[EM] One benefit to nonmonotone methods

[Forest Simmons]

Very Good!

That should cure my bad habit of treating Implicit Approval and MaxPS as
though they were interchangeable.

I wonder if we replaced MaxPS with MaxPS+MinPS ... would that work?

For three candidates with complete rankings, MaxPS+MinPS should be the same
as TotalPS which should be equivalent to Borda ... which is monotone... at
least in a stand-alone context ... right?

Let's see ... before the seventeen changed their mind, the respective Borda
Counts for A,B,and C were

44-28, 0, and 28-44

Afterwards they become ...

-1, 17, -16

So both before and after, C had the least Borda Count.

So there's a possibility that this sum of max and min PS might work.

Put another way ...  average PS is equivalent to Borda ... and when there
are only three candidates average is just half the sum of max and min PS.

Why not just going with Borda?

Because Borda is clone dependent.


fws


On Sun, Jul 30, 2023, 6:17 PM James Faran <jjfaran at buffalo.edu> wrote:

> Not monotone?
>
> 44 A>B>C
> 28 C>A>B
> 28 B>C>A
>
> An A>B>C>A cycle, but C has the least support, so C and, because C beats A
> pairwise, A as well, are eliminated so B wins.  Yay, B!
>
> Hold on, 17 A>B>C voters decide they like B better than A and become B>A>C
> voters.
>
> 27 A>B>C
> 28 C>A>B
> 28 B>C>A
> 17 B>A>C
>
> Now we have the same cycle, but A has the smallest MaxPairwiseSupport, so
> A and B are eliminated and C wins! The 17 voters made their new favorite
> lose.
>
> Or I may be misunderstanding something.
>
> Jim Faran
> ------------------------------
> *From:* Election-Methods <election-methods-bounces at lists.electorama.com>
> on behalf of Forest Simmons <forest.simmons21 at gmail.com>
> *Sent:* Sunday, July 30, 2023 8:36 PM
> *To:* Kristofer Munsterhjelm <km_elmet at t-online.de>
> *Cc:* EM <election-methods at lists.electorama.com>
> *Subject:* Re: [EM] One benefit to nonmonotone methods
>
> 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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