[EM] MinMax Opposition

John Karr brainbuz at brainbuz.org
Thu Nov 5 14:05:10 PST 2020

Thanks for your reply!

If MMPO could be fixed or fixed with a trivial LNH violation, then it 
would be a very attractive option. It sounds like others have looked at 
this before. I think it warrants more coverage in the main electowiki, 
but I don't have the background to add it.


Given sincere ballots I consider any method that meets the Smith 
Criteria superior. Opposing that for the Voters to cast sincere ballots 
LNH is a juggernaut. I currently support Smith-IRV as it is simple and 
has the least LNH possible for a Smith compliant method. Smith-MMPO is 
probably still worth further investigation, but would require extra 
steps to exclude plurality violation.

As an advocate I'm searching for a compromise option with less LNH 
effect than Smith-IRV (or Smith-MMPO) that produces better results than 
IRV. To have sincere ballots the voter must perceive dropping a 
supported choice for LNH concern to be far outweighed by the increased 
chance an unsupported choice will win.

For Vote::Count I spent some effort exploring Redacting Condorcet vs IRV 
Methods, one of the approaches can be used to measure the later harm 
effect (by determining how many second choice votes the Condorcet winner 
needed from the IRV winner), and also to use it to set a Later Harm 
Tolerance threshold against the Margin of the Condorcet Winner over the 
IRV Winner. With no tolerance it almost never overturned IRV. A simpler 
variant which only redacts the first choice votes of the IRV winner 
produced better results, and is likely to fall within the Later Harm 
tolerance I expressed earlier, but is moderately complex, which detracts 
from its viability when we're in the phase of trying to get RCV adapted.

The documentation is here: 

On 11/2/20 10:11 PM, Kevin Venzke wrote:

> 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 think
> he may have DSC in mind there.)
> I think I agree with Kristofer at least in that, if you modify the 
> method such
> that you break compliance with the criteria, you'll have the burden of 
> showing
> that the method still performs better than average according to your 
> metric. And
> you 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 
> from
> Woodall's CDTT, which is the Schwartz set defined using only the 
> majority-strength
> pairwise contests. This set is more LNHarm-friendly (basically because 
> it is less
> responsive to changes in the matrix), but remains incompatible with 
> LNHarm given
> 4+ candidates. The combined method also doesn't satisfy Plurality. Off 
> the top of
> my head all it really does is fix the standard MinMax Clone-Winner failure
> scenario.
> 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 with
> something that isn't quite satisfying from a Condorcet perspective.
> I'll mention a couple other ranked LNHarm methods. There's Woodall's 
> Descending
> Solid Coalitions (DSC) which satisfies Participation and also clone 
> independence.
> Your ranked ballot is basically translated into votes for each set of 
> candidates
> you prefer over every candidate ranked lower. Then there's a Tideman-like
> procedure to lock results. You can easily make your vote useless if 
> you have an
> unusual 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 think
> Chain Runoff is a more evocative name now. Sort the candidates by first
> preference count. (You can't equal rank.) You examine the pairwise contest
> between each adjacent pair of candidates, starting at the top and 
> going down. But
> you stop as soon as the lower-ranked (i.e. fewer first preferences) 
> candidate
> does not have a full majority (i.e. of all voters) win over his 
> opponent. That
> opponent is elected.
> (Equivalently, elect the candidate with the most first preferences who 
> both has a
> majority-strength win over the candidate ranked above him (or has no such
> candidate), and also does not have a majority-strength loss to the 
> candidate
> ranked beneath him (or has no such candidate).)
> This satisfies LNHarm because adding a new lower preference A>B can 
> only have an
> effect if B is currently the winner. It satisfies Plurality since the 
> winner of
> the method is either the first preference winner, or else has a 
> majority-strength
> pairwise win over somebody (meaning only a majority favorite could 
> disqualify
> them). On the negative side, there is a monotonicity issue in that a 
> losing
> candidate can wish they had received fewer first preferences, as it 
> would have
> given them more advantageous match-ups.
> Just a few comments on the topic.
> Kevin
> 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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