I've said previously on this group that non-deterministic elections can be a good way to simplify proportional representation. It doesn't have to be as crude as simple random ballot where you have one representative per constituency selected by the drawing of a single ballot. As I said here just earlier this month:

Proportional methods tend to just be more complex by their nature. But if you allow them to be non-deterministic then that goes away. E.g. COWPEA Lottery which uses approval ballots. Or if you have a region that elects, say, 6 candidates, voters just rank their top 6 candidates. Then you consecutively pick six ballots at random and elect the unelected candidate that is highest ranked on that ballot.

This type of method, while it doesn't guarantee a very proportional result in each region, would actually give better proportionality nationally than deterministic methods that use these smallish regions (like STV), and they also keep the election candidate-based, which other nationally proportional methods tend not to.

Random ballot with just one representative per region guarantees that honest voting is the best strategy, but I tend to think that it becomes too lotteristic at that point. With e.g. five or six chances to be elected (as in the above methods), particularly popular candidates would not be on such a knife-edge of being elected.

I also think that non-deterministic methods send out a good message - that there are no "safe seats", and that representing the electorate is a privilege and not some guaranteed right.

So while non-deterministic methods might be a tough sell, I personally prefer them for national parliaments.

Just bumping this again. Since cycle removal works quite cleanly for 3 candidates, you could have a STAR-type method where the top 3 by score go into the run-off instead of 2, and with the top 3, you then remove cycles and find the Condorcet winner.

Alternatively you might want to come up with a cloneproof measure to find the top 3, perhaps similar to the score excess method that I posted here, based on Chris Benham's approval opposition.

@gregw

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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.

@toby-pereira very interesting. Many ancient cultures employed sortition for allocating responsibilities or making decisions, though perhaps this will be a more difficult sell without the appeal to "the will of the gods" becoming rhetorically effective again.

As said, voters can often face a dilemma of whether to approve someone or not. What counts as approval etc. If I approve my second favourite candidate, what if it turns out my favourite could have won after all?

Also under ranked voting, ranks have less of an obvious meaning so a voter doesn't have to feel they are explicitly endorsing a candidate when they rank them over someone else. Say my preference order is A>B>C and B and C are the frontrunners, but I hate both B and C while preferring B to C. I might happily rank A>B>C. But to explicitly approve B might be a step too far, even though it's the strategically optimal vote for me.

Also, it really invites people to say that it violates one person, one vote, and you have to explain why it doesn't.

@k98kurz 3-2-1 Voting comes to mind for a method which uses a proper negative vote in the form of a "reject" option which is treated differently

@toby-pereira said in Optimal cardinal proportional representation:

By the way, since PAV with infinite clones passes core (which it doesn't with a limited number of candidates), I presume the optimal version probably is properly proportional (passes perfect representation). I might update my paper with this in at some point.

I have updated the paper to mention the proportionality of Optimal PAV (with variable candidate weight allowed), which allows for a proper comparison with COWPEA - these two methods being the main candidates for a truly optimal cardinal PR method (practicalities aside).

@toby-pereira that's correct. And I believe that if this teaming is honest (the candidates are actually similar and don't want to spoil each other) then it is not the problem. Note that under standard (not spoiler-proof) voting rules, one of the candidates in the cycle could just quit the election, allowing the other candidate to win. We get rid of such strategic considerations here.

On the other hand, dishonest teaming shouldn't happen, since it is only profitable for the candidate who wins, not for the ones who lose nevertheless. Besides, in close battles, the very fact of dishonest teaming can outrage the voters (especially the supporters of the still losing candidate) and affect their preferences enough to change the whole situation.

We who want to eliminate vote-splitting and spoiler effects have grounds to choose a system that the public can easily understand. Does anyone think this system passes muster in that regard?

@jack-waugh This seems to be a very abstract proof of something that doesn't even seem to be true - an ordinal voting system can't be continuous, respect anonymity and unanimity. At the end of the video he asks about an election (using FPTP) used to elect a pizza topping. He says he personally thinks the most likely condition to fail is continuity. He personally thinks? I mean, does it? I'd say that by any reasonable definition of continuity, FPTP doesn't fail. You don't get any weird jumps in the result after changing one vote, like you might do in a Condorcet method if e.g. a cycle suddenly appears or gets broken. You wouldn't get any discontinuities in the Borda count either.

Edit - Just looking at the comments, people are talking about how any change in a vote is a discrete jump so it's not continuous in that respect, but that much is obvious from the start.

@lime definitely, that’s a major problem with the agent based models, the choice of parameters can’t be validated without the data. A friend of mine is trying to work with ABMs for tumor microenvironments, which in a sense may not be too far off from what we’re trying to do lol

@lime

I do not understand this part:

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.)

@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.

@isocratia yeah that kind of thing really seems counterproductive, and strange.

@gregw I think this is sensible, I would fully support it if it could be shown to stand up to formal legal scrutiny, in the sense of constitutionality. I’m not a constitutional scholar by any means, it would be advantageous to have this kind of language drafted by a competent team of constitutional lawyers if possible (if it wasn’t already). My concern is the same as before, that if it’s not very carefully approached, it could lead to rulings that become very prohibitive to reform efforts. The less possibility of any kind of constitutional challenge, the (very much) better.

@chocopi said in New voting method: Linear medians:

As part of an experiment to see if it's possible for the Democrats to hate someone more than Trump, or just to set a Guinness World Record for biggest political career implosion?

I didn't say it would be a good idea. As I mentioned, he'd have no hope, since voters are using the primary to settle on an equilibrium. The question is whether Democrats have a gun to their head that would keep them from voting for Buttigieg's third-party, even if Biden looked hopeless.

@chocopi said in New voting method: Linear medians:

I agree more with you that these edge cases can plausibly be disregarded. The very idea of anyone executing a pushover strategy is absurd--you would need exact polling, exact coordination, no counter-strategy, and face a worst-case backfire if you get any of that wrong.

I don't think voters supporting a pushover is where this really falls apart. The problem with Tideman's framework is the strategies he finds are often:

Individually unstable, and therefore couldn't occur with strategic voters. You need voters to do things like betray a favorite, even though that favorite has a good shot at winning. Sometimes they're impossible to pull off with imperfect coordination (improper equilibria, i.e. trembling-hands rule them out). Prosocial or neutral—FPP has lots of opportunities for strategy, which is a good thing, because without strategy it turns into a random lottery. Easily countered by basic defensive strategy.

Every voting system has strategy. The real concern is whether voters playing their optimal strategy creates a bad result, e.g. a turkey winning. After all, in Borda, the Strong Nash equilibrium is still the Condorcet winner, but that doesn't happen in real elections. The reason Borda is bad is because the only proper equilibrium ends up selecting a winner at random.

In Benham's method, optimal strategy looks like a center-squeeze, because whenever you have a center-squeeze setup, the largest faction can bury the Condorcet winner and elect a candidate on the wings. (That's especially true if the wings tend to be overconfident.) By contrast, in cardinal methods, the optimal strategy looks like, well, the Condorcet winner being elected.

I'd like to clarify that I think party strategy does play a huge role in FPP, IRV, or Condorcet elections, because strategy is either too complex for typical voters or there are many equilibria (and voters have to coordinate on just one). In these specific situations, voters have to follow instructions on voting cards issued by their party. In approval or score, any idiot with a pulse can work out that your best strategy is to give as many points as possible to the best frontrunner.

@chocopi said in New voting method: Linear medians:

Baldwin's is a ying-yang similarity, a method that is practically only impacted by said esoteric NP-hard strategies. (Simple compromise-burial does almost nothing.) These non-trivial Baldwin strategies are the hardest to calculate of any method, even with perfect [everything]. I think it's a fair and interesting academic question to quantify these, but I'd also raise an eyebrow (or two) at anyone listing them as a point against Baldwin's.

This is a good example of why "NP-hard"ness results are not very useful in practice. What matters is what happens if voters execute their ideal strategy. For Baldwin's method, the strategy is an absolute disaster, just like for Borda: it ends in a turkey winning with high probability.

In practice, elections have 2-5 viable candidates, so even "NP-hard" manipulation is trivial in practice. If you have just 2 candidates and a turkey, Baldwin is Borda-with-runoff, with a simple strategy: bury the leader to make sure they can't make it out of the first round. Does this have a shot of backfiring? Yes. (It has a good shot of picking a turkey, in fact.) But at its core, it's still Borda, and has the same result.

@cfrank $50+ for an ebook is excessive. Is this a college text book?

@toby-pereira said in Promoting Plain Score:

I don't see how adding half marks is simpler than doubling the range of integers.

If you have individual bubbles for 0-10, fitting all of them on one piece of paper gets hard. In addition, finding the bubble you want to use is hard.

The main distinction is between ≤6 bubbles (subitization range) vs. >6 bubbles. For more than 6 bubbles, finding the bubble you want requires a "search", which is mentally costly and discourages intermediate ratings (which are more complex).

Usually this is handled by breaking the problem down into two subitization steps. This makes finding the best bubble easy, and also makes it easy for voters who don't want that extra precision to ignore it.

@jack-waugh said in Condorcet // Score:

@toby-pereira said in Condorcet // Score:

Under Condorcet//Score, the winner could be a candidate outside the top cycle.

But she would be the Score winner, so not a bad outcome.

Not necessarily a bad outcome in its own right, but it makes the method more discontinuous than it needs to be. A candidate who isn't in the running can suddenly win because those that are in the running get too close to each other.