Balinski and Laraki come out for a robust and more meaningful version of range voting, in which each voter assigns a score to each candidate (using names, not numbers; for instance, if you want to think of this in the context of program committees, these scores might be strong accept/accept/weak accept/neutral/weak reject/reject/strong reject) but then, rather than calculating the (not meaningful) average of these scores, we rank the candidates by their median scores.
The result satisfies many of the axioms that we might like a voting system to have, is easily explained, and avoids one problematic case where a minority with strongly held views is overridden by the whim of an apathetic majority. Clearly, however, it doesn't avoid what I see as the major problem of range voting in partisan issues, of giving more weight to people who intentionally game the system by exaggerating their scores and less weight to people who try to play fair by assigning scores that match their actual beliefs.
Originally shared by Alexander BogomolnyA new voting method by M. Balinski & R. Laraki http://www.cut-the-knot.org/Curriculum/SocialScience/(171)2015.pdf Agrees with majority for "polarized" electorate, bad for apathetic
There are many issues in the U.S. for which a minority with a strongly held view holds sway over an apathetic majority; this is often a bad thing, at least to my taste. But regardless of the voting scheme, is there a single compelling model of social utility?
If you have four reviewers that say neutral, weak accept, accept, accept (to take a random example), then the median is somewhere between weak accept and accept. The paper doesn't discuss this situation because "it's a technicality that doesn't occur when you have many voters" (inexact quote). But, the number of reviewers is usually small so this technicality will occur often.
I would have liked if the paper confirmed that the naive solution (take the median to be ‘in-between weak accept and accept’) is OK. My only reason to believe it is OK is that I can't think of a better option -- a rather weak reason.
This is a common logical fallacy, explained here for a lay audience.
www.electology.org/tactical-voting
In a nutshell, suppose we have two cooperative mechanisms for pulling water from a well.
System One gives both parties 1 liter of water, and cannot be gamed.
System Two gives both parties 2 liters of water. But it's possible for one participant to cheat the other out of a half a liter, causing one party to get 1.5 liters, and the cheater to get 2.5 liters.
Now, clearly the second mechanism is better. EVEN IF YOU ARE THE SCREWED PARTY. If you contend that you'd rather have 1 liter of water than a guarantee of 1.5, with a possible chance of 2, then you are insane.
Moral: social choice theory is complicated and counterintuitive, and basically everyone gets it wrong.
Regarding Majority Judgement, it seems Score Voting is likely better.
http://scorevoting.net/MedianVrange.html
Which is to say that convincing me that range voting is the right system to use in all circumstances (despite my having seen it abused as a way to game votes in some specific circumstances) is going to require some actual philosophical argumentation, not just showing tables of randomly generated numbers and telling me I'm doing it wrong if I don't believe them to be an accurate model of reality.
Utilities are obviously not ordinal, and this can be trivially proved with probability-based revealed preference scenarios. This is not remotely contentious.
http://scorevoting.net/Mill.html
Further, it is mathematically proven that the correct social welfare function cannot possibly be ordinal, and must be cardinal. See Arrow's Theorem and Independence of Irrelevant Alternatives.
> Using regret as your end-all decider of result quality also requires that you believe that an outcome in which one person is very very happy and the rest are miserable is still a moral outcome as long as its average is slightly better than the alternatives.
However repugnant that may sound, it can be trivially shown via logic that there is absolutely no alternative. You show me ANY alternative social welfare function, and I can show you a reductio ad absurdum proof that it is incorrect.
http://scorevoting.net/UtilFoundns.html
That's wrong. It is part of any sensible definition of "group choice" or "democracy". We are seeking to aggregate preferences to know whether the group prefers X or Y; clearly that has to be a function of the group members' preferences about X and Y, and cannot have anything to do with the presence of Z. If you are actually trying to aggregate preferences, then IoIA is obviously necessary and absolute.
As for independence of irrelevant alternatives, I'm also not convinced that it is or should always be true. Consider, for instance, the 1977 Hugo best dramatic presentation award, in which an irrelevant alternative (the release of Star Wars after the nominations had closed) seems to have caused voter preferences to change (ranking no award higher than the nominees when otherwise it would have been lower).
You're making a common error here. In that example, the preferences for the prior releases ACTUALLY CHANGED. That's fine and has nothing to do with IoIA. IoIA is about getting a different result based on the presence of Z, even if preferences for X and Y are the same.
Moreover, your "total lifetime utility" associated with event (e.g. the election of Hillary Clinton for President) already takes into account everything that will happen in the future. Even if your preference for her may go up or down, your total lifetime utility (which is the integral of that over many years) is fixed. You calculate Bayesian regret based on total lifetime utility, of course.
> I claim that it is perfectly reasonable for X and Y to be so close to each other that I can't tell the difference and don't have a preference
It is theoretically possible for your utility for X and Y to be identical, yes. That doesn't refute anything I've said.
If you believe that an individual can only be indifferent to two alternatives that have exactly the same numerical value, then the preference orderings you get are necessarily weak orders, and indifference will be a transitive relation. But if you believe that there is some threshold of imperceptability, such that an individual will be indifferent to alternatives whose numbers are within that threshold of each other, you get a different class of preference orderings, the semiorders. For semiorders, it is not true that x~y ∧ y~z ⇒ x~z. But that's one of your starting axioms, so its untruth destabilizes your whole tower of logic.
Huh? There are n oxytocin molecules (or pick your neurotransmitter of choice) in your brain. Every single aspect of your perception of the world boils down to precise quantities and states of particles in your neurological system. There is nothing "non-numerical" here to discuss.
> But if you believe that there is some threshold of imperceptability
It doesn't matter whether you can perceive the difference between two similar utilities. For the purposes of calculating Bayesian regret, you start with made up numbers that you know with precision, since you can't read minds.
Imperceptibility is not useful to this conversation whatsoever. Note that EVERYTHING perceptible can be changed in imperceptible increments. I can gradually increase the volume on your music in increments that you cannot perceive, yet over the course of several minutes, you will perceive that the music is louder than it was at first.
Again, perceptibility is just completely irrelevant, and it's strange that you're talking about it.
Again, you're confusing two different issues: the social welfare function and the voting method.
Of COURSE Score Voting (a voting method) will introduce loss of preference information, for a multitude of reasons, such as normalization, voter ignorance, tactical behavior, and rounding error. There is actually nothing special about the issue you're describing where two candidates are similar to the point of imperceptibility; the same amount of error exists even if I clearly prefer X to Y by a huge margin. I may not be able to perceive my actual utilities enough to know whether X deserves a 3 or 4, for instance.
The social welfare function is an altogether separate issue. The social welfare function is NOT a voting method. It is what we use to EVALUATE voting methods. When you calculate Bayesian regret, you compare the ideal result (based on perfect knowledge) to the actual result (based on all the loss-causing issues I just described).
The fact that Score Voting is imperfect has NOTHING TO DO with whether the actual social welfare function is cardinal.
I've watched this evolution of understanding for the past 9 years, in hundreds of people like you. I made the same mistakes myself when I got into the subject. It's highly counterintuitive, and EVERYBODY goes through the same logical fallacies and misunderstandings. It's a process.
This doesn't address the flaw that I pointed out in your last argument. You confused voting methods with social welfare functions. Again, you said:
"Imperceptibility is completely relevant, because we're talking about aggregating the actual votes that voters are capable of expressing, not aggregating magic numbers that exist only inside your over-idealized model of what the voters actually believe."
"Aggregating the actual votes" is about voting methods. But the actual choice of which social welfare function is correct has nothing to do with actual votes or the accuracy of measurements. It is a question of, given that I have some set of exact preferences (which are totally hypothetical as if measured by an omniscient being), what is the group's preference.
Nothing I said there depends whatsoever on an axiom that "social welfare is what we use to evaluate voting methods".
But, social welfare IS what we use to evaluate voting methods. The entire point of choosing (the reason natural selection gave you a decision-making machine between your ears) is to maximize your welfare. The is the REASON that you make choices each day. An election is just "a choice made by more than one entity."
> the major problem of range voting in partisan issues, of giving more weight to people who intentionally game the system by exaggerating their scores and less weight to people who try to play fair by assigning scores that match their actual beliefs.
EVERY deterministic voting method is capable of rewarding tactical behavior. And in fact this is particularly bad with ranked voting methods such as Condorcet and Borda.
http://scorevoting.net/CondBurial.html
http://scorevoting.net/DH3.html
So much so that Score Voting may be a better Condorcet method than real Condorcet methods:
http://scorevoting.net/AppCW.html
There are three strategy-proof voting systems. The simplest one is, everyone writes down his favorite candidate and we pick a random ballot to determine the winner. Now, if voting isn't about actually satisfying preferences, then this system ought to be highly desirable to you, since it satisfies this notion of preventing any voter from having more power.
But when you propose this system to people, they almost universally recognize that it is bad, because it could allow the election of candidates who are unsatisfactory to huge swaths of the electorate. People obviously recognize, nearly universally, that voting is about satisfying the "will of the people". You will be held back by any thoughts that there is an alternative interpretation of voting that is not about maximizing social welfare. It wil prevent you from actually understanding this topic.
It seems incredibly naive to not only ignore strategic behaviour but also insist that one's axioms are "obviously" the right ones. Life is a lot more complicated that that.
> It seems incredibly naive to not only ignore strategic behaviour
You'd have to be asleep to think I didn't address strategic behavior. Observe that the original Bayesian regret figures I cited are for any ratio of tactical/honest voters.
http://scorevoting.net/BayRegsFig.html
And there was this one, arguing that with highly tactical voters, Score/Approval will tend to elect the Condorcet winner, plausibly more often than real Condorcet methods.
http://ScoreVoting.net/AppCW.html
Also this one, about Majority Judgement vs. Range Voting.
http://scorevoting.net/MedianVrange.html
This page has over 14 additional pages analyzing various esoteric aspects of tactical behavior.
www.electology.org/tactical-behavior