@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.

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."

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).

@jack-waugh I agree soundly with you. There are many ultimately nihilistic profit seekers who are driving destructive tendencies of the global market, and that’s a full euphemism. It isn’t clear whether that nihilism is actually a value construct (well, it seems if anything to be quite rightly the opposite of one, really) or whether it’s due to a typical lack of awareness or contemplation. But a third alternative is also available, which is a simple (and in enough cases, severe) deficiency in moral character.

Another related topic I consider in this area is the attention economy. You allude essentially to addiction and what I don’t have vocabulary for beyond “post-modernist consumerism.” In my opinion, global attention is a public good that is now being subjected to the tragedy of the commons, and that is all resulting from a de-compartmentalization of access points to attention. It’s also another prisoner’s dilemma. Space and time no longer serve the functional roles of localizing attention to natural social public spheres and communities, and this only drives the lack of awareness and other issues related to mental health (I.e. attention starvation on a global scale, with concomitant depression, I.e. “influencers,” onlyfans, TikTok, etc.). More and more pornographization, commodification and exploitation of human life, even people exploiting themselves.

The only thing I can see that could possibly supplement those barriers is either an artificial enforcement of barriers (a frightening thought) or awareness and personal character. In other words, externally imposed barriers, or barriers of personal choice. Interesting times we live in. Anyway I’m glad at least that others can see this is all more than “just” a moralistic issue.

On a side note, while we’re at the water cooler, I will just mention that I watched a portion of the first Republican candidate debate. I will summarize my thoughts as, “Wow.”

@masiarek

Condorcet method, so the main thing (in my view) to look out for is whether or not its cycle-resolving rule makes it immune to turkey-raising or not.
I've heard that a few Condorcet methods are immune to turkey-raising but I don't have more info about this.
Perhaps, in the event of a false Condorcet cycle generated by tactical voting, the smallest-margin victory will always belong to the "turkey".

@jack-waugh said in Condorcet Score:

@cfrank, Ouch!

OK, then, how about this one?

Collect Score-style ballots. If there is a Condorcet winner, elect her. Otherwise, elect the straight Score winner.

I think Smith//Score is better than Condorcet//Score. Condorcet//Score could elect the Condorcet loser.

Or what I was discussing here, which I think is just Landau//Score. But maybe that's getting a bit complex.

What about This one?

@cfrank said in Ranked Choice Star Voting ?:

@isocratia I’m not sure how score and approval can be said to solve the problem of burial at all, if one considers bullet voting to be a form of it.

I think burying is generally seen as putting a candidate underneath other preferred candidates. Normally in score/approval they'd be equally scored zero or unapproved.

@masiarek

I'm fairly sure it's straightforward. Look at the final two candidates, and any candidate ranked below either of them on a voter's ballot is red.

Edit: Also I think that example image is slightly wrong, the ballot that has D > F > B > ... should have B in black.

I believe that the later-no-harm criterion is so confusingly worded that people think it means something it doesn't. It's defined in terms of not harming a candidate, but people think that it means that adding a second, third, ranking etc. will never harm the voter. So they think that LNH means that every voter has an incentive to give their full ranking.

Because IRV fails the participation criterion, it's possible that the voter can be harmed even by adding their first choice. Sure, this will never change the winner from their first choice to someone else, but it could change the winner from their second choice to their 15th choice.

LNH is meaningless without the participation criterion and it's trivial to show that failing the participation criterion means that a voter can be harmed by adding their second choice as well (e.g. their first choice gets eliminated and their second choice causes a participation criterion failure).

The only method that satisfies both LNH and the participation criterion is... plurality voting. Or some kind of plurality-equivalent ranked voting which only looks at the first choices. And here it's clear that it only satisfies LNH by completely ignoring everything else after the first choice.

@masiarek A is the only Nash equilibrium, while not a Condorcet winner it is in my opinion the only sensible winner of the election (being the only weak Condorcet winner). Every other candidate has another candidate that is preferred over them by a majority.

Once A is elected, if they are removed from the running for second place, then B becomes a Condorcet loser and C becomes a Condorcet winner. If you continue with this process, either maximizing the rank of a remaining Condorcet winner and minimizing the rank of a remaining Condorcet loser, you arrive at the rank A,C,D,E,B. This process fails or is nondeterministic when there is a strong Condorcet cycle or more than one weak Condorcet winner.

That ranking might not be your favorite, but it’s the most stable in terms of game theory. It’s strange that some voters didn’t use the full range of scores but in a rank order system that doesn’t matter.

Another thing that one should keep in mind is that voting is for large populations. If the population is small, making social agreements is definitely way better for everyone!

@cfrank I'm not really the best person to ask about these methods probably. I don't know off the top of my head what criteria they pass/fail. However, the Landau set and others are discussed more here.

@cfrank said in Pairwise Matrix / Preference / Ranked Pairs / Cardinal pairwise:

Cardinals are ordinals with an enriched structure, since in addition to ordering they have some sort of “difference magnitude” structure.

This is the answer. You can rank three candidates 1, 2, 3 but give them scores (out of 10) of 10, 1, 0. So that tells you more than just your ranking.

Obviously in real life elections, there's debate about the meaning of the scores and whether they're just used as a strategical device rather than a genuine measure of preference difference, but that's for another day.

@toby-pereira a historical re-enactment in the style of this video is to have one of the kids tying his shoelaces together with another’s or something, and then the third winning because the other two fell over 😂 Also, the ridiculous irony of using a race like that to demonstrate their argument is: the winner of the race IS the Condorcet winner!

In fact, I think using a race analogy is a great way to convince people that the Condorcet winner is at least worth consideration when it exists. And a Condorcet cycle could be shown with runners chasing each other in a circle rather than proceeding toward the finish line.

@masiarek yes, B is the Condorcet winner and fails to be elected by STAR, so this example demonstrates that STAR is not Condorcet compliant. In this example we find

A>B: 10-9-2=-1
A>C: 10-9-2=-1
B>C: 10-9+2=+3

Therefore the digraph is

A-->B<--C<--A

and B is the Condorcet winner.

I suggest that, assuming that the purpose you have in mind is to research based on hypothetical electorates, that instead of positing STAR-style ballots and trying to transform them into strict-ranking ballots for comparison of voting systems, use instead a slightly different method, in which you would derive the ballots from a common origin.

A given case for study would start with a model electorate in which you would assume that each voter has a degree of affinity toward each candidate (I'm assuming you are only modeling single-winner elections). This affinity would be represented with a number in a range. You would normalize a given voter's affinities so as to assign if possible the most hateful number possible to at least one of the candidates and the most loving number possible to another. If a given voter has no spread, you might as well throw her vote out.

Then your attention forks to the voting systems under study. You assume for each system an algorithm to convert affinities to votes.

Sometimes a voting system shows limited interest in the voter's affinities. For example, what do you do if a voter's affinities toward the candidates are A:1 B:0 C:0 D:-1 but you are studying a voting system that requires strict ranking? The nearest possible votes are A>B>C>D and A>C>B>D. I think that among the best approaches you could take for simulation studies would be to use sufficiently large sample sizes so that you would expect random noise to cancel out, by and large, and choose randomly from among the closest votes but using a seeded random-number generator and starting with the seed as part of the givens at the outset.

@toby-pereira The scenario is around the 1:37:00 mark, ( which is a debating example in its own right ) but that was only the example that lead me down this thought process. Has anyone ran the numbers to find the first loser, second loser, ... to get the winner. With the assumption that I choice candidates Z, Y, X, W, V, B, A ( in that order I want to win ) ( assuming ranked choice ) and they all lose in the same order, would it make a mathematical difference it the ballots are calculated winner to loser or loser to winner. My thinking on it is that if it were counted loser to winner than my vote would count all the way up, but if counted winner to loser than it would not.

@dominikpeters Thanks for the information on this. Do you think that MES + completion is a good method for electing a committee of a fixed size or do you think a single method that works without an add-on would be better?

@evanstucker Thanks for working on it!