Posts made by Lime

I've thought of a slightly-simpler variant on MARS: Each candidate's score is equal to their range score, plus the score of the strongest (highest-scored) candidate they majority-beat. Thinking through what properties this would have.

@gregw said in ABC voting and BTR-Score are the single best methods by VSE I've ever seen.:

Are you uncomfortable with BTR-Score? As a Condorcet method, it should be safer than most new systems. It would elect the “beats all” winner if there is one. Otherwise, it would elect someone from the Smith set.

The problem is with strategic voters. Lots of Smith-efficient methods do really badly when voters are strategic, unfortunately, including the ones I listed (Ranked Pairs & such).

@toby-pereira said in ABC voting and BTR-Score are the single best methods by VSE I've ever seen.:

What we really need (and which is unattainable right now for most methods) is to see what would happen in real life elections with real voters. Not under the assumption that a particular simplistic strategy model gives good results, and not even that the game theoretically optimal strategy leads to good results, but that real life voter behaviour would lead to good results.

Technically yes, but I'd feel very uncomfortable with any method where the game-theoretically optimal strategy leads to bad results, even if experiments showed the method doing well. I'd be worried voters just haven't figured out the correct strategy yet, and as soon as someone explains it to them all hell will break loose.

This is how Italy's parliament got so screwed up. They had a theoretically proportional mechanism that can be broken. It looked fine at first—because it took Berlusconi 2 or 3 election cycles to recognize the loophole and exploit the hell out of it.

So, in other words, you need an actual proof, not just "well, when I tried a couple strategies..." Otherwise, you'll find out 5-10 years later that there's some edge case where your method is a complete disaster, and after the whole IRV fiasco, electoral reform will end up completely and thoroughly discredited. (Italy went back to a mixed FPP-proportional system after the screwup.)

@ex-dente-leonem said in ABC voting and BTR-Score are the single best methods by VSE I've ever seen.:

@lime said:

The CPE paper shows very strong results for Ranked Pairs under strategic voting. This is well-known to be wildly incorrect: the optimal strategy for any case with 3 major candidates is a mixed/randomized burial strategy that ends up producing the same result as Borda, i.e. the winner is completely random and even minor (universally-despised) candidates have a high probability of winning.

I don't believe Ranked Pairs is analyzed in the STAR paper, unless you're thinking of Jameson Quinn's original VSE document or a different paper.

I think the important takeaway here is less about trying to game out every strategy possible than the fact of how these models perform under the same conditions as what the authors believe to be their best modeled simulations, given that such simulations are an integral part of EVC's and others' advocacy efforts. (For quite necessary reasons, as we have no historical results for many methods, and as noted such historical samples would likely be unacceptably small or fail to capture the development of strategy over time.) I'd definitely welcome further testing in other simulations with mixed strategies and other voter models as realistic as we can make them.

I believe the above should be taken as impetus for theoretical analysis of why these methods seem to perform so well, and the key may be that they're all hybrid methods involving pairwise comparisons and sequential eliminations for all candidates at some point, which reasonably makes potential strategies that much harder to coordinate.

I'm talking about the original VSE document, yes. And my point is that I think the strategic voting assumptions are wholly unrealistic to the point that they will probably miss the vast majority of pathologies, like it does for Ranked Pairs and Schulze.

Thanks for these simulations, they're definitely interesting @Ex-dente-leonem

That said, I think we might be making the mistake of getting sucked deeper and deeper into a drunkard's search. The simulation results here don't really say much, except that we haven't figured out a strategy that breaks Smith//Score or ABC voting yet. That's not surprising, given we only tested 5 of them.

The difficult part of modeling voters isn't showing that one strategy or another doesn't lead to bad results. It's showing that the best possible strategy leads to good results. There's nothing wrong with testing out some strategies like in these simulations, but these are all preliminary findings and can only rule voting methods out, not in.

Just because every integer between 1 and 340 satisfies your conjecture, doesn't mean your conjecture is true. You still need to prove your conjecture.

This isn't just hypothetical. The CPE paper shows very strong results for Ranked Pairs under strategic voting. This is well-known to be wildly incorrect: the optimal strategy for any case with 3 major candidates is a mixed/randomized burial strategy that ends up producing the same result as Borda, i.e. the winner is completely random and even minor (universally-despised) candidates have a high probability of winning.

The methodology here completely fails to pick up on this, because it only tests pure strategies (i.e. no randomness and everyone plays the same strategy). In practice, pure strategies are rarely, if ever, the best. Ignoring mixed strategies has led the whole field of political science on a 15-year wild goose-chicken-chase that would've been avoided if anyone had taken Game Theory 101.

The issue is that defining VSE for the multi-winner case is, uhh, complicated. In particular, PR doesn't do a good job of satisfying VSE under the most intuitive model, one where voters' utilities are additive, i.e. satisfaction equals the sum of scores you assign to each candidate. If that was actually the case, the best methods would be winner-take-all (pick the candidates with the highest scores).

The ideal situation would be to have voters score each set of candidates, e.g. "a committee with A, B, C has a score of 3; one with A, B, D has a score of 5, ...". Then we could maximize the sum of scores. However, that's completely impractical for voters, it's difficult to model utilities, and a method like this would be extremely vulnerable to strategic exaggeration.

So, in the proportional context, so far we've found it easier to just deal with pass/fail criteria rather than VSE. That's not to say VSE couldn't be extended to the multiwinner context, it's just that it's complicated and we don't know how yet.

@jack-waugh said in A simple improvement of Maximin:

How would candidates who are in partial agreement about issues that are important to them (such as bombing other countries or not) but in disagreement on other issues (e. g. cutting up children) decide whether to ally?

Dunno, that's up to them. In my own proposal, it would be if two candidates want an enforced guarantee of later-no-harm so they don't end up locked into a Burr dilemma.

(That said, I'm becoming increasingly convinced that the Burr dilemma isn't real, and it's caused by unrealistic modeling or a poor understanding of game theory.)

I already gave my response to this in DMs with you, so I'll copy-paste it here:

I like the rule well enough, and it seems good! I’m a bit more interested in whether we can use party identification to solve the Burr dilemma, and score's problem with ensuring zero-information honesty.

Say we made it so that, in the first step, we used score voting: each alliance's score is the score of its best-performing candidate, and we eliminate any candidates with score less than or equal to the second-best alliance's score. Then, in the second round, we use some method like MMPO or quadratic voting that encourages honest rankings in zero-information elections.

The goal being to get semi-honest rankings of parties, combined with fully-honest rankings of candidates. Voters will probably know a lot about the viability of different alliances, so those votes can't be guaranteed to be honest. But candidates within each alliance are likely to be closely-matched, so in that case, voters are encouraged to give a sincere ordering.

This method is effectively STAR+; it's like STAR, but the runoff includes all similarly-popular candidates of the same party.

@cfrank said in What type of party system are STAR and approval voting likely to promote, are there papers on this?:

I don’t think there are any good empirical and longitudinal case studies on emergent behaviors in government like party formation or coalitions as a consequence of either voting method. Approval voting and STAR aren’t used in many national elections as far as I am aware. Studies that suggest any patterns of emergent behaviors of that type related to approval voting or STAR voting would likely be simulations via agent-based modeling.

So far, no modern country has used a system other than plurality or plurality-with-runoff to elect its head of state/government. (Although Venice did use approval voting for most of its history.) So, sadly, there's not much—if any—empirical research.

@gregw said in score interval: score with additional protection against the chicken dilemma:

Unfortunately I do not understand this. A simple as possible explanation might help.

As in, eliminate any candidate with an average rating below 50% of the maximum.

@jack-waugh said in On one-sided strategy:

@lime said in On one-sided strategy:

@jack-waugh said in On one-sided strategy:

Give your favorites the top score and your most hated the bottom score. If you have a compromise candidate, and if you are convinced that your favorites are very unpopular or unknown, exaggerate the score of the compromise candidate almost up to the next higher candidates, but not quite up to them.

In practice, this is the same as thresholding, assuming you rate your compromise close enough to perfect.

What you mean, "rate"? In my heart, or on my ballot?

On your ballot.

@casimir said in score interval: score with additional protection against the chicken dilemma:

There is a simpler variant that uses plain score and normalizes the scores in the second round.

1. Voters score candidates on a scale 0-5.
2. Regard any defeat as a tie when it can be reversed by subtracting all common scores between those candidates of the winner's score.
3. Eliminate all candidates with at least one defeat.
4. Normalize the scores for the remaining candidates.
5. The remaining candidate with the highest score is declared winner.

Or even simpler (but less clean):

1. Voters score candidates on a scale 0-5.
2. The two highest scoring candidates and everyone with equal or over 50% of possible score enter the runoff.
3. Normalize the scores for the remaining candidates.
4. The remaining candidate with the highest score is declared winner.

This second variant behaves like STAR in the case when there is at most two candidates with 50%+ scores. This means, it's a simple Chicken Dilemma improvement to STAR.

Here's a particularly simple and attractive method:

1. Eliminate all candidates scored below 50%.
2. Use quadratic voting to pick the best remaining candidate. (Rebrand it as equal-weight voting, by framing it as taking each ballot and dividing by its "weight"—i.e. sum of squares.)

Why the first elimination step? Well in score, approval, etc. with optimal strategy and perfect information, only one candidate should get over 50% of the vote. This candidate should be the Condorcet winner. That means that for candidates scoring over 50%, voters don't have enough information to know which (if any) is the Condorcet winner.

@jack-waugh said in On one-sided strategy:

Give your favorites the top score and your most hated the bottom score. If you have a compromise candidate, and if you are convinced that your favorites are very unpopular or unknown, exaggerate the score of the compromise candidate almost up to the next higher candidates, but not quite up to them.

In practice, this is the same as thresholding, assuming you rate your compromise close enough to perfect.

@toby-pereira said in On one-sided strategy:

@lime Could you give a more fleshed-out example of what might happen in IRV with one-sided strategy? And under Condorcet (whichever versions you think might be illustrative).

In Condorcet-IRV methods, I think one-sided strategy becomes plausible whenever you have a center squeeze. If Democrats buried Begich in Alaska to create a cycle, this would have left Begich with the fewest first-place votes (despite being the sincere Condorcet winner). Given Republicans didn't do favorite-betrayal to elect Begich in the actual race, I suspect they wouldn't have in Benham either.

@chocopi said in score interval: score with additional protection against the chicken dilemma:

In prisoner's dilemma, it is just as rational for two criminals who have telepathy to have each other's backs as it is for two criminals who are isolated to sell each other out. Neither outcome should be surprising.
Chicken dilemma is similar. If Sanders voters have perfectly single-peaked preferences and only care about maximizing their preferences in this one election, then they will line their perfectly-rational and well-behaved butts up behind Clinton to beat Trump.

Wait, but it's not similar. The prisoner's dilemma is taught in game theory classes as a way to teach students a simple game with a dominant (always-best) strategy. The chicken dilemma is a way to teach students about equilibrium-refinement.

Basically, there are some games with multiple Nash equilibria, i.e. there are many "potentially rational" strategies you could use. To predict which one someone will actually use, we need to put reasonable constraints on what kinds of beliefs we'd consider rational. There's two pure Nash equilibria for chicken: If you're 100% certain your opponent will swerve, you should plow ahead. If you're 100% certain they won't, you should swerve.

But what if you're not 100% certain what your opponent will do? Then you have to look for the trembling-hand-proper equilibrium. Say I know my opponent isn't perfect: they can make mistakes or slipups in playing a strategy, or maybe some of their voters won't get the message about the strategy I'm telling them to use. Basically, I'm going to rule out any situations where 100% of my opponent's voters use a certain strategy. Maybe we can say that for each voter, there's a 99% chance they'll use the correct strategy, but a 1% chance they'll mess up their ballot.

This is a very powerful refinement, and you can use it to prove that both bullet-voting and friendly-voting are irrational in the chicken model. 100% bullet-voting risks throwing the election to the Republicans. 100% friendly-voting means you can't the election to the other subfaction with 100% probability. The rational strategy is a mixed strategy, i.e. in equilibrium some Sanders voters will support Clinton and others won't.

For example, say Clinton's faction is polling 35% and Sanders' faction is polling 25%, with Trump at 40%. Then, the optimal strategy is for >20% of Sanders' voters to approve Clinton (or equivalently, for all of them to give a 20/100 on a score ballot). This lets Clinton win with more than 1/5 * .25 + .35 = 40% of the vote, while keeping the margin between Clinton and Sanders as tight as possible in case there's a polling error.

Where exactly the scores end up depends on details like exact utilities and uncertainty. You'll get more cooperation with better polling; that lets you rule the smallest faction out of contention with 100% certainty. You also get more cooperation with more polarization (i.e. if voters care more about blocking the other party than about supporting their favorite).

The main point, though, is that bullet-voting is irrational in this chicken dilemma. Clinton is still (by far) the most-likely winner in this situation, assuming she's the Condorcet winner. We can also work out where, exactly Clinton will end up with perfect strategy, and the answer is "just above 40%, barely edging out Trump and Sanders". In approval, the optimal strategy is to randomize whether you approve Clinton. (In score, I expect a fair chunk of voters to use the intermediate scores instead because that's simpler, but it gives the same result.)

@chocopi said in score interval: score with additional protection against the chicken dilemma:

Perfectly-informed, perfectly-rational tactical voting generate a Condorcet winner. This is true of all (relevant) voting systems (including plurality), and is the inherent nature of a Condorcet winner.

I think this is missing the most important caveat, which is mentioned above. The problem isn't information, it's that any such move has to be perfectly coordinated. Voters need to take actions that are individually irrational, despite there being no way to enforce these strategies. The reason Johnson lost is because it would be individually irrational for a voter to switch from backing Trump to backing Johnson, unless they expected everyone else to do the same. (Whereas anyone who preferred Johnson to Clinton and Trump should've approved Johnson.)

IIRC Vox did a poll with approval in 2016, and found Johnson neck-and-neck with Clinton (which lines up with polls they'd be competitive in a one-on-one).

Before today, I thought one-sided strategy was impossible. It seems bizarre to imagine a situation where only one of the two parties is able to work out the correct solution.

Today I came across a video explaining how to vote strategically in Schulze. It said that, if you really want to make your vote count, you should put your favorite at the top; then, you should truncate your ballot below the candidates you think are unacceptable. This is great, right? Clean and concise explanation of a minimal defense.

Except I lied. The video was talking about IRV. This video—produced by a large, well-funded San Francisco advocacy group—was trying to "educate" everyone into using the exact opposite of the correct strategy for IRV!

This strategy is both highly ineffective and socially disastrous. It dramatically increases the risk of a center-squeeze. It would create even stronger polarization and more extremism than in our current system of FPP-with-primaries, where at least primary voters know to vote for electable candidates.

That's not to say strategy can't be done. Alaska Democrats pulled it off in the 2022 Senate race, where they managed to get everyone to rank Murkowski first. Except... Republicans didn't manage the same for Begich. That's a huge problem.

I don't know if the video I saw was stupidity or intentional disinformation. Either way, it shows a big problem with IRV and Condorcet-IRV hybrids: their complexity makes them very vulnerable to one-sided strategy. We can't expect both parties, or all voters, will be able to work out the best strategy and use it. It's completely possible that only one party will understand runoffs well enough to exploit them.

I don't think you can expect voters to consistently execute any strategy more complex than thresholding, in a way that cancels out across parties and candidates.

An unusual strength of cardinal methods is the strategy is so clearly, blatantly obvious that nobody is disadvantaged. In this sense, unlike IRV, score and approval seem remarkably resistant to one-sided strategy.

@jack-waugh said in BTR-score:

@lime said in BTR-score:

it's just a private association making a decision about whom to support.

If it is a private decision, then why does the public have to pay for it (in the US)?

Good question. You can ask the Supreme Court.
https://en.wikipedia.org/wiki/California_Democratic_Party_v._Jones

@chocopi said in BTR-score:

If a court wishes to "ban non-monotonic voting methods", they would first have to declare all partisan primaries illegal.

I'd agree with you. In practice, partisan primaries determine which candidates you can actually vote for (because of the two-party system). But from a purely legal point of view, a partisan primary isn't "part of the election"; it's just a private association making a decision about who to support.

@lime said in Optimal cardinal proportional representation:

One possible model is one where the score of each candidate is the probability they'll agree with the voter on some vote, and the objective would be to choose the committee that maximizes the probability of a majority vote on any given issue agreeing with a majority vote by the whole population.

(Oh, quick note @Toby-Pereira : I think this is a good example of why perfect location or scale invariance may not actually be ideal. If you rescale every voter's ballot to fall between 50% and 100% instead of 0-100%, that might indicate a meaningfully different situation.)