[EM] One benefit to nonmonotone methods

[Forest Simmons]

Monotone Banks methods are not easy to come by ... but here is the simplest
UD Monotone Banks method that I know of:

MaxPS Sorted Pairwise

Initialize a list variable L as the list of candidates in order of their
MaxPairwiseSupport.

[Break ties by considering in turn 2nd, 3rd,  ... levels of support.]

While no member of L is pairwise undefeated, update L by removing its
bottom member X as well as every candidate defeated by X.

Elect the remaining undefeated candidate highest on the list L.

It seems to me that this procedure yields a very clean, monotone,
clone-free, one pass, precinct summable, Banks efficient, UD, burial
resistant method.

Are we over-looking anything?


fws

On Sun, Jul 30, 2023, 6:21 AM Kristofer Munsterhjelm <km_elmet at t-online.de>
wrote:

> Since it's pretty quiet at the moment, here's another observation. I've
> been testing some methods that pass DMT or DMTC, and I've found out two
> things:
>
> - The "monotonized" contingent vote, where if A is the Plurality winner
> and can give some of his first preferences to some other B to displace
> the other finalist C and get B into the top two instead, A's score
> becomes A>B instead of A>C, is not that much more strategy susceptible
> than the ordinary contingent vote (0.91 vs 0.87 for 97 candidates, 10k
> elections, 32k tries per election).
>
> - But it's much harder to get the true strategy resistance of
> nonmonotone methods, because coalitional strategy is much harder to find
> than two-sided "rank who you're compromising for top, the current winner
> bottom" strategy.
>
> So even if say, a method X and its monotone variant both have strategy
> resistance 0.8, it's often harder to execute strategy against the
> nonmonotone one in practice because you can overshoot.
>
> In a monotone method, if your honest vote is A>B>C>D>E, and the current
> winner is D, and you're compromising for C, then if A>C>B>D>E works,
> then C>A>B>D>E will also work and most likely C>A>B>E>D will also work.
> So you can slam your compromise to the top and your burial target (the
> current winner) to the bottom, and that's a pretty simple strategy.
>
> But in a nonmonotone method, it's possible that A>C>B>D>E will work but
> C>A>B>D>E won't. So even though the honest election is vulnerable to
> strategy with both methods, it's harder to find the correct strategy.
>
> Thus if you absolutely need all the strategy resistance you can get,
> nonmonotone is probably where it's at. I'll still try to find a good
> monotone burial-resistant method, though!
>
> Some stats to show this effect: impartial culture, 97 voters, 5
> candidates, 50k elections, 32k coalitional tries per election:
>
> Smith,Contingent vote:
>         Ties:                      0.00612
>
>         Burial without compromise: 0.11049
>         Compromise without burial: 0.24123
>         Burial and compromise:     0.00278
>         Two-sided:                 0.00254
>          Other:                     0.51588
>
>         Total susceptibility:      0.87292
>
> Smith,Contingent vote with donation:
>         Ties:                      0.00904
>
>         Burial without compromise: 0.13044
>         Compromise without burial: 0.23402
>         Burial and compromise:     0.01158
>         Two-sided:                 0.54180
>          Other:                     4e-05
>
>         Total susceptibility:      0.91788
>
> The "Other" category (which contains pushover and pushover-like
> strategy) has been almost entirely emptied, and that strategy has become
> two-sided instead.
>
> (Two-sided is the fraction of elections where neither burial nor
> compromising works, but doing both at the same time works.)
>
> -km
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>
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