Global Moderators

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.