Ranked choice absolutely conveys more information than approval. It's not as much as score voting, but it's mathematically false to say it's the same amount as approval. Among five candidates, approval would be 2^5-2=30 possibilities (almost 5 bits of information, assuming you can't approve/disapprove all because that's the same as not voting), while ranked choice would be 5!=120 possibilities (almost 7 bits of information, assuming ties aren't permitted). It's only with 3 candidates that they have equal information in terms of possibilities (2^3-2=6=3!).
And individuals don't have intransitive preferences, only populations can. (Assuming mental competence.)
Yes score voting would be ideal if it were easy to convert preferences strength into numbers, but one person's 7 can be another person's 3. There's no objective way to do it. The same as approval voting isn't objective, because there's no objective threshold. Whereas ranked voting is purely objective, a person can always express an ordered preference in a consistent, repeatable way.
> Ranked choice absolutely conveys more information than approval. It's not as much as score voting, but it's mathematically false to say it's the same amount as approval. Among five candidates, approval would be 2^5-2=30 possibilities (almost 5 bits of information, assuming you can't approve/disapprove all because that's the same as not voting), while ranked choice would be 5!=120 possibilities (almost 7 bits of information, assuming ties aren't permitted). It's only with 3 candidates that they have equal information in terms of possibilities (2^3-2=6=3!).
This is a common intuition trap, but it's wrong. Consider the difference between score voting on a 16-point scale vs a million-point scale vs arbitrary-precision score voting. A ballot for the first conveys 4 bits per candidate; the second, about 20 bits per candidate; the last conveys infinite bits of information. You ... probably don't expect a substantial difference between election results with each option.
The trick is that the aggregation rule destroys information, which is kind of the point of aggregation. Different aggregation rules destroy different information. The difference between aggregated approval voting and aggregated arbitrary-precision score voting eats LSBs, sure, but the obvious probabilistic constructions for extracting approval votes from arbitrary precision score votes actually approximate the arbitrary-precision votes quite well, which is not what your intuition predicts, because it turns out LSBs are, well, less significant.
Also, the flat fact is that most single-victor elections in practice don't have more than three "top" candidates that you're practically interested in extracting information about.
> And individuals don't have intransitive preferences, only populations can. (Assuming mental competence.)
> This is a common intuition trap, but it's wrong.
I respectfully disagree. Yes it's true that jumping to lots of information with score voting doesn't produce an equivalent increase of meaningful information and that information is eaten by the aggregation technique, but I would argue that's not the case with ranked voting.
In the larger practical sense, yes there is a good argument to be made for approval voting if everybody voted honestly and gradations in preference strength were truly "dithered" relatively accurately among the population in a way that approval voting could "recover" the actual score-like preferences in aggregate. But the reality is that approval voting is easily subject to bullet voting manipulation, which destroys all of the information that it would otherwise contain in theory.
So in the real world, I submit that ranked voting ends up conveying more information that actually gets used, because there's more incentive to vote honestly.
> > And individuals don't have intransitive preferences, only populations can. (Assuming mental competence.)
> That's one hell of a bad assumption.
I assume you're just joking. Because yes while we can joke "hur hur people are dumb", if you're not taking people's votes seriously then what are we even doing? Every mathematical model must assume that individual's preferences are transitive, or we'd go mad.
> I respectfully disagree. Yes it's true that jumping to lots of information with score voting doesn't produce an equivalent increase of meaningful information and that information is eaten by the aggregation technique, but I would argue that's not the case with ranked voting.
You would be largely wrong for single-victor elections, and even trivially so for those without more than three major candidates in the race (to wit: most of them). So you're going to have to make that argument.
> But the reality is that approval voting is easily subject to bullet voting manipulation, which destroys all of the information that it would otherwise contain in theory.
No, this is not the reality. At an individual level, bullet voting is part of your strategic frontier of (all sincere!) votes, but the only strategic bullet vote is for your sincere favorite who is also a likely candidate to win. It is possible to get your most preferred candidate elected over a more widely approved candidate, but this still requires a plurality of second-candidate approvers to prefer your most preferred candidate (and enough to bullet vote them!), which is, like, not the worst outcome in the world, realistically speaking.
Meanwhile, at a campaign level, it only makes sense to push bullet voting to (a) people who most prefer your candidate, whose only viable competition is a more widely preferred candidate who shares largely the same voter base, which in context is basically betting on your targeting specificity, and (b) people who are going to vote for multiple candidates, none of which are yours, who you're convincing to vote against their own interests.
Also, you don't have a 100% success rate on convincing people to bullet vote, so your ability to convince people to bullet vote your candidate is still a proxy for strength of preference. You're making it a lossier proxy, but since you're destroying information from people who you were able to convince to follow your suggested voting strategy, this is not really a winning strategy unless you're already winning.
All in all, bullet voting simply is not remotely as much of a bogeyman to approval voting as it is to some ranked voting systems. There is some degree of strategic influence available, but it certainly happens less easily than in a ranked vote and is weaker in approval voting than in pretty much any other voting system under discussion—I challenge you to find a bullet voting "manipulation" that manages to make approval voting contain less information after aggregation than your favorite ranked choice model.
> Every mathematical model must assume that individual's preferences are transitive, or we'd go mad.
It's okay to accept some error. People genuinely have non-transitive preferences. This only has to drive you mad if you insist on generating a total ordering.
And individuals don't have intransitive preferences, only populations can. (Assuming mental competence.)
Yes score voting would be ideal if it were easy to convert preferences strength into numbers, but one person's 7 can be another person's 3. There's no objective way to do it. The same as approval voting isn't objective, because there's no objective threshold. Whereas ranked voting is purely objective, a person can always express an ordered preference in a consistent, repeatable way.