> 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.