User talk:BetterVotingAdvocacy/Big page of ideas

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Condorcet as Approval, Approval as Condorcet

About your comparisons between Approval and Condorcet: you can go in the opposite direction (i.e. Approval to Condorcet), too, by considering Approval voting a method where each voter decides what the most important pairwise comparison is, puts his approval threshold there, and says that everybody on the approved side of the threshold beats everybody on the non-approved side. Kristomun (talk) 12:31, 25 May 2020 (UTC)

Yeah, I've thought of that, but didn't know quite how to word it. On the Approval voting#Connection to Condorcet methods section, I made clear that Approval voters can always ensure the loser of a matchup loses if they set their thresholds based on their preference in the matchup, but they can only guaranteeably make the winner of the matchup win if the winner majority-beats the loser. Maybe I can make some kind of image/GIF for this, I don't know. BetterVotingAdvocacy (talk) 19:08, 25 May 2020 (UTC)
To sort of extend the thought, Score is where the voter's support margin in each matchup must add up transitively, and the sum can be no greater than 1 vote. In other words, if you give A max support and B 60% support, then you can give B no greater than a 60% margin (0.6 votes pairwise) in support against C. BetterVotingAdvocacy (talk) 00:15, 27 May 2020 (UTC)

Condorcet reweighting

Regarding your example, "Here is an example illustrating the difficulty of creating a Condorcet multiwinner method along the lines of RRV", see Left, Center, Right. Any Condorcet method that does reweighting must elect the CW as the first seat. This immediately breaks Droop proportionality. Kristomun (talk) 09:04, 27 May 2020 (UTC)

Good point. The interesting thing my example brings up is that in a Condorcet PR method based on divisor-type reweighting rather than quota spending, the reason it would have to fail to give representation to a bullet voting Droop quota is essentially because the faction that ranks multiple candidates starts off by getting to indicate maximal preference for their favorite over their 2nd choice, and then after the favorite wins, they get to basically "change their ballots" and now maximally support the 2nd choice (disregarding reweighting). In other words, the first round can be thought of as 34 A 35 B 31 C, and then the second round as 34 A 48.5 C. In SPAV, the B>C voters can either bullet vote or approve both candidates, but they can't do both in the same election, and that's why proportionality isn't broken in that method. BetterVotingAdvocacy (talk) 10:08, 27 May 2020 (UTC)
To rephrase in simple terms: what happens is that the ranked ballots say "there's this group that wants L, that group that wants R, but both think C is a reasonable compromise". Condorcet finds the compromise right away, but including the compromise in a two-seat election would unbalance the result. It's better to directly represent both factions. But in Approval, the voters can't both express that they prefer their favorite to their compromise and the compromise to their rivals. If they express that they prefer their favorite to the compromise, then one of the favorites wins in the single-seat, and no problem. If they express that they prefer the compromise to their least favorite, then by ballot interpretation, the compromise is just as good as the favorite, so the compromise gets into the two-seat, and there's no problem there either. Kristomun (talk) 10:38, 27 May 2020 (UTC)
Your analysis works for the LCR setup, but not my example, because my example doesn't feature a candidate all voters see as an acceptable compromise. My example is basically showing how, in a situation where all but one of the factions bullet vote, we have to struggle with the fact that because of the ranked information, we can identify that there is a faction that is large enough to deserve to get its 1st choice, but that faction is in a sort of "semi-solid coalition" with another faction; if we elect this largest faction's own 1st choice, then divisor reweighting means you can only justifiably take some fraction around half or less of their ballot weight. Yet if we do this, then this largest faction will still have plenty of ballot weight to back their 2nd choice, the candidate they semi-solidly supported. Maybe a simpler way to point to what I'm saying is that if, in the example, C wins first, then reweighting by half means that B can't win; but if B wins first, C can still win. This is all due to the ranking allowing the voter to change who they back in a given round; but in SPAV, if B-top voters approve C, then this guaranteeably means C wins before B (because of LNH), so no problems occur. BetterVotingAdvocacy (talk) 11:10, 27 May 2020 (UTC)