@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.

Just to clarify on the Phragmén thing:

If you just have a fixed quota then the voters that get their candidates early can get a bad deal because they pay a whole quota, whereas later on, the might not be a candidate with a whole quota of votes and yet you have to elect one anyway, so the voters of this candidate get their candidate more "cheaply".

So you might then look for a quota that distributes the cost more evenly, and that's all Phragmén really does. It distributes the load or cost across the voters as evenly as it can.

I see subtractive fixed-quota methods as a cheap hack really.

@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!

@wolftune OK, that's fine. I don't disagree with your point. But I was clarifying in case your post was a response to my bit about the candidates that are the favourites of nobody, but obviously it wasn't.

But just to be clear anyway - when I was talking about not wanting to elect the favourite-of-nobody candidates, I wasn't referring to stopping the election of such candidates in principle. But we've discussed certain specific scenarios where we all seem to agree that electing the candidates that are the favourite of nobody isn't the best thing to do. And I was discussing ways to elect the candidates we would want to in this situation.

@isocratia I had a look at the user list, and you haven't got a green tick by your e-mail address so it might be that. Hopefully you should now receive a validation e-mail. Check your spam if it's not in your inbox.

@toby-pereira Right, that's what I'm saying. I should have been more clear.

Approval, STAR, Ranked Robin, Score, etc. all pass the Equality Criterion. The Equality Criterion is literally the test of One Person, One Vote, ie an equally weighted vote, according to the Supreme Court, but because you're voting for multiple candidates and you're literally casting multiple votes, it really doesn't seem like it.

The Approval pitch that "the candidate with the most votes wins" explicitly defines an Approval as a vote and states that each voter can cast multiple votes. (This makes Approval comply with Plurality laws, but not "vote for 1" laws.)

So, explaining why Approval does pass One Person, One Vote isn't easy, especially on the scale needed. In any case, it's absolutely something CES needs to get in front of.

In contrast, in STAR and RCV your vote ultimately only counts for one candidate, or as an abstention between the finalists. Oregon, South Carolina, and Pennsylvania all have constitutions that requite voters to only cast a vote for one candidate, so this is important legally.

@psephomancy said in GPT and I invented a new voting system metric?:

@toby-pereira said in GPT and I invented a new voting system metric?:

I think if a measure isn't cloneproof it's probably not a good measure.

Why would that matter for a measure?

Because you can have a candidate that is the closest to being the Condorcet winner but not the Copeland winner. E.g.

14: A>B>C
4: B>C>A
12: C>A>B

A>B - 26:4
B>C - 18:12
C>A - 16:14

A has the biggest winning margin and smallest defeat, and is the nearest to a Condorcet winner by any reasonable measure. But then you can clone C and have a C1 and C2 but where C1 is always ranked above C2.

In this case A now has two defeats (against C1 and C2) so loses to both B and C1 in Copeland. But A is still the nearest to a Condorcet winner in terms of defeat sizes, so I would say they are still the "most Condorcet" winner.

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 OK, there are obviously various competing Condorcet methods, and on the EM mailing list there's discussion and debate going back years, but a good starting point is ranked pairs, which has good criterion compliance (such as being cloneproof) and is relatively simple to explain. It's also far more likely to pick a unique winner than Copeland.

After that, the rest is just tie-breaking, so if you're not using Copeland any more, it's not such a worry.

With the Borda count, although it's normal to give points to positions in a linear manner, it is equivalent to just summing the margins of the head-to-head wins so it looks equivalent to this Dasgupta/Maskin score. It's rare you'll reach that stage if you use ranked pairs. You'll almost never have to use your scores. So at this point, it's a case of just picking your favourite Condorcet method.

@mosbrooker said in Voting Theory sooo boring if not for the key to everything!:

All roads pointed to law, the rule book of society. All laws pointed to the US Constitution. I have no interest in other nation’s laws because we are, by very far, closest to the people rule the law not vice-versa.

Are you sure about that? I don't think the US is generally seen internationally as a shining beacon in terms of democracy.

I started to game theory this whole business. Start with an island (so no outside influence or interference) and One Leader. When does the OL face an opponent?
…this is about where I start to fall asleep. I’ve written this so many times it’s killing me. SOOO tired

Fast forward…
The OL (me because who else is going to get this ball rolling if not the discoverer of Democracy?) is subject to immediate removal upon the simultaneous dissent of over half of all people. I choose my opponent, Lisa of course.

I think we discussed your leadership model before and getting to choose your opponent was a bit of a sticking point for me.

Now that we are living in harmony and budgeting our resources, what’s the end plan? No way are we going to fly a spaceship to a near (1000 light years away) planet to set up shop. Not gonna happen. Get used to it. When we are done with Earth, we are done as a species. Been a good run.

BUT we must help life get a footing elsewhere. We can load bits of life (amoebas, cells etc.) abord a flying freezer and hurtle it off to other galaxies. Whether we aim for a planet in or throw a dart at a massive galaxy, our offering might just spark life somewhere else. Maybe, just maybe, life will take hold, and, in 20 million short years, people will be picking up dry cleaning and are back to leaving bad yelp reviews. From there, the planet will begin to succumb to the mismanagement of its resources, a person will design a blueprint specifying a system so that people can live with each other in peaceful and fun harmony until their last day upon which a spaceship carrying life’s building blocks is launched…

This is getting a bit off-topic now, but you think there's no chance of getting intelligent life away from Earth without evolving again from scratch? What about uploading minds and beaming the information across the universe?

Some things that came out of the paper:

If A, B, C and D are parties fielding multiple candidates, then with the following ballots, what proportion of the seats should each party win?

250: AC
250: AD
250: BC
250: BD
2: C
2: D

COWPEA would say that A and B would each win just under 1/4, and C and D would each win just over 1/4.

However, Optimised PAV would elect C and D with half the weight each, and A and B would not get any weight. The multi-winner Pareto efficiency criterion assumes that a voter's satisfaction with a result can be measured purely by the number of elected candidates they have approved. And going by that, any result containing any A or B candidates is Pareto dominated by CD.

This can be seen as a two-dimensional voting space with an AB axis and a CD axis. PAV would ignore the AB axis. Arguably though COWPEA makes better use of the voting space.

That was an example where any proportions are allowed, but here is another where 2 candidates are to be elected.

150: AC
100: AD
140: BC
110: BD
1: C
1: D

Basically any deterministic would elect either AB or CD. CD Pareto dominates AB in this multi-winner sense as all 502 voters have an approved candidate under CD, compared with 500 under AB (no-one has two approved candidates). However, AB is more proportional. 250 have approved A and 250 have approved B. 291 have approved C and 211 D. So under the CD result, the 211 D voters would wield a disproportionate amount of power. So what do you think? Does that matter or is it all about number of approved candidates?

If you go for AB, then you are rejecting the multi-winner Pareto efficiency criterion, but also consistency as a by-product. This is because you can have a set of ballots where the C and D approvals are just swapped round. So it's 211 for C and 291 for D but otherwise the same. Then combining the two sets of ballots together you get:

250: AC
250: AD
250: BC
250: BD
2: C
2: D

If there are 2 to elect here, it must be CD. So if you went for AB in the other examples, then you are rejecting the consistency criterion in multi-winner elections.

@wrightmethod Your name is even wrightmethod. That's commitment to the method. But as it happens, I'm unfamiliar with the method, sorry.

I'm not saying NodeBB can't be reverse engineered, but it might not be the easiest program to do that to. It uses some kind of abstraction layer on top of the DBMS.