@andy-dienes and rightfully so. Now how can we mathematically embody the intuition that throwing out pairs of votes, when compared to keeping all the votes and tallying them to arrive at scores (which may have pairwise indexing) that are sums over the votes, violates something?

[edit]

Suppose we have the system I described above, with the rule of matching ballots and throwing them out in pairs.

Let's say the candidates are Gore, Bush, and Nader and I vote Nader, 511. Let's account for the votes in terms of their effects on the pairs of candidates. In fact, let's ignore Nader-Bush and concentrate on Nader-Gore. What is the effect of my vote on the Nader-Gore accumulator? It has to be canceled by a vote of Nader, -511.

@cfrank Ok, I guess I can't disagree with that, especially since I consider this all hypothetical anyway.

@rob I'm just going off of the definitions, no assumptions needed 🙂

Agreed that voters' ballots will likely change depending on the candidates in the race in Approval more with a higher probability than in most other voting rules.

@Toby-Pereira to answer your question I'm looking into it. Arrow's Theorem actually has quite a few (slightly different) formalizations, and it looks like what I said is technically not true for the version defined on Wikipedia since that one only allows (strict) linear orders, but I feel quite sure I saw a formalization where the domain was all (weak) linear orders. I will try to find it.

@bternarytau Pretty sure it was that the average was not theoretically motivated

Here is a variation for ranking ballots that permit equal-ranking (and so would be an RCV-c system):

From each ballot, derive an "implied set of ranks". If the ballot ranks every candidate, the implied set of ranks equals the explicit set of ranks. Otherwise, add a rank at the bottom and fill it with the remaining candidates. For each possible count of implied ranks, other than unity (which is an abstention and can just be thrown out), form a mapping via a logistic function, from each rank to a score. The sharpness of the logistic function is characterized by the mapping [6, 5, 4, 3, 2, 1, 0] => [100, 99, 90, 50, 10, 1, 0]. Use the mappings and rankings to derive a score for each candidate from each voter. Proceed as before.

Some may say, why a logistic mapping and not a linear mapping? I ask them, why a linear mapping? I think fineness near the top will provide needed support to lesser-evil candidates in case true favorites don't win. Of course, any mapping from ranking to rating is imperfect and presumptuous, but I'm suggesting this as one of the least bad from the viewpoint of defeating two-party dominance (2PD) and as a sop to RCV advocates. They don't seem to appreciate the benefits of collecting actual scores from voters. And my example to try to show the importance of that is to compare the meaning and intent of Score votes Gore 0, Bush 1, Nader 100 vs. Gore 0, Bush 99, Nader 100. These would affect the pairwise scores of the candidates very differently in Score, but in RCV with whatever tallying, would collapse to the same vote Nader > Bush > Gore.

It's like this, then, to restate it?

In each round, the effective "votes" for the round are the ballots where a given candidate is the top-ranked on that ballot, from among the candidates still in the running. The round is going to eliminate someone from further consideration and you are going to find also the one candidate from among the remaining candidates in the round who received the second-lowest count of "votes" in the round. You will take the ratio of "vote" counts of those two candidates and remember that as the ratio between the scores you will report for those candidates. Eventually this chain will lead to the winner, and you assign the score 100 to the winner and use the remembered ratios to calculate the rest of the scores. Since every score is a product of 100 with some numbers that are strictly greater than zero and less than or equal to one, every score will be positive.

@multi_system_fan said in New voting method? What is 'minmax-TD'?:

I understand this problem, altough I doubt simplicity of voting methods or rationality in general will prevent this.

It won't prevent it, but it would help in terms of adoption when there is already resistance coming from people who think they'd lose power if such a system is enacted.

But yeah, from what I know of the political system of The Netherlands, all of this should be a lot easier there. I envy you.

@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.

@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.

I'm not sure why we can't have proxy representation; it seems to me to give the people more power than merely filling seats does.

But anyway, assuming proxy is off the table, what is the most important criterion for choosing among proportional voting systems?

@brozai Bear in mind that this was one of the systems used to choose Allocated Score so getting the same result is not a surprise. Also, SSS performed equivalently from my recollection. Allocated Score was chosen because there was some intuition that it was better than SSS in terms of strategy.

@marylander Thanks yup, this looks like a counterexample.

Using some of the ideas in your construction I found a slightly smaller one on 8 nodes

cd7a0a63-764a-466c-ab71-8fa9552bf2fb-image.png

@jack-waugh Well the whole issue with president is complicated by the electoral college, so for such hypotheticals such as this, it's probably easier to imagine some system that doesn't include the electoral college. Adapting a better voting method to presidential elections is a complex topic of its own.

But the point is, under a better election system, middle ground candidates would be more likely to run and to be elected. Political figures today that are closer to the middle include Democrats like Sinema and Manchin, and Republicans like Liz Cheney and Adam Kinzinger and Mitt Romney. John McCain was fairly in the middle (but Palin wasn't, of course). Perot was in the middle in that he appealed almost equally to both sides. Arnold Schwarzenegger is centrist by national standards, but was on the right relative to California.

None of these are centrist on all things, of course. Cheney is very conservative on most policies, she just doesn't toe the Republican line on things related to rejecting election outcomes and other things specific to the changes in the Republican party in the last few years. And none are really great examples because they are operating in a system that is biased against centrists, so they have a lot of hate directed at them (more from their own party than the opposite party).

As for Biden, that's a bit tricky. He's actually considered quite moderate. I suspect most of the hate directed at him from the right is because the country had gotten highly polarized in the few years prior.

@robla Yeah, I didn't mean "object" in the sense that I care so much what is on Wikipedia, but just in the sense of "I wish they didn't report RCV elections this way." I guess they (not just Wikipedia, news articles as well) want to make it seem like the winner has a majority, as if majority really makes sense with more than two candidates. There are way better ways of visualizing such elections.

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.

@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.

What about This one?

Plurality has a spli- vote problem, which is why we need a Progressive Primary. But, lacking that, the Green Party & their nominee are the obvious natural combining point for Progressive votes

…& any forum that includes voting strategy doesn’t need to avoid voting-strategy specifics.

We who want to eliminate vote-splitting and spoiler effects have grounds to choose a system that the public can easily understand. Does anyone think this system passes muster in that regard?

@lime said in MDD//Score:

eliminate any candidate who would lose in a runoff

If that's what it amounts to, then maybe a restatement of the definition in terms of predicting such a runoff would make the definition easier to read for a broad and skeptical audience.