@sarawolk said in Allocated score (STAR-PR) centrist clones concern:

In any case, I think that Clones are a much bigger problem in hypothetical math scenarios than they ever will be in real life campaigns, and if a faction can really pull off running 2 or 3 clones that all break through and win over voters then that's frankly impressive. The reality is that if voter behavior doesn't do them in, limitations in campaign funding and volunteer power likely will.

I'm not sure I really see this as a problem of clones specifically. If parties exist, then it's fairly normal for parties to field several candidates in a multi-winner election.

But I do think the particular voting behaviour in the example election is a bit "edge case", although it's still best to avoid vulnerability to it.

While people aren't likely to cast votes that are perfectly related to utility, I still see scores as more akin to utility than to something like money, where the increase in utility drops off the higher up the scale you go.

So what I'm saying is that I see a 5 and a 0 as in the same ballpark as a 3 and a 2, rather than the 3 and 2 being preferable for equity reasons.

How good score voting is generally is a separate debate obviously, but where it gives the same tie as a pairwise method, I don't see any reason in principle to prefer one result over another. But as a tie-break, it's probably fine to choose the result you might consider less divisive.

An interesting follow-up question would be whether you would consider divisiveness over score where there isn't an exact score tie (but is a pairwise tie still) or whether it's only useful as a tie-breaker. You could, for example, reduce C's score of 3 to 2. That way, the pairwise result is still a tie but on average scores, A and B are now marginally ahead of C despite being more divisive. Is there still an argument to elect C?

Well, it partly depends on what you do with equal ranks or incomplete ballots. If an unranked candidate is scored as 0 then a 4-3-2-1 system would be different from 3-2-1-0. But if it's done in a more sensible way, they would be equivalent.

Well, aside from that, I think Arrow's Theorem is overstated in terms of its importance anyway. Pretty much all ranked-ballot methods fail IIA and if they don't they are unreasonable in some other manner. This has been known for ages anyway as it is a logical consequence of the Condorcet paradox.

So Arrow's Theorem was no great paradigm shift in our understanding. It's a non-event if you ask me.

Yeah, I mean ChatGPT has some big holes in its ability (as I've complained about), but it's also a bit scary what it's capable of sometimes. I don't think anything we can do is off limits in principle to a ChatGPT type thing.

I've been looking at this and I don't think it is the best. One (minor) problem is that when you're summing the scores, for voters that haven't had any candidates elected and also gave a score of 0 to the candidate in question, you get 0/0. Obviously you just need to count it as 0 to get it to work, but it can make one suspicious that there are problems lurking beneath.

But the main problem is that it fails scale invariance. Well it passes in a multiplicative way as it is defined on the wiki, but not if you add to the scores.

For example, if everyone scores 1 to 10 instead of 0 to 9 (so just adds 1 to every score), you can get a different result. KP + SPAV (also known as Sequential Proportional Score Voting or SPSV) passes this. I know it might seem unsatisfactory to "split" the voter with KP, but in terms of passing criteria, it seems to do the job.

@jack-waugh Right, I see. Though I think it's no better or worse than what I thought it was. Just arbitrarily favouring voters who approve a particular number of candidates. And it encourages putting up clones or non-entities accordingly.

@robla said in Paradox of Causality from Arrow’s Impossibility Theorem:

Kenneth Arrow absolutely deserved his Nobel Prize, because Arrow's Theorem was (and is) a big deal. The exact choice of criteria was beside the point; what Arrow did was describe a few "common sense" criteria and then showed them to be mutually exclusive.

But my point is that we already knew that. Amongst Arrow's criteria is IIA. And that's the one that always fails in reasonable methods. It's not like some methds fail this, others fail that. How many methods are there that are just dictatorships, for example? It's IIA all the way. Arrow's Theorem can be reworded in plain English as "With a few reasonable background assumptions, any reasonable ranked-ballot voting method fails IIA." And that has been known for centuries. Arrow just dressed it up differently.

I suppose he's used that assumption because a hereditary monarch is essentially a leader arbitrarily picked, like in random winner (as opposed to random ballot). But this is obviously very simplistic. When you have an all-powerful monarch versus some other system, the entire political and cultural landscape is likely to be very different and that isn't modelled by this.

@wolftune I'm not sure this is just an Allocated Score thing. I think that sequential methods that start by electing the candidate with the highest total score and go from there are always likely to have this sort of thing happen. Non-sequential methods may avoid it more easily, but that's obviously more expensive computationally. The other option is to not go by total score.

@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.