A method that elects the "most stable" candidate set

@toby-pereira said in A method that elects the "most stable" candidate set:

@andy-dienes said in A method that elects the "most stable" candidate set:

@toby-pereira

each voter to be uniquely assigned to 1/n of the representation (whether that's a fraction of a candidate or more than one candidate), then that's "perfect representation" in the way I would extend the definition

I just can't shake the feeling that this better describes priceability and (stable priceability) than it does perfect representation. I think many academics, and I personally, agree more or less with this intuition, but formalizing it without introducing unforeseen side-effects of the definition is the hard part. As it happens, I think the attempted formalization in the axiom labeled "perfect representation" does have some unfortunate side-effects, but you can get the same spirit of proportionality in (to me) a more principled way via priceability.

OK, but does Webster pass priceability? I wouldn't want to throw that out.

As Andy said, it does not, since Webster does not pass lower quota.

Toby Pereira

@spelunker Fair enough. I'm not as familiar with priceability and what it rules out, though I have read the definition. I knew Webster failed PJR.

Toby Pereira

@A Former User said in A method that elects the "most stable" candidate set:

Also "more stable" I think might not even be resolute whatsoever, forget resolvable in polynomial time. Imagine like a condorcet cycle but of committees.
Just use MES or party-list and be happy

Just to revisit the initial topic - If there was a cycle of "most stable" then like with single-winner Condorcet methods, there could be a system in place to determine the winner. Also if this sort of thing were ever adopted in any sort of election, it would likely have to be used sequentially for computational reasons, which should make it workable.

And on Condorcet methods, it has been said that this core stability is a sort of multi-winner analogue of Condorcet.

Another thing about Condorcet methods is that the Condorcet winner is, as far as I understand, the game theoretically stable winner for approval voting. I don't think core stability in the sense that it's discussed for multi-winner cardinal methods is necessarily the same as game theoretically stable. So perhaps that would be an interesting thing to investigate. I think it would be interesting to see what winner sets were game theoretically stable under, for example, single non-transferable vote.

Has Andy left the forum by the way?

Toby Pereira

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.