[EM] MinMax Opposition

Kevin Venzke stepjak at yahoo.fr
Mon Nov 2 19:11:00 PST 2020

 Hi John,
We've discussed MMPO a lot in past years. Its main advantage is not just LNHarm,but also FBC (favorite betrayal). (Kristofer mentions Participation, but I thinkhe may have DSC in mind there.)
I think I agree with Kristofer at least in that, if you modify the method suchthat you break compliance with the criteria, you'll have the burden of showingthat the method still performs better than average according to your metric. Andyou have to keep people's attention long enough to make the case.
I can't think of too many efforts I made to "fix" MMPO while salvaging LNHarm.The closest I can think of is my idea to use MMPO to choose the winner fromWoodall's CDTT, which is the Schwartz set defined using only the majority-strengthpairwise contests. This set is more LNHarm-friendly (basically because it is lessresponsive to changes in the matrix), but remains incompatible with LNHarm given4+ candidates. The combined method also doesn't satisfy Plurality. Off the top ofmy head all it really does is fix the standard MinMax Clone-Winner failurescenario.
There is tension between Plurality, LNHarm, and respecting pairwise majorities.If you secure the first two and weaken the third, you'll probably end up withsomething that isn't quite satisfying from a Condorcet perspective.
I'll mention a couple other ranked LNHarm methods. There's Woodall's DescendingSolid Coalitions (DSC) which satisfies Participation and also clone independence.Your ranked ballot is basically translated into votes for each set of candidatesyou prefer over every candidate ranked lower. Then there's a Tideman-likeprocedure to lock results. You can easily make your vote useless if you have anunusual preference order. This gives it a strange burial strategy (technically)that resembles responding to the incentives of a chicken dilemma criterion.
I made a LNHarm method that I called Quick Runoff (QR) or Chain Runoff. I thinkChain Runoff is a more evocative name now. Sort the candidates by firstpreference count. (You can't equal rank.) You examine the pairwise contestbetween each adjacent pair of candidates, starting at the top and going down. Butyou stop as soon as the lower-ranked (i.e. fewer first preferences) candidatedoes not have a full majority (i.e. of all voters) win over his opponent. Thatopponent is elected.
(Equivalently, elect the candidate with the most first preferences who both has amajority-strength win over the candidate ranked above him (or has no suchcandidate), and also does not have a majority-strength loss to the candidateranked beneath him (or has no such candidate).)
This satisfies LNHarm because adding a new lower preference A>B can only have aneffect if B is currently the winner. It satisfies Plurality since the winner ofthe method is either the first preference winner, or else has a majority-strengthpairwise win over somebody (meaning only a majority favorite could disqualifythem). On the negative side, there is a monotonicity issue in that a losingcandidate can wish they had received fewer first preferences, as it would havegiven them more advantageous match-ups.
Just a few comments on the topic.

    Le dimanche 1 novembre 2020 à 23:51:13 UTC−6, John Karr <brainbuz at brainbuz.org> a écrit :  
 I've seen very little written about the MinMax Pairwise Opposition 
Method. Which is surprising, given that it is the only Later Harm Safe 
RCV method other than IRV (that I'm aware of).

It counts the votes against each choice and elects the choice that had 
the lowest opposition in its worst pairing.

It appears to agree with Condorcet more often than IRV does and handle 
Clones much better than IRV. Its' weakness is that it fails the 
Plurality and Condorcet Loser Criterion.

The obvious fixes involve pairing it with other methods such as 
restricting it to Smith Set when there is no Condorcet Winner (only 
helpful when there is no Condorcet Winner) or having a Runoff of the IRV 
Winner vs the MMPO winner, both of which introduce some later harm 
potential. Or alternately Dropping all choices lower in approval than 
the first choice votes for the plurality leader (while fixing Plurality 
it does not guarantee to eliminate the Condorcet loser) also introduces 
a later harm concern.

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