@cfrank Yeah, there's always the incentive not to vote for a preferred candidate in PR for the reasons you give.

With the monotonicity, Phragmén is not actually non-monotonic as I say, but only weakly monotonic. E.g. with 2 to elect:

100 voters: ABC
100 voters: ABD

Phragmén methods tend to be indifferent between AB and CD (unless modified in some way), and that leaves them open to:

99 voters: ABC
99 voters: ABD
1 voter: C
1 voter: D

Where CD would be preferred. Electing in a greedy sequential manner rather than optimally would actually lead to more monotonic results in these cases, but other examples can be found.

@toby-pereira That is true. This would matter most when the election is reasonably competetive and this could make the difference.

In my original email I specified that I thought of this specifically in the context of an electoral system (the one in Hungary), where it matters which how many votes a candidate wins or loses, as wasted and surplus votes are transferred and reused as list votes. In that case, a party or block running a losing candidate has an incentive to minimize the margin instead of getting a more in-group appealing candidate since it actually gives them more seats, and same for safe districts - a larger margin brings in in more surplus votes which may bring in more seats.

You have a nice description of how to add a automatic runoff to a multi-winner election. However, what your describing would be a type of Block Star, it is not a type of proportional representation. Your weighting step achieves a different sort of proportionality then what is referred to as proportional representation.

@toby-pereira See the "effective power" more as something over time. So for the random ballot, with a guaranteed 51% of the vote you'd be in power 51% of the time, but with a guaranteed 51% of the vote in a majoritarian system, you'd be in power 100% of the time. I'd gestured at this by saying "if you have 51% of the vote you are in power 100% of the time", but I'll make this all a bit clearer if I use this graph again in the future.

@mkeypaige A lot of those topics have Wikipedia or Electowiki pages, which describe them quite well, and there are also YouTube videos which discuss a lot of them. Some of the later stuff I wouldn't even know what they are. But I'll give you some links.

Ranked voting - Wikipedia

Plurality system (also known as First Past the Post) - Wikipedia, CGP Grey video

Ranked Choice Voting (also known as Instant Runoff Voting, Alternative Vote among others): Wikipedia, CGP Grey video

Condorcet methods: Wikipedia, Carneades.org video

Borda Count: Wikipedia, Carneades.org video

Majority criterion: Wikipedia, Becky Moening video

Unanimity criterion: Wikipedia article on Pareto Efficiency, Eric Pacuit video

Condorcet winner criterion: Wikipedia, Carneades.org video

Monotonicity criterion: Electowiki article, Becky Moening video

IIA (Independence of Irrelevant Alternatives) criterion: Wikipedia, Carneades.org video

Manipulability: Wikipedia article on strategic voting, Katherine Heller video

Random dictator: Wikipedia article, Carneades.org video

Approval voting: Wikipedia, CGP Grey video

That's the first section covered. Let me know if this is useful at all and I can get some links for the others.

@jack-waugh I think anything except the minimum for unmarked candidates makes it too easy to mark bullet burials. But I don’t know.

Who knows how the Gibbard theorem applies to ABC voting? In optimizing my vote, how do I take into account the stances of the other voters? Assume I know them perfectly. Do I maybe exaggerate support for a compromise candidate from D to C, with a metered probability?

@masiarek this may be slightly tangential, but another consideration for the future is making sure any encryption in voting systems is also quantum secure.

@wolftune IRV wasn’t largely in the public consciousness of the USA until groups like FairVote started promoting it in the 1990s. It took a decade for acknowledgment of the system to grow, and by then it had subsumed the name “ranked choice.” So it wasn’t as if people made a concerted effort to change the widely accepted name in that case. In fact, I would say more people try to reverse the name change, because it’s a presumptuous moniker that obscures other ranked choice systems.

Anyway, maybe there are examples. But I doubt whether they were efforts not in line with the mainstream or status quo.

@cfrank @Jack-Waugh Drumming short slogans without clear definition or explanation can be problematic. Even "one ballot per voter" could lead to people insisting that all offices and questions, up for vote on the same day being crammed on one sheet of paper. Or originalist judges going back to little ball used for secret voting as the definition of ballot. We need to remind people that a vote: is the opinion of one member of a group, used in an effort to determine the opinion of the group, on a matter that they are trying to make a decision upon. The more often people are exposed to longer explanations of what a vote is, the less they will assume a narrow definition based on exposer to only one voting method.

@cfrank I agree this is probably unnecesary conflictive, so I will avoid a discussion on that by editing the post.

Still, the two articles are to related for puting them in different threads.

@lime I think that since multiwinner elections are generally for electing legislatures, we can say that generally the goal is for the set of winners to be able to vote on laws in such a way that the laws passed maximize voter utility (i.e. come closest to their preferences on the issues). Now since this is difficult to simulate, how about simplifying it down to an election-based process: have the winners of the multiwinner election conduct a single-winner election among themselves to choose a leader (presumably using whatever single-winner voting method the original multiwinner election's voting method simplifies to), and then see how much utility the original voters in the multiwinner election receive from that leader compared to the amount of utility those original voters would get from the leader they would have elected if they had themselves voted in the single-winner election.
Essentially, test how much utility voters would get from the Prime Minister chosen by Parliament versus their utility if they directly elected a President instead.

The same idea is covered at [https://rangevoting.org/BRmulti.html](link url)

@casimir again this is just a criticism of the law and the judgment made about it: I still think even their reasoning (in bold) is pretty absurd. It means essentially that any system whatsoever that gets put into use is automatically constitutional, regardless of any negative or unexpected consequences, even those that directly contradict the letter of the law 😂 So what is the point of the law? It seems only to prevent the use of unconstitutionality to enact technical voting reform.