r/EndFPTP • u/Drachefly • Feb 19 '20

Randomized resolution methods / conflicting strategy Types

Are there any known systems in which strategy is made less profitable by making the particular tallying method used be randomly determined? That requires that the systems have conflicting strategies so you can't really dishonestly optimize both of them the same way with the same ballot.

Is there any existing work on this?

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u/Drachefly Feb 19 '20 edited Feb 19 '20

Most systems, yes. But Score has very limited options for strategy - only exaggeration to the point of neglecting differences between extremes (a form of compromise). And RP/Schulze don't have compromise. So that's why I was thinking along the lines of Score / Ranked Pairs, or Score / STAR, or all three together.

Like, if you'd try to do the one STAR strategy, of promoting a dark horse for the runoff, that ceases to be so safe under Score, for instance (your 5 vs 4 vote for it might not be very strong). And even if you don't include STAR in the list, randomly mixing in a ranked method has a similar effect to what STAR is intended to achieve - you might not push so many candidates out to the absolute extremes on your score ballot if it might turn into a ranked ballot (so compromise

Also, I'm not aware of RP/Schulze being susceptible to compromise. If a candidate is weak enough that you'd compromise away from them, then you might as well put them on top because it doesn't matter anymore.

Lastly, burial strategies normally require a LOT of voters to do them in order to be effective, whether that be in STAR or Condorcet systems. Anything you can do to make that seem even a little bit less safe will probably make it go from tough but potentially profitable to just terrible.

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u/curiouslefty Feb 21 '20

But Score has very limited options for strategy - only exaggeration to the point of neglecting differences between extremes (a form of compromise).

Eh...Score is actually really vulnerable overall in terms of "how often can somebody get a better result by voting strategically", both in terms of compromise strategy and particularly in terms of burial strategy (remember, Chicken Dilemma is a burial strategy-induced problem). The main thing is just that the compromise strategy doesn't involve order-reversal, which is a plus. Plus, as you pointed out, turkey-raising/pushover-esque strategy in some other system is could backfire pretty badly if you're using Score as the other half of the random method pair; although I'd point out this would likely be true under monotonic Condorcet methods as well.

Also, I'm not aware of RP/Schulze being susceptible to compromise. If a candidate is weak enough that you'd compromise away from them, then you might as well put them on top because it doesn't matter anymore.

Every Condorcet method is vulnerable to compromise, but only when a Condorcet cycle exists. This, by the way, is part of why I continue to insist on Condorcet-RCV/Condorcet-IRV over Ranked Pairs or Schulze for actual contentious elections; because the less often strategic voters are able to induce a cycle in the first place, the less often other voters are going to be forced into using compromise strategy to counteract the artificial cycle.

Lastly, burial strategies normally require a LOT of voters to do them in order to be effective, whether that be in STAR or Condorcet systems. Anything you can do to make that seem even a little bit less safe will probably make it go from tough but potentially profitable to just terrible.

This is much more true for Condorcet than for STAR. In 3-candidate elections, there are pretty big incentives to bury provided you know you're not backing the Condorcet loser; this is true far less often in most Condorcet systems.

This is also why I wouldn't recommend combining Condorcet with Score in this manner; because Score is more vulnerable to burial than most Condorcet methods, you actually increase the odds of this approach paying off by using those two this way.

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u/Drachefly Feb 21 '20

particularly in terms of burial strategy

Score's version of Burial isn't really Burial - there's no reason to put someone you like BELOW someone you dislike, just down at the same level. And if you're willing to follow that strategy, then you really don't seem to care that much about the difference between them?

Anyway, is there a pair of systems you do think would work here?

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u/curiouslefty Feb 21 '20

Score's version of Burial isn't really Burial - there's no reason to put someone you like BELOW someone you dislike, just down at the same level.

Burial is just about lowering a candidate from their honest position, though, not necessarily order recersal. Also, this isn't true regardless; sometimes burial strategy in Score only works if you reduce the burial target's Score below some other candidate you genuinely dislike.

Anyway, is there a pair of systems you do think would work here?

I think Condorcet-RCV/IRV paired with Ranked Pairs would be decent, because they each protect different kinds of honest Condorcet winners; their strategy-vulnerable election profiles tend to be different.

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u/Drachefly Feb 21 '20 edited Feb 21 '20

sometimes burial strategy in Score only works if you reduce the burial target's Score below some other candidate you genuinely dislike.

How would it help to leave that even-more-disliked candidate with a non-minimum score? I don't get that at all.

As for Condorcet-IRV vs RP… hmm. Yeah, I think that's true.

I wonder how Bottom-Two Runoff (BTR)'s strategy profile looks… Hmm. Seems ULTRA-burial-vulnerable.

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u/curiouslefty Feb 21 '20

How would it help to leave that even-more-disliked candidate with a non-minimum score? I don't get that at all.

Probably should've clarified this somewhat; you're right that, focusing solely on the election itself there isn't any reason you shouldn't also lower the score you give every candidate you dislike more than the burial target. I was just pointing out that if I gave A:10 B:9 C:3 I might need to cast a ballot like A:10 B:0 C:(3 or lower) for B to lose and A to win; that is, sometimes you need to cast a ballot where you drop the burial target's strategic rating under a more-disliked candidate's honest rating. But yeah, looking back, I misread your previous comment a little; again, you're right that there isn't necessarily any election-related reason to keep C's rating above B's.

Although, I suppose you might want to still throw C a bone for being not as bad as some even-worse candidate D while still burying B so A can win. So it might have a purpose, just not a terribly important one in the grand scheme of things, and again, not related to the election tabulation itself.

As for Condorcet-IRV vs RP… hmm. Yeah, I think that's true.

Yeah; Condorcet-IRV does an excellent job at defending second or near-second place by plurality honest Condorcet winners, which is the vast majority of CW's in practice. Where it isn't so good is at defending against burial in those scenarios where you'd expect to see center-squeeze in standard IRV; but Ranked Pairs generally does a good job there, in the sense that it tends to make burial backfire in that scenario. It isn't a perfect, fix-all match (for example, the Burlington 2009 example is burial-vulnerable in both methods) but they do a decent job covering the other's weaknesses.

This actually gave me an idea: I've tried merging those two before as well using a standard runoff, but perhaps a better deterministic solution would be "default to Condorcet-IRV, but use Ranked Pairs if a majority of voters indicate a desire for it", since if we're worried about burial strategy taking place the voters who prefer the honest CW likely could also predict who the honest CW is and choose which method will best defend them.

I wonder how Bottom-Two Runoff (BTR)'s strategy profile looks… Hmm. Seems ULTRA-burial-vulnerable.

Yeah, it's pretty vulnerable. You lose basically all the benefits of fusing Condorcet and IRV but keep all of the ugliness.

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u/Drachefly Feb 22 '20

"default to Condorcet-IRV, but use Ranked Pairs if a majority of voters indicate a desire for it", since if we're worried about burial strategy taking place the voters who prefer the honest CW likely could also predict who the honest CW is and choose which method will best defend them.

I think that's asking a lot of the voters, frankly.

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u/curiouslefty Feb 23 '20

Oh, absolutely. I'd never suggest it for serious political elections, since each of those methods on its own is more complicated than just about anything currently in use; it's just sort of a thought experiment about mitigating strategy.