Posts made by Toby Pereira

@A Former User said in Kennedy Jr’s Candidacy as a Route to Voting Reform:

This thread made me lose interest in this forum. RFK Jr. is a monster.

Just one person posting something you disagree with made you lose interest in the whole forum?

There is an online obituary if you want to read it here.

@cfrank While I'm not an expert in how to make methods pass particular criteria, participation seems to be a very hard one to get. Most of the methods that pass it seem to be simple adding up ones (e.g. FPTP, Borda, approval, score), although Descending Solid Coalitions and Descending Acquiescing Coalitions are slightly weird methods that do pass it apparently.

@cfrank said in Fixing Participation Failure in “Approval vs B2R”:

(6) Run a secondary, independent head-to-head election between the B2R winner and their adversary, with the following caveats:
--> Voters are not tied down in any way to their original preference between the B2R winner and the adversary, and can freely vote for either in the independent head-to-head. Also, voters who did not participate in the first round are fully allowed to participate in the final round. By default, voters' original ballots will be used to determine the preference, but voters may opt in to swap their rating either 0 or 1 times, whichever amount is necessary to indicate an advantage that they wish to disclose.
--> However, based on these swaps, we can count the net number of swaps that are advantageous to the adversary over the B2R winner compared with the original ballots. If this number is positive, the election proceeds as you would expect, with ties broken by the sort order. However, if the number is not positive, if the original head-to-head was in favor of the B2R survivor, and if a material difference would be incurred, then the adversary will be conferred an automatic +1 head-to-head advantage, and will also automatically win ties.

I find this part a bit hard to understand.

Also, if it's an independent head-to-head, do you mean a separate trip to the polling station, or just a separate part of the ballot paper? If it's a separate trip, then it would be impossible to manage the swaps and each voter's default position without losing anonymity.

@kodos I've changed it so new users have to register with an e-mail address. I don't think that's too onerous, and it should make the problem go away.

@kodos I'll have a look to see if I can find a way to change that or if it's "hardwired" in.

If you're pitting the winners of two methods against each other, what do you do if it's the same candidate? Are they just the winner, or does there need to be a final head-to-head between two candidates?

@kodos I also have admin powers but wasn't aware this was a thing either. But I've just looked at the user list in the admin section and it seems that you have no e-mail address by your name. That could be the problem. It might be worth trying to add an e-mail address to your account. I think you'll then need to verify it by clicking on a link that gets e-mailed to you or something.

@toby-pereira said in General stuff about approval/cardinal PR:

This project hasn't purely been altruistic - it's been helpful to me by laying everything out for reworking my COWPEA paper!

And the new version can be seen here (as I mentioned in the separate COWPEA thread anyway).

The paper has been updated and some errors corrected.

I've just learnt from Rob Lanphier on the election methods mailing list of the death of Jameson Quinn after an accident while hiking in Guatemala. This is very sad news and a lot of you will be familiar with Jameson from his contributions to the voting method community over many years. I used to communicate with him about cardinal proportional methods and he's the only person from the community that I've ever met in person, back in 2017 I think.

Rob's original message can be seen here and the message from his mother posting the news is here.

I discussed something similar here and there's a video here as well. There's a video as well which shows a potential ballot design.

In what I discussed the top voted candidate in each district was automatically elected in the first phase.

@matija Do you need the first step about the electing the candidate with most votes in each district but only if they have a Hare quota? You could just do the whole process using the PR system. Or just elect the candidate with most votes anyway and just use the PR system for the second ones to be elected.

I tend to think quotas are somewhat arbitrary.

@matija True. If individual ballot data can be used, then the funding that results from each could be split equally across the candidates approved on that ballot. But this still might not be very satisfactory.

@matija If public funding is proportional to votes, then I'd say it's easier with approval voting than ranks. With ranks, you could use top votes as you say, but then you might give less funding to the election winner (by IRV, Condorcet or whatever).

@cfrank I've seen a few as well which I've deleted, but they're not overwhelming the board or anything, so I wouldn't want to make anything worse for any new users we might get, which isn't that many anyway! So I'd probably say leave it for now, but keep an eye on the situation.

@cfrank Yes. I think parties have their place as it makes it easier to know what someone is standing for in some cases and can simplify the process for voters, but I don't think they should form an essential part of the process, and it should be just as possible for independent candidates to stand.

@gregw COWPEA doesn't pass consistency. Fairness is subjective. But COWPEA itself is just a proportional weighting thing rather than an election method itself. The lottery version could be used for elections but being non-deterministic would likely be a difficult sell.

One other method would be to pick a voter and split their representation equally among the candidates that they have approved. This would be strategy-proof. However, it fails candidate Pareto efficiency.

1 voter: AB
1 voter: A

B would get 1/4 of the weight, and A 3/4. But B is Pareto dominated by A.

Another method is called the Conditional Utility Rule. This puts all the voter's representation onto the candidate that is most approved overall (or splits it equally if there's a tie). This guarantees a the maximum total approval score among a proportional result. But it fails IIB.

2 voters: A
1 voter: B
7 voters: AB

This would weight A:B 9:1. Passing IIB would give 2:1. But despite guaranteeing the maximum total approval score for a proportional result, it still fails multi-winner Pareto efficiency. It can sometimes be possible to find a set that dominates the winning set, although the result won't be proportional. See the result on this page. This is another reason why the multi-winner Pareto efficiency criterion is not necessarily a good thing within the voting election landscape.

I think this is largely it. This project hasn't purely been altruistic - it's been helpful to me by laying everything out for reworking my COWPEA paper!

Strong multi-winner Pareto efficiency: A set of candidates S Pareto dominates set S′ if every voter has approved at least as many candidates in S as S′ and least one voter has approved more in S.

For a method to pass the criterion S′ must not be the elected set.

(For optimal methods it would refer to weight in the committee rather than number of candidates.)

COWPEA fails this.

250 voters: AC
250 voters: AD
250 voters: BC
250 voters: BD
1 voter: C
1 voter: D

Optimal PAV would simply elect C and D with half the weight each. COWPEA would elect each with about 1/4, but C and D slightly more.

This example can be seen as a 2-dimensional voting space with A and B at opposite ends of one axis and C and D at opposite ends of the other. No voter has approved both A and B or both C and D. Viewed like this, electing only C and D seems restrictive and arguably does not make best use of the voting space, which may include policy areas not considered by all candidates. This potentially calls into question the utility of the multi-winner Pareto efficiency criterion. It's certainly not a "slam dunk".

In certain allocation scenarios, it would make more sense as a criterion where utility is purely determined by number of approved things, but it's less clear for voting.

Also in normal election cases with fixed candidates, the case against it is clearer.

2 to elect

150 voters: AC
100 voters: AD
140 voters: BC
110 voters: BD
1 voter: C
1 voter: D

The winning set must be AB or CD. If we elect any other pair, then too many voters would be without any representation. Candidates A and B are each approved by 250 voters, distinct from each other, and adding up to 500. Candidate C is approved by 291, and candidate D by 211, also distinct from each other, and adding up to 502. The strong multi-winner Pareto criterion would insist on the election of CD, since every voter would have one candidate that they approved in the committee. Under AB, there would be two unrepresented voters. However, CD is a disproportional result, as the D voters, numbering only 211 wield a disproportionally large amount of power. Without the two voters that only vote for one candidate, it seems clear that AB would be the better result, as it is more proportional with no disadvantages.

It purely comes down to whether the Pareto dominance caused by the single C-only and single D-only voter is enough to overturn the better-balanced result of AB. Unless level of proportional representation is of only negligible or tie-break value, AB must be the better result. Deterministic PAV would elect CD but other methods such as Phragmén would elect AB.

Consistency is where when two elections that give the same result are combined, the overall result must still be the same. Sticking with the fixed candidate case, we could swap the C and D voters above:

150 voters: AD
100 voters: AC
140 voters: BD
110 voters: BC
1 voter: D
1 voter: C

If it was reasonable to elect AB before, it still is now. But we can combine them:

250 voters: AC
250 voters: AD
250 voters: BC
250 voters: BD
2 voters: C
2 voters: D

And clearly CD becomes the best result, meaning consistency isn't essential. Obviously COWPEA and Optimal PAV can elect candidates in different proportions so they are not directly affected by this.

However, take these election examples:

2 voters: AC
1 voter: A
3 voters: B

C is Pareto dominated by A so COWPEA would elect AB with half the weight each.

3 voters: A
2 voters: BC
1 voter: B

Similarly here, COWPEA would elect AB in the same manner. Then combine the ballots:

4 voters: A
4 voters: B
2 voters: AC
2 voters: BC

COWPEA would now elect C with 1/9 of the weight as it is no longer Pareto dominated. Combining the ballots sets has changed C’s position within the electoral landscape. It does not seem unreasonable to elect C with some weight in this election, and it is therefore not clear that passing the consistency criterion is necessary for a proportional approval method.

Next I will briefly consider a couple of other optimal methods, one of which will also show problems with the multi-winner Pareto criterion.