@sarawolk yes more or less a thought experiment, trying to address some dissonance between the possibility of a Condorcet winner having low support and a support (approval) winner being different from the Condorcet winner even when one exists.

In this case, I mean that a candidate is either supported or not supported by a voter according to the support cutoff of their ballot. I’m using the word “support” rather than “approval,” because I don’t think approval is an appropriate word philosophically (or mathematically). The positive emotional connotation of “approve” is all that bothers me. “Support” seems more emotionally neutral and has a mathematical meaning that aligns well with what is happening in the system, for example, “the support of a distribution.”

https://en.m.wikipedia.org/wiki/Support_(mathematics)

The quantity of support of a candidate is simply the number of voters who formally support that candidate on their ballot.

Here is another attempt at a modification. In sequence, if there is a Condorcet loser, they are eliminated. If there is no Condorcet loser, a candidate with the least quantity of support is eliminated, with ties broken by rank runoff if possible. Repeat until one candidate remains.

@psp_andrew-s

2CV now ensures, unlike any other proposed system, that the winner will, under all circumstances, be one who received at least 51% of 1st or 2nd choice votes.

A voters 2nd choice may be as good as their favorite or almost as bad as their last choice. There's no way to know, so ensuring a majority of 1st and 2nd choice votes is meaningless. Also, in any election where you can support multiple candidates there could be multiple majority supported options. The key is to find the one with the most support by looking at strength of support and/or number of voters who prefer them, ideally both.

I think we've already gone in circles about your other responses in previous conversations so I won't repeat that again here.

@isocratia hmmm I still would like to see an example of the difference. Like I said I think your method is sufficient but I’m not sold yet on the necessary part. It might not matter anyway since sufficiency is by definition good enough! But I’m just curious.

Maybe it would make sense to regard a canonical preference matrix as having only an upper triangle. However, for software, I think it is convenient to represent it using the whole matrix.

Also, I haven't read the paper so don't know how they technically define that criterion, but it doesn't pass it as it's worded in English. Say we have:

35: A>B>Everyone else
33: B>A>Everyone else
32: Everyone else>B>A

Under IRV, B will win this election. That doesn't pass "majority rule, which ensures the election of a candidate from the majority coalition while preventing opposition voters from influencing the choice of candidate from the faction they oppose."

@jack-waugh this I’m not sure about. It seems like a multi-winner system, in fact the proponents don’t seem to be advertising it as a single winner method, probably because it suffers from vote splitting.

It seems more like a polling method to assess the relative importance of issues voters consider, but even then it seems like those issues on the poll need to be mostly mutually exclusive, or else vote splitting will take effect. And once the options are mutually exclusive, it seems to draw focus on hedging bets about what others are likely to agree upon rather than on indicating true individual preferences, although those true individual preferences might show through if the “survey responses” (ballots) rather than the QV results alone are investigated.

I think it’s probably too arbitrary and also almost surely doesn’t make do on its promise.

@cfrank

Here's a simple example to show proportionality. This example works the same no matter what the measure of support. Basically, all these measures are clones of STV but without vote splitting. The measures I'm talking about are score, smallest pairwise win, and strongest beatpath. Also, I should say that I don't really know if the measures would work for sorting.

Setup:
2 parties: A, B.
2 seats.
100 voters.
quota: 50 voters.

Round 1:
The votes are A 55, B 45.
The best quotas of 50 voters give A 50 and B 45.
A gets a seat. The quota of 50 A-voters are removed.

Round 2:
Now we count the remaining voters, A 5, B 45.
B gets a seat.

@masiarek I really like a new method that takes some time to understand. It's called a dodgson-hare synthesis
see http://jamesgreenarmytage.com/dodgson.pdf
Abstract: In 1876, Charles Dodgson (better known as Lewis Carroll) proposed a committee election procedure that chooses the Condorcet winner when one exists, and otherwise eliminates candidates outside the Smith set, then allows for re-votes until a Condorcet winner emerges. The present paper discusses Dodgson’s work in the context of strategic election behavior and suggests a “Dodgson-Hare” method: a variation on Dodgson’s procedure for use in public elections, which allows for candidate withdrawal and employs Hare’s plurality-loser-elimination method to resolve the most persistent cycles. Given plausible (but not unassailable) assumptions about how candidates decide to withdraw in the case of a cycle, Dodgson-Hare outperforms Hare, Condorcet-Hare, and 12 other voting rules in a series of spatial-model simulations which count how often each rule is vulnerable to coalitional manipulation. In the special case of a one-dimensional spatial model, all coalitional voting strategies that are possible under Condorcet-Hare can be undone in Dodgson-Hare, by the withdrawal of candidates who have incentive to withdraw.

They said they would post a recording of the debate on Youtube.

It was generally rather biased against alternatives to Hare.

I started on some simulation code. The simulation in it is incorrect and even then, only attempted to address one voting system. The parts of the program where it collects the problem definition from the user/researcher and abandons the simulation if it is still running when the researcher changes the problem (which can require so little action as moving a slider control), work correctly. However, since the start of 2023, I have been acting out an obsession with rewriting the underlying computer-sciencey stuff as cleaner code (but not changing the basic strategy).