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@cfrank The problem of having an exactly proportional result whenever possible is that it drastically weakens the monotonic properties of a method. E.g.

2 to elect

99 voters: AB
99 voters: AC
1 voter: B
1 voter: C

The Perfect Representation criterion would demand the election of BC, even though A has 99% of the support with B and C having just 50% each. And I think that's too much of a demand.

And if you want the result "as close as possible", that pretty much just is the var-Phragmén method. And this has the same problems.

You could specify some sort of convergence requirement. Maybe this could be in terms of maximum variance.

Something to add here is the discussion of what it means to be proportional. I said above that I used the Perfect Representation In the Limit (PRIL) criterion. As discussed in this thread, most of the proportionality criteria that have been used for approval methods rule out methods that reduce to Sainte-Laguë in the case of party voting. A former member here went off the deep end insisting that those methods must then not be proportional in this thread.

But really it just shows that the criteria are not up to scratch. I acknowledge that PRIL is not perfect either, because it's not at all demanding in how a method reaches perfect representation, only that it happens in the limit.

For example, if you had the following ballots for party voting:

200 voters: A
100 voters: B

A method could pass by awarding the first 200 seats to A and then the next 100 to B. So in a 200-seat scenario, A would get all the seats. But obviously a method would have to be very contrived to do that, and it would likely cause it to break other symmetries and fail other criteria.

Another criterion I would demand for deterministic methods is that they would pass perfect representation when the number of elected candidates is a multiple of the number of voters (so 300, 600 etc. in this case).

But if you required that a method also only looked at voter ratios, rather than absolute numbers, we could massively reduce that problem.

2 voters: A
1 voter: B

This ballot would have to give perfect representation whenever the number of elected candidates is a multiple of 3, so the previous example would have to as well. But you could have:

201 voters: A
100 voters: B

This doesn't divide down further. But then if you also demanded monotonicity, it would have to give B at least as many seats as it would in cases where the B vote is lower. So:

3 voters: A
1 voter: B

B gets at least every fourth seat right from the start so the above case would do that as a minimum. And you could go further with the demands.

But PRIL works quite well with non-deterministic methods with fairly minimal demands. You probably only need to specify that each one is an independent pick.

There has been another update to the paper. The paper discusses how COWPEA Lottery is the only ABC (approval-based committee) method that is proportional and passes, monotonicity, strong candidate Pareto efficiency, participation, Independence of Irrelevant Ballots (IIB), Independence of Irrelevant Alternatives (IIA), Independence of Universally Approved Candidates (IUAC) and independence of clones.

Optimal PAV Lottery passes all of these except monotonicity. Both of these methods are obviously non-deterministic, but I think it's probably impossible for a deterministic method to pass all the criteria.

@marcus_sir I would agree with @cfrank that some examples would be good to get a feel for how it works. I've always tended to think that quota removal methods are fairly unsophisticated, and I believe MES falls into this category. See the thread here.

@cfrank There was a vote on electorama not that long ago Ranked Pairs with winning votes (as opposed to margins, which wasn't on the ballot) won the poll. It was the Condorcet and approval winner. In that poll I put approval as my top method.

@clay I have watched that video, so thanks for that. But the bottom line is that I am making an argument about semantics, not ethics. And you insist that it's an argument about ethics. There's nowhere to go from there.

@clay I think you totally missed the point of what I was saying. The thing I was disputing was:

@clay said in election by jury (www.electionbyjury.com/manifesto):

"ought" means "I would subjectively prefer that". this is ethics 101.

Ethics 101 does not determine what a word means. Words are used in English by English-speaking people in many ways, some informal, some formal and with varying degrees of vagueness etc. It does not matter if someone's meaning for a word is at bottom incoherent or that the thing they mean doesn't exist in real life. The word doesn't then not mean what they were using it to mean. Experts in ethics do not have ownership of the word "ought". So:

as i've pointed out, you cannot show me any actual objective physical law of nature that the word "ought" could possibly refer to. it's just expressing a vibe.

No, and I wasn't trying to. You just missed what I was saying. I'll repeat the example, but with a bit of added commentary for clarity.

Someone might say, "I suppose I ought to try and save those people drowning in the sea, but I don't really care about other people, so I'll just carry on eating my ice-cream."

I initially said this doesn't fit your definition of "ought" above because he's not expressing a subjective preference. You countered by saying:

that would be using "ought" as in society would prefer i do it. thus they might judge me for not doing it" or something along those lines.

(So therefore still a subjective preference.) But I then said actually, he could be referring, not to anyone's subjective preference, but to a moral framework that exists outside of his (or anyone else's) subjective preferences.

So therefore his use of the word "ought" does not refer to subjective preferences. It refers to this objective framework that he believes exists. Even if it doesn't exist. And however you cut it, it's still a long way from:

"ought" means "I would subjectively prefer that". this is ethics 101.

But I'm not sure how else to get the point across. OK, someone believes in ghosts. A ghost (by some definition) is the soul of a dead person that still in some manner inhabits our physical realm.

It doesn't matter if ghosts are real - this is what it means to be a ghost under this definition. Someone might say:

"A ghost is just an illusion. That's what it means to be a ghost."

It might be the case that all the ghosts that people have claimed to have seen are all illusions, and indeed that no "magical" ghosts exist, but this does not change the definition of what a ghost is. A definition can be of something that doesn't exist, or is at bottom incoherent.

That's all I'm saying. Words mean what people use them to mean. There is no dictionary in the sky that defines a word in a very specific way. And there is certainly nothing that cancels out the definition of a word based on the non-existence or incoherence of a concept.

If someone uses the word "ought" to refer to some objective morality, then that is what they are using the word to mean.

This is a silly argument anyway, and far removed from election by jury!

Edit - you do this routine of incredulity when you think people aren't getting what you're saying, but I could do the same on you here. Your lack of comprehension of what I am saying is staggering.