@andy-dienes True. But I feel that there's a clear precedent of sorts for what I suggested: currently, the US Vice President (who is meant to represent majority views, if we look past the twisting effect of the Electoral College) can break ties in the Senate.

@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)

@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").

@andy-dienes said in Point about centrist candidates winning in cardinal PR methods:

Might be more elegant just to require an odd number of seats though!

That works in a lot of cases. But (at least theoretically speaking) there could still be some legislative votes where ties legitimately occur i.e. if one legislator wants to abstain on a bill because they truly don't have an opinion on it.

@andy-dienes True. But I feel that there's a clear precedent of sorts for what I suggested: currently, the US Vice President (who is meant to represent majority views, if we look past the twisting effect of the Electoral College) can break ties in the Senate.

I wanted to mention something I thought of in response to an archived thread (found at https://votingtheory.org/archive/posts?where={"_id"%3A2367}). Here is the part I am responding to:

<<<<<<<
The center is the score winner, and just walking into this example, you can see that if the center is elected, nomatter who you elect in the 2nd round, you will leave a large chunk of the electorate underrepresented. If the center is elected, the next winner will either be the far right or the far left, since the voters who liked the left or right candidates but not the far left or far right candidates already helped to elect a candidate and thus their votes don't matter enough (no-matter if you use reweighing or quota allocation) to elect just a left or right candidate. This would mean that in a district where the center of public opinion is the center, you are electing either the center and the far right or the center and the far left.

A much better solution in this scenario would be to elect just the left and right candidates. You aren't electing the center candidate, though the center of public opinion is still the center because both the left and right candidates are elected. However you cannot reach this scenario if you always elect the center candidate. Thus electing the score winner in the first round round isn't always isn't always a good thing.
<>>>>>>>

What I thought of was that, since everyone knows that the score winner will win in the first round of certain cardinal PR methods, this means that the score winner would actually be considered to have more legitimacy in making decisions for the entire constituency compared to whoever else wins a seat. In other words, in a 2-seat PR election where the Score winner and some more extreme candidate wins seats, the more extreme candidate would be forced to concede on basically everything to the Score winner when the two of them make decisions (assuming that the two of them have to agree to make some kind of decision i.e. if the legislature is just made up of those two legislators, or something like that).

This makes me wonder if it might be a good idea in legislatures with even number of legislators to allow a legislative tie to be broken by having the half of the legislators that received more score points in the elections (or something along those lines) to win the vote.

Is there a way to get pictures from the old forum? For example, there was the diagram I (formerly AssetVotingAdvocacy) made to represent Sequentially Shrinking Quota.