Making Voters Equal in Power

Do you agree that choose-one voting privileges some voters over others, depending on their affinities toward the candidacies?

I think my opinion is certain to be a controversial one, but I actually think the answer to this question (in the general sense) is no. I do not think any particular voters are privileged over others. I think the arguments saying that choose-one does not constitute an equal vote really in the end boil down to the claim that "strategic votes are more powerful than unstrategic votes," which of course is true, but not relevant to question of vote equality.

So, yes, I think choose-one provides an equal vote to all voters, fight me
(of course choose-one is awfully-terribly-nogood-bad, notwithstanding)

From a first principles approach, I do not see any reasonable way to define rigorously an "equal vote" besides just Anonymity and Neutrality.

Jack Waugh

Maybe before asking whether choose-one provides equality, I should back up and ask a question that should come prior: what is your problem with choose-one voting (I'm asking only in the single-winner context)? @rob

rob

@jack-waugh My #1 problem with choose-one is that it is extremely vulnerable to vote splitting, incentivizing the formation of parties so they can nominate a single candidate to protect them from voting splitting. This leads to two dominant parties, and those parties often become highly polarized (which can lead to all the crazy shit we've seen recently, from "stop the steal" and the capital attack, to death threats to voting officials, to culture wars over "wokeness", to hundreds of thousands of deaths due to people associating vaccination status with their political identity, and so on).

Here is an article I wrote that explains it pretty well that has been on the web for 17 years now: https://www.karmatics.com/voting/why-we-have-parties.html

Do you agree that choose-one voting privileges some voters over others, depending on their affinities toward the candidacies?

Kinda? I think choose-one distorts things a lot, and I guess you could call that an effect of that.

But it isn't why I care about this stuff. Life has never been fair. It's not fair that some people are born into rich families in stable countries and some people are born with genetic diseases or get cancer, and that some people are smarter or more attractive than others. You can't fix that everywhere.

What you can do is have systems that promote harmony rather than discord. That's the low hanging fruit I see in voting systems. Small changes could make big differences.

Should I lay my thought out in straightforward fashion, or try to engage you using the Socratic technique?

Yeah let's stick with straightforward, unless you really feel the Oracle of Delphi has deemed you to be the wisest of men.

Is that your story of setting the temperature in the office to the median of everyone's stated numbers?

Yes I think voting for a numerical value by expressing your exact preference, and then selecting the median value, is as close to perfect as a voting system can get, when it comes to two things: being immune to strategy (it is "game theoretically stable"), and giving everyone equal "pull". I think it serves as a good model for what we should be aiming for.

There are certain assumptions, such as that the number of voters makes the averaging that is necessary with even numbers of voters insignificant, as are various rounding issues. Also that the number being voted for is going to be seen by all voters as "the closer I get to my preferred value, the better". I'm sure someone who is determined to miss the point could find other places where it deviates from perfection. But it certainly comes closer to perfection than any single winner method could, given that candidates will never be nearly as evenly spread across the ideological spectrum.

But the most important point is that someone who wants the temperature to be 90 degrees has no more upward pull than the person who wants it to be 80 degrees... they are both above the median, and therefore pull that median upward equally.

And you can further demonstrate that by contrasting it with using average. (which might appeal to a utilitarian, but it should be obvious how that would be insanely subject to exaggeration)

I think you can demonstrate that some single winner systems approach this, which you can demonstrate by actually voting for numerical candidates using single winner system. For instance, you could have people rank a list of proposed temperatures, and show that a Condorcet-compliant system should best approach the above "vote directly for the number and select the median" system.

Jack Waugh

Yeah let's stick with straightforward

I agree with you that vote splitting is a problem. I consider it just about the top problem. Maybe the very top problem.

Let's look at how vote splitting works in Choose-one Voting. Choose-one Voting is tallied exactly the same way as Approval Voting is. We can validly think of Choose-one Voting as what you get if you start with Approval Voting and add a restriction on the ballots.

I think a fair way to characterize, in a summary way (i. e. it could leave out some precision or detail) the will of a voter about the electoral outcome is to ask, if the voter is thinking strategically, what Approval Vote would that voter cast?

Suppose for example the candidates are Mussolini, Gandhi, and King.

At this point, I have decided that for the purpose of this discussion, I am going to talk of Approval Voting as instead Disapproval Voting. I think this viewpoint, as I have suggested in this forum already, helps dissuade listeners from the accusation that Approval Voting violates One Person, One Vote (OPOV), while according to them, Choose-one Voting implements OPOV, and my position is exactly the opposite.

Assume we have a faction among the voters whose strategic Disapproval votes are -Gandhi -King. And assume we have another faction whose stance by the same measure is -Mussolini. Under Choose-one Voting, how many count of voters in one of those factions does it take to counter a given count of voters in the other faction?

If we had agreed on the Socratic method, I would at this point stop and await your answer. But since we are in the Straightforward mode of argumentation, I will give my answer.

If the -Gandhi -King faction numbers a million voters, then it takes two million -Mussolini voters to balance off the effect of the former on the tally. Choose-one Voting allows a -Gandhi -King vote (and counts it fully), but it does not allow a -Mussolini vote. The -Mussolini vote type is split into a -Mussolini -Gandhi vote type and a -Mussolini -King vote type. If we assume the -Mussolini faction is unable to coordinate on a decision of which of King and Gandhi to throw under the bus, or are unable to discipline their members so each one follows the plan, their vote is going to be split. In the quite likely case that they have no coordination at all, it will be split about equally. That's why it takes two million of them to counter the one million -Gandhi -King voters under Choose-one Voting. If say 60% of the electorate belongs to -Mussolini and 40% to -Gandhi -King, the rightful outcome would be to elect one of Gandhi or King, but Choose-one Voting will elect Mussolini.

It takes two million members of faction -Mussolini to counter one million members of faction -Gandhi -King. To find the power of the individual voter, divide by the necessary size to prevail. A single member of faction -Mussolni only has half the power of a single member of the opposite faction.

Choose-one Voting does not meet the standard of Wesberry vs. Sanders, that the effective "weight and worth" of a citizen's vote must be "as equal as practicable."

[edit]

In regard to your example of the temperature in the office:

I resisted this idea for quite a while because I thought that candidates do not necessarily sit on a linear scale, or even a multidimensional space made of the product of a number of linear scales. But some of your recent writing argues pretty convincingly that candidates kind of do so sit. I said there is no middle ground on abortion, but you put up a picture showing a whole range of opinion on abortion. And in my mind, I came to realize that the same thing could be said about torture, even though I had thought of an antitorture position as absolute, radical, and nonnegotiable. But when I thought about it by analogy to the series of pictures you put up about abortion, I had to admit that my absolutist thinking about it had been too narrow and left out valid considerations. Consider for example there was a report a few years back that someone had been hounding one of the astronauts in public and repeating that the Moon shot had been faked. After a certain amount of this hounding and harassment, and basically saying the astronaut's life and career had been a lie, the astronaut, according to the report, slugged his harasser in the face. Did I feel that the astronaut was in the right? On an emotional level, definitely. But a radical antitorture position would say hitting a person in the face is torture, and should not be excused. And I believe the law would not excuse it; it's assault. But as you showed, these things can be looked at as filling out a linear scale. Hitting someone once is a mild form of torture, and slapping an adult is an even milder form.

You argue that a median provides equal "pull" and an average does not. On the other hand, Score Voting used to be called Range Voting, and I say that since it limits the pull of a single voter to a range that could be normalized to between 0 and 1 or if you will between -1 and 0 or between -1 and 1, whatever is convenient to compute or argue with, that prevents anyone from having more pull than anyone else, provided that everyone uses the optimal tactic for the faction to which they belong.

But that doesn't mean I'm against all Condorcet-compliant systems. I think a way to measure "pull" is with respect to pairs of candidates. If my pairwise pull can balance off your pairwise pull, and if no regions of reasonable vote types are arbitrarily excluded, and if my expression of my stance about candidates A and B (and the full counting of that in the tally) is not restricted based on my stance about candidates C and D, I'm probably in favor of the system.

rob

@jack-waugh said in Making Voters Equal in Power:
(regarding score voting and the temperature voting thing)

I say that since it limits the pull of a single voter to a range that could be normalized to between 0 and 1 or if you will between -1 and 0 or between -1 and 1, whatever is convenient to compute or argue with, that prevents anyone from having more pull than anyone else, provided that everyone uses the optimal tactic for the faction to which they belong.

Score voting is almost like saying "everyone write down their preferred temperature for the office, but it has to be between 65 and 75 degrees. Then we'll pick the average."

Sure, there is a limit to how much they can exaggerate, but the smartest voter is going to try to guess what others will pick, and then exaggerate their preference as far as they are allowed.

@jack-waugh said in Making Voters Equal in Power:

I had to admit that my absolutist thinking about it had been too narrow and left out valid considerations.

Cool.

And keep in mind, even if we say some issues are lacking a middle ground, you can still have a middle ground candidate. Example: Liz Cheney. She is far to the right/Republican side on some things, and far to the left/Democrat side on the "DT must not be re-elected" issue. That sort of averages out to middle ground.

Jack Waugh

@rob said in Making Voters Equal in Power:

Score voting is almost like saying "everyone write down their preferred temperature for the office, but it has to be between 65 and 75 degrees. Then we'll pick the average."

Room temperature is on an interval scale. If you take the median, you are treating it as an ordinal scale. I doubt whether candidates are on either an interval scale or an ordinal scale. The numbers that Score voters put on their ballots are not proposed temperatures or anything like that. They are related to the voter's affinity toward each candidate. The equivalent for office temperature would not be my submitting a single number. It would be my submitting a score for 65F, a score for 65.1F, a score for 65.2F, and so one, up through a score for 75.0F.

I don't remember how the discussion went that convinced me that Score is preferable to Majority Judgment or Bucklin. I think those are the outcome of the medianist thinking.

Sure, there is a limit to how much they can exaggerate, but the smartest voter is going to try to guess what others will pick, and then exaggerate their preference as far as they are allowed.

If I remember correctly, Warren D. Smith said that Score never provided an incentive to invert ranks. If that is correct and he was correct, that means that "so far as they are allowed" may be too far for what would serve their interests.

Note by contrast that RCV IRV Hare without equal ranking does provide an incentive to invert ranks (an implication from Gibbard and the fact that the ballot is nothing but a total order).

rob

@jack-waugh said in Making Voters Equal in Power:

Room temperature is on an interval scale. If you take the median, you are treating it as an ordinal scale. I

It is not a perfect analogy, you are looking at it too literally to see the point I am trying to make.

The point is that score gives you an incentive to exaggerate, but puts an artificial cap on it. As opposed to all voters voting sincerely being a Nash equilibrium, an idea expressed by my temperature/median thing (with near perfection). With discrete candidates, Condorcet methods comes far closer to this ideal, but there is a lot of messiness (due to there being discrete candidates) which can obscure things..

Anyway, all voters voting sincerely under score is not a Nash equilibrium.

Using average with the temperature voting is the extreme, where the incentive to exaggerate would make it insane.

But yeah, I think you'd do better to try to see what analogies are trying to demonstrate, rather than trying to pick apart where they differ.

Jack Waugh

@rob said in Making Voters Equal in Power:

As opposed to all candidates voting sincerely being a Nash equilibrium

I assume you meant to say voters. And is this possible? Is there a system that does this? By the Gibbard theorem, there is a better way to vote than "sincerely". This is of course an existence theorem; it does not construct the way. So maybe with some systems, even though the way exists, it's too hard to find for practical purposes, even for monied factions. I don't know.

[edit]

Anyway, all voters voting sincerely under score is not a Nash equilibrium.

Blimey, of course not! But what about all voters voting strategically under Score?

rob

@jack-waugh said in Making Voters Equal in Power:

And is this possible? Is there a system that does this?

I believe Condorcet systems are very, very close to this. They are not perfect, but nothing is. (again, at risk of tiring people with this, I think my temperature example is a good model for a system where honest voting is a Nash equilibrium. So is majority for a two-way race, but I don't like that example as much because two way races are inherently divisive and there is obviously no middle ground)

@jack-waugh:

But what about all voters voting strategically under Score?

Well, think about that. In a sense, it a Nash equilibrium by definition. Nash equilibrium is another way of saying that everyone is being maximally strategic. The ideal is where sincere voting and strategic voting are equivalent.

You can't vote strategically under Score (or approval, or choose-one) until you know how others vote. The only way for it to actually reach that equilibrium is in a context where everybody gets to adjust their vote after seeing how others have voted, until it stabilizes.

So that isn't a desirable equilibrium, for several reasons. One, you can't vote "strategically" without a more cognitive effort and research. Two, many people find that voting insincerely is against the spirit of the method, so they won't do it.

So now you've got a method that disadvantages people who are some combination of a) bad guessers, b) bad at math, or c) have a strong sense of ethics and honesty. That doesn't seem to be "equal."

Jack Waugh

@rob said in Making Voters Equal in Power:

You can't vote strategically under Score (or approval, or choose-one) until you know how others vote.

Do you have to know how they will vote, or does it suffice to know their affinities toward the candidacies?

rob

@jack-waugh said in Making Voters Equal in Power:

Do you have to know how they will vote

Really you have to know how they will vote. I have referred to this as the "hall of mirrors" effect.

Perot, Clinton, Bush was a good example of this. Going back to Nash equilibrium, I think there were multiple equilibriums in that election (under choose-one), one with Clinton winning, and one with Perot winning. A lot of people liked Perot best but weren't confident enough that similar people would vote for him.

This would be true for Score as well, just not quite as strongly.

But any reasonable formula I can imagine for choosing the most strategic vote under Score (or approval or choose one) that had access to what other voter's affinities were, would attempt to convert those affinities to votes in the process. That's why my vote simulator did that in an iterative process.

Jack Waugh

@rob In principle, this is an infinite recursion. To predict how they will vote, you have to model their prediction of how you will vote. Where do you stop?

@jack-waugh said in Making Voters Equal in Power:

Where do you stop?

At the Bayes-Nash equilibrium

rob

@jack-waugh said in Making Voters Equal in Power:

In principle, this is an infinite recursion.

And hence, "hall of mirrors."

In practice, my iterative vote simulator stops when the ordering of candidates doesn't change between two rounds. Since the ordering is all the "vote caster" algorithm looks at, there is no point continuing because it will always get the same result.

But keep in mind, that doesn't mean it has reached the one and only equilibrium. There can be multiple equilibria.

But again, I'd rather have a method that doesn't encourage this sort of thing. If I did a vote simulator for Condorcet, there would be very little, if any, iterating, since there isn't an obvious way to adjust your ballot even if you know how others will vote.