Posts made by Toby Pereira

@abel I suppose you could see the primary system as a bit of a gamble in this sense. You want to beat the other party, but you also want to do so with a candidate that is as popular as possible within the party. If your party is favourite to win anyway, you might be more inclined to just pick the most popular candidate within the party. If it's a closer election you might look at who is most likely to beat the other party. So there would be some balancing.

@bmjacobs OK, I think I get that. But I still don't think the graph is correct - it's giving a different measurement for a deterministic and non-deterministic systems. For non-deterministic methods, it seems to be working on the probability of getting elected, which I presume is what the "controlled winning probability" on the y axis means. But for the deterministic methods, it just gives a score of 100 if they are guaranteed to be elected and 0 otherwise.

If it's a about guaranteed election then the non-deterministic methods should give 0 across the board. If it's probabilistic, then the non-deterministic methods are correct on the graph but the deterministic ones are wrong - though there isn't an exact probability you can give as it depends on voting patterns.

@bmjacobs Interesting article, but a couple of things. Where does it come from that in Borda you need 2/3 of the vote to ensure a win? Also Borda and winner-takes-all systems wouldn't have the step function if there are more than two candidates. E.g. having 40% of the vote under First Past the Post will still give you the win in many elections. If it's to guarantee the win then yes, but I don't think it's clear that that's what the graph is trying to say.

@mkeypaige A lot of those topics have Wikipedia or Electowiki pages, which describe them quite well, and there are also YouTube videos which discuss a lot of them. Some of the later stuff I wouldn't even know what they are. But I'll give you some links.

Ranked voting - Wikipedia

1. Plurality system (also known as First Past the Post) - Wikipedia, CGP Grey video

2. Ranked Choice Voting (also known as Instant Runoff Voting, Alternative Vote among others): Wikipedia, CGP Grey video

3. Condorcet methods: Wikipedia, Carneades.org video

4. Borda Count: Wikipedia, Carneades.org video

5. Majority criterion: Wikipedia, Becky Moening video

6. Unanimity criterion: Wikipedia article on Pareto Efficiency, Eric Pacuit video

7. Condorcet winner criterion: Wikipedia, Carneades.org video

8. Monotonicity criterion: Electowiki article, Becky Moening video

9. IIA (Independence of Irrelevant Alternatives) criterion: Wikipedia, Carneades.org video

10. Manipulability: Wikipedia article on strategic voting, Katherine Heller video

11. Random dictator: Wikipedia article, Carneades.org video

12. Approval voting: Wikipedia, CGP Grey video

That's the first section covered. Let me know if this is useful at all and I can get some links for the others.

@cfrank said in Nonmonotonic methods are unconstitutional in Germany?:

What I mean is, it should not be the case that two rational voters with equal access to information, and who cast the exact same ballot, nevertheless conflict in their expectations about how that ballot will contribute to the electoral result. Non-monotonicity introduces unnecessary conflicts of interest. So I really doubt that under sufficient scrutiny, any non-monotonic system would actually stand up to the phrasing of the law.
Whether or not they are unconstitutional in Germany or elsewhere, I do believe that any voting system that is not monotonic or that fails independence of clones should be considered fully improper and disqualified from being part of any official public elections. I.e. they should by all reason be illegal in that context. And perhaps actually are in spirit or will be found formally illegal in Germany.

I consider failing participation to be on the same level as failing monotonicity. Philosophically I'd say they are very similar, even if they tend to happen for different mathematical reasons. But because participation is a more "expensive" criterion, people tend to be less harsh on methods that fail it.

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.

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 said in Cumulative voting: more popular in corporations than in politics:

@cfrank the main issue with STV is that it is fairly complex, making it somewhat challenging to implement and also to follow the algorithmic logic with any real detail. I read through the ballot tallying report for an Australian Senate election a few years back, and it was awful and tedious -- iirc it was over 60 pages long. By comparison, a cumulative vote tallying report would just be one page of numbers.

It seems that MMP is a much simpler and easier method than STV that gives reasonable results. (Whether the official inclusion of parties is a problem or not is philosophical speculation considering that political parties exist in reality, but that is a separate matter.) Are there any other methods for proportional representation that are simple enough to be both practical and easily comprehensible to concerned citizens?

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.

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

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.

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.

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

@toby-pereira said:

@ex-dente-leonem Is Viability-aware just strategic voting?

More or less; each simulated election is preceded by an approval poll which factors into viability-aware strategies.

Also how do all the methods do under one-sided strategy? So strategic voting versus honest voting.

The original vse-sim had one-sided strategy analysis, but the newest version appears to have dropped that in favor of Pivotal Voter Strategic Incentive, which seems to measure how much coordination by one faction it takes to change the outcome. The lower the coordination needed, the greater the PVSI, while near-zero means little strategic effect and negative PVSI indicates greater risk of the strategy backfiring.

I see. While also a useful metric, it is different enough for it to be worth having both. As it is we just see the VSE scores and separately this co-ordination measure. But it would be nice to know how much it could drop the VSE by.

@ex-dente-leonem Is Viability-aware just strategic voting? Also how do all the methods do under one-sided strategy? So strategic voting versus honest voting.

@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).

@aetius said in A simple improvement of Maximin:

@toby-pereira sure, that's a reasonable doubt. I'll respond in three ways:
(1) In section 5 of our paper we perform experiments to check whether our rules decrease the total social welfare of the voters (measured by Borda scores - I believe that any other measure would yield similar results). This is not the case, so we do not sacrifice the voters' satisfaction by taking parties into account.
(2) The rule I described in the post is Condorcet-consistent, so over 90% of time when the voters' ballots clearly indicate the winner, alliances do not matter. They start to matter only if there are cycles, which means that no candidate has a clear support from the voters.
(3) Besides, this rule cannot elect weak candidates only because they are from the winning alliance. E.g. if there is a candidate who'd be Condorcet winner if they are the only nominate of their party, they'll be the winner.

Thanks for the reply. One thing I meant to mention was that in a close three-way battle, two candidates could just "team up", and if there is a cycle, one of them would be guaranteed to win (if I understand correctly).

@aetius I have only read the beginning of the paper, but my initial thought it that elections are not there for the benefit of parties, but for voters to choose the candidate(s) the like, so I'm not sure I see this as a good thing in principle. If voters decide the muddy the waters by not voting strictly along party lines, it's up to them.

@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 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).

@k98kurz Cumulative voting for committees is very like single non-transferable vote (and First Past the Post for single-winner). As said, it fails independence of clones, and it requires much more precision strategic voting to get any sort of sensible result.

@Lime As mentioned upthread, there is the probabilistic transformation as well, which you might prefer from the point of view being discussed. I'm not a big fan of it though.

@toby-pereira said in Optimal cardinal proportional representation:

There is also the probabilistic transformation, which I see as inferior to KP as well. Someone might give scores of 9 and 1 (out of 10) to 2 candidates A and B respectively. KP would split the voter as follows:

0.1: -
0.8: A
0.1: AB

The probabilistic transformation would give:

0.09: -
0.81: A
0.09: AB
0.01: B

@lime said in Optimal cardinal proportional representation:

@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.)

Yes, that is a way that someone could vote. However, I wouldn't see it as some sort of objective standard, so would still see scale invariance as desirable. I think you mentioned this point previously in a discussion about normalising ballots, and I didn't get round to responding at the time.

The method being discussed renormalises using ratios when candidates are eliminated, so if someone gives scores of 1 and 0 (out of e.g. 5) to two candidates, this could later become 5 and 0 after some elimination, whereas scores of 5 and 1 would be locked in as that. However, even if it is assumed that people vote in the manner you described, I still don't think this is good voting method behaviour. If I give scores of 5, 1 and 0, I would still prefer the 5 to the 1 by more than I prefer the 1 to the 0, and I think voters generally would not be happy that they lose some of the normalisation power in the 5-1 situation but not in the 1-0 situation.