtlety of tiebreakers (random voter
hierarchy for MAM) nor margins vs wv.

> If you want a method that (like WV) meets Minimal Defense then I prefer
> Forest's  "Max Covered Approval"  (which would nearly always be equivalent
> to Smith//Approval, which I also like.)

If you had to pick a method passing Minimal Defense but not using
Approval information, which would it be? (That is, do you have any
favorites in that category, and if so, which?)