Topics created by masiarek

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.

@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).

@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".

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!

@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.

@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.

https://www.equal.vote/fv

@sass said in Ranked Robin Disadvantages -:

As I've thought about it more, if there's a Condorcet Winner, then cloning is irrelevant under Ranked Robin, making it an unreliable strategy.

It's not just about strategy though, as said above. A potentially "wrong" result could still happen by accident.

Also, basically all Condorcet methods fail Participation. It comes with the territory.

Yes, it's very hard for methods to pass it in general. So relative to other Condorcet methods this doesn't count against Ranked Robin.

Moreover, focusing on pass/fail criteria is the issue that caused voting enthusiasts not to achieve real-world progress for 200 years. The question is not "Does this method pass this criterion 100% of the time?"; the question is "How well does this voting method perform on this metric in practice?". Considering that cloning is only helpful under Ranked Robin when there's no Condorcet Winner and that scaled elections without Condorcet Winners are incredibly rare and difficult to predict, I see it as a nonissue.

I agree that overall performance (however one might measure it) isn't necessarily the same as just how many criterion boxes you can tick. However, if a method does fail a criterion, it still doesn't look good if there is another method that is as good elsewhere that also passes this criterion.

And just to set the record straight, I think Approval and Score are great methods. I absolutely support them and would be very happy to see their use in public elections.

That's good. I think they and Condorcet methods have merit.

@Toby-Pereira I was on mobile, so the link didn't copy properly. Here's the section discussing frequency of ties:
https://electowiki.org/wiki/Ranked_Robin#Frequency_of_ties

OK thanks, but I'm not seeing anything to suggest that a three-way cycle would not be the most common tie.

I need to clean up the electowiki page, but the Equal Vote site on Ranked Robin is a much better reference:
https://www.equal.vote/ranked_robin

Thanks for the reference.

@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.

Dear team,
I would like to sincerely apologize for my mistake regarding the graphics shared in the public forum.

I acknowledge that I did not follow the proper protocol for graphics in draft status and in private channels,
and
I also understand the importance of maintaining the context and consent when sharing someone else's work.

@jack-waugh I don't disagree with BTR being a good option, but Sass's video makes obnoxiously unsupported assertions, such as that IRV is worse the plurality, which is ridiculous. I think he does far more harm than good by putting all his efforts into attacking the one alternative to plurality that is having some success. He also says that plurality and IRV are unconstitutional, which is just dumb.

@spelunker The primary ballot format @masiarek uses is the one I have recommended. It is commonly used within forums, and is easy to parse. Even easier to parse if you just drop in the code I wrote for it... 🙂 (although it's js code not python)

See: https://codepen.io/karmatics/pen/poLPpzW

For example:

134: a[5] b[4] c[2] d[1] e[0] f[0]
64: a[5] b[4] c[3] d[1] e[0] f[0]
94: a[3] b[5] c[4] d[1] e[0] f[0]
70: a[2] b[2] c[5] d[2] e[0] f[0]
63: a[0] b[0] c[0] d[3] e[4] f[5]

It's also the format I recommended people use for signatures.

@masiarek It is intended to be single winner, and the results can be seen here under a few different systems https://codepen.io/karmatics/pen/ExKZVjM
(click on tabulate in bottom right)

Notice that different systems show different results, and there is no Condorcet winner, that's on purpose.

You can also generate "blurred" ballots to make examples more realistic, that just generates additional random ballots but within the general range of the existing ballots.

Yeah we can talk soon, I can't at the moment though.

@masiarek STAR should handle floats fine. If you want to round them to simulate real world, you can.

Look at my signature as to how I am planning on doing my "voting on voting methods" project (see my score for cardinal-alt). I was going to have them range from 0 to 10, but you can add as many decimal places as you want. STAR would have no problem with this.

Of course anyone who wants to scale them to range between 0 and 5, and round to an integer, is welcome to do so when they tabulate. (keep in mind that for this project, we'll tabulate in many different methods with none of them being "the official one", a luxury we have because we aren't actually using the winner for anything real)

Obviously in real world political elections having floats probably isn't practical, but there is no reason to not do it in this context.