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.

I discussed in this thread how COWPEA can fail a multiwinner version of Pareto efficiency, which you could define as follows:

If every voter has approved at least as many candidates in set X as set Y, and at least one voter has approved more candidates in set X than set Y, then set Y should not be the winning set.

But I then countered in this thread that it might not actually be such a desirable property.

However, it does leave me wondering how optimal candidate Thiele voting would behave. Thiele's biggest failing is that it fails ULC, but with different candidate weighting allowed, a universally liked candidate would get all the power, so the problem might go away. But there might be residual problems when a candidate isn't universally liked, but is by certain factions, or if factions mix in a certain way. So I'm not sure if the problem would remain. Thiele would automatically pass the Pareto criterion above, though as said, it's debatable how desirable it is.

I think in general it would lead to more majoritarian but less purely proportional results than COWPEA.

Do you know if the quota updates between rounds?

I do not believe in this method that was the intent but perhaps there is something more slick that could be done incorporating the ideas of Sequentially Shrinking Quota.

The RRV reweighting scheme doesn't decrease the total number of votes by a quota each time, so it could change.

The RRV system has more issues than that as is pointed out in the Single distributed vote page. So the potential system here is a way to combine the changing quota idea in Sequentially Shrinking Quota, the balanced reweighting from Single distributed vote and the selection from Sequential Monroe. It may not be possible but if I find some time it might be straight forward. The issue with Sequentially Shrinking Quota was always the calculation of quota size but reweighting gives some insight there.

My initial reaction was that this system would discourage the use of the middle of the range, because if you give some points to a candidate but are not in the quota, then you pay for that candidate but don't contribute to their election.

As I pointed out in my first post a mismatch between selection and exhaustion/allocation is likely to cause strategic vulnerabilities. The vote management things you highlight could sink the system. However, there are many strategies people can use and it remains unclear (at least to me) how their effectiveness balances out. A weak exploit which is easy and obvious may be better or worse than a strong but rare exploit. These are things we cannot really simulate. Things like vote management require a group effort and that relies on the organizational abilities and cohesiveness of factions. I suspect the worst exploits are those which are obvious to a single voter and unlikely to back fire.

Independent of if it is viable in the real world it would be a great extension of the field to have a system like the one I propose. It is good to compare and contrast.

Sounds good. I have thought over the problem of cutting out too many candidates with a large percentage of the vote in their ridings. Maybe re-programming my computer again to limit the party percentage to 5 and limiting the riding percentage to 10 will help people be more acceptable to the system although it would restrict smaller parties and independents.

@brozai I don’t think what I’m suggesting is the same as the Kemeny-Young method, though it may be related. I added another example, and changed some of my wording to be more clear. I’ll definitely look into those systems you mentioned, I know I like ranked pairs.

@brozai Received!

@marylander said in Point about centrist candidates winning in cardinal PR methods:

If a tie in the legislature genuinely reflects a near deadlock of public opinion, 49.9% of the public getting their way over 50.1% is hardly a travesty.

I suppose, but I think that there could be interesting effects (some potentially negative, maybe) to think about in the context of the elections themselves if such a legislative tiebreaking rule were implemented. For example, in a 2-seat cardinal PR election, if the candidates are aware that the seat-winner who gets more score points will be given ultimate power in the 2-seat legislature, that would be an incentive to try to be more of a consensus candidate (to whatever extent possible without upsetting one's "base").

another way to look at the difference between EPA and AS (at least, on approval ballots) is that EPA spends ballot power such the variance in amount spent per utility gain is exactly minimized, and AS spends ballot power such that the variance in amount spent per utility is exactly maximized. Despite their similarities, in that respect they represent two ends of an extreme.

@andy-dienes said in An argument against committee monotonicity:

There are rules which are committee monotone which will elect AC (e.g. SAV)

That means that SAV elects C for k=1, which is definitely illogical. As for MES, part of that might be because it's a little unclear for which values of x the following generalization should elect AC instead of BC:

A (1-x)/2
AB x/2 - epsilon
BC x/2 + epsilon
C (1-x)/2

All-at-once d'Hondt PAV elects AC for x < 2/3. I think my argument is more persuasive if x is closer to (but still more than) 1/2, and epsilon is small compared to x-1/2.

@andy-dienes Awesome. Pandas definitely can make things concise if done right. There are lots of functions.

@toby-pereira said in Lottery PR methods compared:

COWPEA Lottery with layers of approval - Voters score or grade candidates. The actual values are irrelevant, but when a ballot is picked at random only the top layer of (relevant) candidates is looked at. A pro is that it gives voters more distinguishing power between candidates. The cons are that it becomes more complex and to vote optimally a voter would have to grade basically all of the candidates, which could be quite a lot of them.

This one could be used nicely with the 0 to 5 "star" ballot. So to clarify the process to elect a candidate - pick a ballot at random and eliminate all but the top or joint top rated candidates on that ballot. Pick another ballot and retain only the candidate(s) that are the highest rated among those still in contention. Continue until one candidate remains. Elect that candidate.

Thanks for the replies everyone. My confusion was because I wasn't aware that the load could be spread arbitrarily. Interestingly I think this is equivalent to the idea of partially or wholly removing approvals that are detrimental to a candidate set's "score", which I suggested years ago, but seems to be a case of reinventing the wheel. There's quite a good discussion of Phragmén's voting methods in this paper by Svante Janson.

Thanks for the links.

Here is one by Piotr Skowron as well titled "Consistent Approval-Based Multi-Winner Rules".

And here's one called "Proportionality and the Limits of Welfarism" (comparing Phragmén and Thiele). I didn't actually catch the guy's name. It didn't sound like the names in the paper - Dominik Peters or Piotr Skowron (and it doesn't look like Piotr Skowron) - and the subtitles have it as Scott Anand, which is a name I'm not familiar with.

If this was extended to score voting, I think it should elect the Condorcet winner in the single-winner case, if there is one. Otherwise, obviously it would have to choose between the candidates in some way, like other Condorcet methods do so it's not a big problem.

When there's more than one winner, what happens depends on how you interpret the scores. You could measure a voter's satisfaction by adding up the scores the voters have given to the elected candidates, but I think that might be unsatisfactory in a few ways. There's always debate about how to interpret scores and what they mean, and whether absolute numerical values should really be used in their raw form.

Instead, the scores could be used as layers of approval. This basically means that a voter's satisfaction with a candidate set is determined by the single highest score they've given to a candidate in the set, next best used as a tie-break, and so on. So for scores out of 5, a single 5 is better than multiple 4s etc.

This should keep it relatively simple. Also if candidates are elected sequentially, it should be simple enough to calculate the results.

I think this should be a decent enough method and I think I'd prefer it to things like Allocated Score and Sequentially Spent Score.

Obviously COWPEA Lottery using scores as layers of approval is God-tier in terms of criterion compliance, and very simple to implement, but it is non-deterministic, which might be too much for some people, so this method could be a good compromise.

Edit - You'd have to work out exactly how to measure the stability of a candidate set though. Let's say the first 2 candidates elected are AB. Then you need to test e.g. ABC, ABD, ABE etc. to find the 3rd candidate. But I think you might be able to test them against each individual candidate not in the set. So test ABC against, D, E, F etc. separately.

Edit 2 - You'd probably have to test each potential set against all the other subsets. So ABC would go against ABD, ABE etc., plus AD, AE, BD, BE, as well as D, E etc. Still not that many in the general scheme of things.

@wolftune OK, that's fine. I don't disagree with your point. But I was clarifying in case your post was a response to my bit about the candidates that are the favourites of nobody, but obviously it wasn't.

But just to be clear anyway - when I was talking about not wanting to elect the favourite-of-nobody candidates, I wasn't referring to stopping the election of such candidates in principle. But we've discussed certain specific scenarios where we all seem to agree that electing the candidates that are the favourite of nobody isn't the best thing to do. And I was discussing ways to elect the candidates we would want to in this situation.