Posts made by BTernaryTau

@SaraWolk @Jameson-Quinn Thank you for responding. I've emailed Sara about next steps, and I hope to hear back from you soon.

So a group from the Equal Vote Coalition has just had a paper published (https://link.springer.com/article/10.1007/s10602-022-09389-3) regarding STAR voting, VSE, and what they call the Equality Criterion. This is the first time I've been able to see a full copy of the paper, and thus it's the first time I have able to confirm that a.) some of my work was used, and b.) I was not given any credit for this.

I had been approached previously about the possibility of using one of my criteria definitions as the formal definition of the Equality Criterion in this paper. However, this occurred roughly a day before the paper had to be submitted to the journal. This was unfortunate because I was under a lot of stress and really didn't have enough time or mental bandwidth to address the questions about my work that came up. I tried to give a decent answer, but after a little back and forth I stopped getting responses.

At the time the issue of how to credit me did come up, since I generally post under BTernaryTau rather than my full name. Because I wasn't sure how to handle this and didn't even know if my work would be included, I said that I'd prefer to determine whether and how my work would be used first, then specify how I would be credited. However, because the conversation about the relevance of my work was never concluded, this topic was never returned to.

Eventually a preprint of the paper (https://www.researchsquare.com/article/rs-2050377/v1) was made available publicly, which I did check out. This preprint mentioned the Equality Criterion but did not include a definition. I was not included in the citations or the acknowledgements, so I assumed they decided to go with a different means of formalizing it. However, it is clear that the full paper does in fact draw upon my definitions for the cancellation criterion (https://bternarytau.github.io/miscellaneous/voting-theory/cancellation-criterion) and opposite cancellation criterion (https://bternarytau.github.io/miscellaneous/voting-theory/opposite-cancellation-criterion) in order to create its definition of the Equality Criterion, and yet this version also fails to credit me in any way.

On the one hand, I don't want to make a big deal out of this since I really like what the Equal Vote Coalition does, and since the paper ultimately used a fairly small portion of my work. On the other hand, a lot of my efforts with regard to voting methods are intentionally "hit-or-miss" with respect to whether they turn out to be relevant more broadly, so when part of my work does turn out to be relevant, I end up caring a great deal. This is especially true when my work is relevant to an organization that I have donated to and publicly advocated for. I also want to avoid setting an implicit precedent that it's ok to use my work without crediting me. I don't have a good solution for balancing these concerns, so I've settled on making this post. If nothing else, I hope making this public knowledge can prevent any future incidents of this kind.

@andy-dienes said in Way too many categories:

Single Winner
Proportional Representation
Other Reform Discussion
News / Advocacy / Projects
Meta / Forum Business

This seems like a good set of categories, though it does awkwardly place non-proportional multi-winner methods under "Other Reform Discussion".

@jack-waugh said in Way too many categories:

More background: two people volunteered to moderate the forum and the council accepted them. Only one of those two has taken an action by way of moderating. I did not volunteer to moderate, because I felt I had put in enough work by setting up the server VM, installing NodeBB, setting up a half-assed backup scheme, and coding the archive presenting software and the site home page. I have not even really bothered to master the admin ifc to NodeBB; I pointedly left that work to others. I mention this in reply to @rob saying that I "run" this forum. I do not run it, in a social sense. I do have the keys to the server and can change privileges in the user list.

I know at one point I tentatively volunteered to be a moderator if necessary. Unfortunately I haven't been active enough on these forums to justify an application, but maybe it would be worth it for me to try and become more active if the forum is in need of moderation? Or maybe I'm just misunderstanding the situation.

@jack-waugh Given the available alternatives I see no reason not to trust Equal Vote here.

Seat capping is a technique I've been working on developing for a little while now. It allows various multi-winner voting methods, including many proportional methods, to be made precinct-summable by limiting the number of seats that the voting method can fill. Many specific instances of seat capping have been discovered by others, but to my knowledge I am the first person to generalize this insight to a wide variety of voting methods, including allocated score (the current STAR-PR proposal), sequentially spent score, reweighted range voting, harmonic score voting, and Bucklin transferable vote.

@keith-edmonds Don't worry, I'm not planning to stick with Thiele-type methods forever. For now I'm just trying to get a better feel for exactly what went wrong and what I need to look out for in the future.

Looking at the criteria tables on Wikipedia, there don't seem to be any voting methods listed that pass participation but fail monotonicity. And given how similar participation failures are to monotonicity failures, it seems plausible that these two criteria are linked in some way. However, when I investigated this further I found what I believe is a counterexample to the claim that participation implies monotonicity.

Consider an election with candidates A, B, C, and D, where the winner is chosen by plurality voting with ranked ballots and alphabetical tie-breaking. Now modify the voting method slightly such that when D>C>B>A is the only ballot cast, B wins, and when D>B>C>A is the only ballot cast, C wins. This creates an instance of non-monotonicity where ranking B higher changes the winner from B to C. However, it does not create any instances of participation failure. In a single-voter election, a voter who honestly casts either of these ballots improves their result (B or C is elected instead of A). In a two-voter election, if one voter casts either of these ballots, the other voter is guaranteed to have their top candidate win (since D never wins when there's a tie). And all other cases consist of elections identical to those under plurality voting.

Assuming I didn't make any mistakes, my next question is whether there are any restrictions that can be placed on the class of voting methods being considered to change this result by eliminating contrived examples like the one above. For example, maybe the combination of unanimity, anonymity, neutrality, and participation implies monotonicity, and as a result pretty much any "reasonable" voting method that passes participation will also pass monotonicity.

Thought a bit about the results of applying other means in place of the arithmetic mean. The geometric mean seems to remove the issue where a party can win an arbitrarily large number of seats with a fixed number of voters (the relevant limit is 0), but it doesn't eliminate the more general problem of being able to win more seats by giving all preferred candidates lower scores. The harmonic mean doesn't have either problem, and in fact using it in place of the arithmetic mean yields RRV.

@marylander I see, thank you for catching this! I'm honestly quite surprised that this sort of behavior arises from what to me feels like a pretty natural extension of SPAV. Are there any other methods known to behave this way? I need to think more about what exactly went wrong here. If there aren't any other examples, I guess that would at least mean I discovered a voting method with a novel failure mode!

@Keith-Edmonds SDV should not have this issue. If you give all candidates from your party the same initial score S and all others 0s, then your ballot will always contribute a score of S²/(S + K · SUM) = S²/nS = S/n, where n is a positive integer (assuming K=1 or K=2) that depends on how many candidates from your party have been elected. This means that a greater initial score will maximize your ballot power in this case.

More generally, the limit of S²/(S + K · SUM) as SUM goes to infinity is 0, so no party should be able to win an arbitrarily large number of seats with a fixed number of voters.

While thinking about how to keep some of the advantages of SPSV while ditching the KP transform, I came up with a new voting method that I'm currently calling sequential threshold average score voting, or STAS voting for short. It essentially operates the same way RRV does, but reweights ballots using a different formula (see the link above) that was inspired by the KP transform. This formula seems to preserve (and sometimes even strengthen) SPSV's tendency to avoid heavy deweighting when candidates are elected that were given low ratings on the ballot in question, while simultaneously using a simple "one weight per ballot" system instead of splitting ballots up like SPSV does. In my opinion this makes it a candidate for best Thiele-type proportional voting method (though I doubt it's the best rated party-agnostic proportional voting method), but I'd like to see if anyone has any major objections or other comments.

Ok, I think I figured out how to get around the key-based version's issue. The problem is that the key is essentially exposing the voting method's internal randomness mechanism to the criterion rather than treating it as a black box. So to get around that issue, we can require that, for some non-deterministic method m, there exist a function f(k, e) that passes the key-based version of the criterion such that for all elections e and candidates c, P(f(k, e) = c) = P(m(e) = c). That way we can isolate the randomness of f to one variable just as before while still treating the voting method itself as a black box.

@Marylander do you see anything I'm missing here?

Alright, I've determined that this approach would not behave exactly like Marylander's version. Specifically, it's possible to have two voting methods with the same probability of electing each list of candidates in every election and yet have only one of them pass the random key version. As a concrete example, here are two implementations of breaking approval voting ties uniformly at random:

1. break an n-way tie by picking the ith candidate, where i = key mod n
2. break an n-way tie by picking the ith candidate, where i = key + (total number of approvals) mod n

Here is a simple example election:

1: approves A and B

And here is a pair of cancelling ballots:

1: approves A and C
1: approves B

For the first tie-breaking implementation, i stays the same when the cancelling pair is added, so the tie is broken the same way and no violation of sequential cancellation occurs. For the second tie-breaking implementation, i is flipped by the addition of the cancelling ballots because the total number of approvals increases by 3. Thus, the tie is broken in favor of the opposite candidate and sequential cancellation is violated. This behavior generalizes such that the first implementation passes key-based sequential cancellation while the second does not.

This is unfortunate because one of the intended advantages of the sequential cancellation criterion is that if two voting methods always produce the same results, either both will pass it or both will fail it. This is already weakened a little by requiring the order in which candidates are elected to remain the same, and under the random key implementation it would need to be weakened more by requiring the candidates elected to remain the same for every key.

As of now, I still prefer the key-based version to the fully probabilistic version, but this seems like a major downside. I'm not sure if there is any way to combine the advantages of both approaches, but if there is a way it would be very helpful.

Coming back to this, I'm wondering if a better approach would be to model non-deterministic voting methods as functions that take a random key as input in addition to the ballots, similar to the way that pseudorandom functions are handled. Then if the deterministic sequential cancellation criterion is passed for every possible key, we can say that the non-deterministic method passes sequential cancellation.

If I'm correct, this version of the criterion is equivalent to Marylander's version but isolates the randomness to a single variable (the key) in a way that allows it to be ignored for the most part. I believe this makes the criterion easier to reason about, and this feels like the approach that I was searching for when I started this thread. Is there any reason to avoid it?

@Marylander Thank you for this! This is exactly the criterion I was picturing for handling non-deterministic methods. I have decided I'm going to keep the deterministic version of the criterion as the default, but this is definitely worth mentioning as an extension.

I'm trying to figure out what the best way to handle ties would be for the sequential cancellation criterion. For the cancellation criterion, I was able to get around this issue by treating voting methods as functions without worrying about the specifics of what those functions output. Thus, voting methods that break ties randomly could simply output something like a weighted collection of candidates, and the cancellation criterion would be satisfied if that output stayed the same, even if the non-deterministic outcome did not. However, the sequential cancellation criterion has to set a specific output format since it cares about whether an individual candidate is elected at the same time across multiple elections, so that approach isn't an option.

My initial thought is to have the voting methods output a weighted collection of lists, then require that the individual lists satisfy a modified version of the sequential cancellation requirements. But this adds a lot of complexity to an already complex criterion. Another option would be to just restrict the criterion to deterministic methods and have those methods handle ties by violating neutrality (e.g. breaking ties by alphabetical order). Are there any better ways to handle this issue?

It's easy to show that MJ fails the opposite cancellation criterion.

2: A/Excellent, B/Very Good, C/Reject
1: A/Good, B/Very Good, C/Reject

Medians: A/Excellent, B/Very Good, C/Reject
A is elected

We can add a pair of opposite ballots to change this result.

2: A/Excellent, B/Very Good, C/Reject
1: A/Good, B/Very Good, C/Reject
1: A/Good, B/Excellent, C/Poor
1: A/Acceptable, B/Reject, C/Very Good

Medians: A/Good, B/Very Good, C/Reject
B is elected

Demonstrating that MJ fails the cancellation criterion is a bit more difficult since we must consider all possible cancelling ballots for A/Good, B/Excellent, C/Poor.

2: A/Excellent, B/Very Good, C/Reject
1: A/Good, B/Very Good, C/Reject
1: A/Good, B/Excellent, C/Poor
1: A/?, B/?, C/?

Medians: A/?, B/Very Good, C/Reject

Luckily it's possible to construct an election where B and C's medians are independent of the final ballot (as I did here), so we only need to consider the possible ratings for A. An Excellent rating will lead to A keeping their median rating of Excellent and winning, but no other rating will. A Very Good rating creates a tie between A and B which is broken in B's favor, and anything lower leads to B winning as well.

Now all that remains is to find another election in which A/Good, B/Excellent, C/Poor cannot possibly be cancelled out by a ballot with an Excellent rating for A.

2: A/Poor, B/Acceptable, C/Reject
1: A/Good, B/Acceptable, C/Reject

Medians: A/Poor, B/Acceptable, C/Reject
B is elected

2: A/Poor, B/Acceptable, C/Reject
1: A/Good, B/Acceptable, C/Reject
1: A/Good, B/Excellent, C/Poor
1: A/Excellent, B/?, C/?

Medians: A/Good, B/Acceptable, C/Reject
A is elected

So MJ fails both of these formalizations of Frohnmayer balance.

In online voting theory circles I am known as BTernaryTau, or just Tau for short. I'm a supporter of cardinal methods like approval, STAR, and allocated score. I write a blog where I often discuss the subject of voting methods and voting method criteria, sometimes with a theory focus and sometimes with an activism focus. I developed the mathematical cancellation criterion as a formalization of Mark Frohnmayer's equality criterion concept, and I am currently working on the sequential cancellation criterion, which extends the cancellation criterion to sequential multi-winner methods in a manner compatible with proportional representation.

@Jack-Waugh How involved would that be? I'm interested but I may not have the time, depending on how long it would take to learn everything and how urgent it is.

I'm familiar with basic SSHing if you still need someone.