[EM] Strategy-free criterion

[Kevin Venzke]

Hi Chris,

> > MD basically says that if there are two frontrunners and everyone truncates their
> > less liked frontrunner, then the worse frontrunner won't win. If this property
> > doesn't hold, it means the majority has done something to stop the method from
> > "seeing" their majority, which is surely that they ranked other candidates above
> > the preferred frontrunner.
> 
> Instead of "above the preferred frontrunner" don't you mean *below the 
> less-liked frontrunner*?

I don't mean that, and I am not sure how "below the less-liked frontrunner" would
apply? Who in 49/24/27 ranks a candidate below the less-liked frontrunner?

> The classic example used by people who like Winning Votes and Approval 
> to flout those method's compliance with MD (versus the MD failures of 
> Margins and IRV):
> 
> 49 A (sincere might be A>B)
> 24 B  (sincere might be B>C)
> 27 C>B (sincere)
> 
> A>C  49-27 (=23)     C>B  27-24  (=3)    B>A  51-49  (=2)
> 
> By Margins A's defeat is the weakest and MinMax (and methods that are 
> equivalent to it with only 3 candidates, such as Ranked Pairs and 
> Schulze) using margins elects A.
> 
> But Minimal Defense says "not A" because more than half the voters voted 
> B above A and A not above equal-bottom.  MD has no problem with the 27 
> C>B voters who ranked a candidate above their preferred (presumably 
> perceived) "frontrunner."

What I'm saying is that if a method fails MD in this scenario, the likely issue
is that the C>B voters ranked C above B, and if they didn't do that, then A
could've been defeated. In this scenario, that is fairly obvious, but it's true
in general, that MD failures are almost always instances of a majority (or part of
one) facing compromise incentive.

In practice you can liken MD / SDSC to a weak form of the strong FBC, and liken SFC
to a weak form of Later-no-harm.

Incidentally I agree with what CLC seems to suggest, that you don't have to discuss
burial to find merit in MD. There are methods with no burial incentive that satisfy
MD and it is certainly not meaningless in those contexts, because it addresses
compromise.

> > I would not like to see SFC as totally obsolete, since it was one of the motivating
> > criteria (along with MD and weak FBC) for my methods MDDA and MAMPO :)
> 
> Inventing those methods was some achievement as a thought experiment to 
> demonstrate that certain criteria are mutually compatible.
> 
> But MDDA spectacularly fails the maximum-absurdity criterion 
> Mono-add-Plump, a very interesting fact that isn't mentioned on its 
> electowiki page.

I can hardly advocate MDDA now due to the Plurality failure. However, it performs
very well in my truncation simulation, as does a method with very similar results,
which I call RMPA (River Majority Pass Approval). However, RMPA doesn't actually
satisfy FBC, so I can't list it in the same breath as the other two.

In RMPA we go down the list of candidates in order of descending implicit approval,
and process each candidate's full majority pairwise wins River-style (using the
"bins" conception, I would suggest). There is no need to sort the propositions; it's
enough to treat each candidate's wins in a batch with arbitrary order. Elect the
owner of the "bin" that the approval winner ends up in.

> Of course the method also fails Irrelevant Ballots Independence. If we now add 3
> ballots that plump for X, the majority threshold rises to 52 and so C's
> majority-strength defeat goes away and C wins again by being the most approved
> candidate.
> 
> This demonstration of Mono-add-Plump failure doesn't apply to MAMPO, but that method
> would also fail Irrelevant Ballots Independence. It may be far less bad.

Something I will have to post about at some point is what a game-changer it is if we
take it as an assumption that elections will have two frontrunners and all voters
use frontrunner truncation strategy. Arbitrary-looking majority rules prove very
useful in maximizing performance.

In such a setting I find that MAMPO is usually not as good as MDDA or RMPA, but all
of them outperform all Condorcet methods at sincere Condorcet efficiency.

It's a different approach from what I usually use, to say "let's just assume voters
act in this way regardless of what the method is." We may not be standing on firm
ground there. But I find it a bit intuitive to think voters will mainly truncate
worse frontrunners. Compromise incentive isn't even completely ignored: By having
voters refuse to compromise, methods that depend on it this to work well (such as
FPP) are penalized in the analysis.

Kevin
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