Oh, I see. That interpretation didn't occur to me because at that point I hadn't noticed that you think of ordinal preferences as what voters fundamentally have, and of scores / approval as being derived from those. Again, I just don't think that's true.

(But: Whatever the cause, I misunderstood your position and consequently misrepresented it, and I greatly regret that.)

It sounds as if you are arguing that it must be true because if you ask people to score things on a scale, people from different cultures tend to give different patterns of scores for a given preference ordering. I'll take your word for it that the "fairly extensive literature" does in fact show that they do, but I don't see how you get from that to the idea that preferences come first and scores are some sort of fundamentally unreal construct on top of them.

A person's culture may well influence their values. That doesn't make those values unreal or illegitimate or mean that when we're trying to aggregate people's values (in order to choose a candidate, policy, etc.) we should ignore that influence. That's obvious (or at least I think it is) in the case of specific values -- e.g., if a country has in it a lot of people whose culturally-influenced values favour peaceful foreign policy, they will tend to elect governments that favour peaceful foreign policy, and that's how democracy is supposed to work.

I think it applies equally if what's being influenced by culture is some other more abstract feature in the pattern of values. If members of one culture are more easygoing in a way that makes them find a wider range of political candidates "acceptable" than members of another, then candidates liked less by the latter culture will do worse than otherwise-similar candidates liked less by the former under approval voting, because being disliked by culture B will lead to more "not acceptable" votes than being disliked by culture A. I claim that's the right thing: being represented by the candidate B dislikes will cause more distress than being represented by the candidate A dislikes.

Now, it's potentially a different matter if what's happening is that people in different cultures have the same actual values -- both think X is a bit better than Y who is hugely better than Z -- but some cultural factor makes people from culture A who feel that way mark Y as "acceptable" and people from culture B who feel that way mark Y as "unacceptable". If you're saying that that "fairly extensive literature" demonstrates that that happens, as opposed to the situation where people in culture B really do feel a bigger gap between X and Y, then I agree that that's an argument against scoring-style or approval-style voting systems. I would be interested in some pointers to the literature in question, if so.

But to whatever extent there are actual differences in values that go beyond mere ordinal preferences, it is simply not true that "approval/score/etc. ballots are at best just ranked preference ballots with either randomized noise or randomized compression".

It seems obvious to me that real people, whatever their culture, can have values that genuinely and importantly don't reduce to ordinal preferences. Would you rather be given $30k, be given $25k, or have $30k taken from you? Would you rather eat a carrot, a radish, or a bowl of mud? Would you rather have your country led by Joe Biden, Adolf Hitler, or Josef Stalin? It's possible that people from different cultures would express their opinions about these options in different ways, but I flatly do not believe that there would be no information in what they say beyond "$30k > $25k > -$30k" or "Biden > Stalin > Hitler" or whatever.

Do you disagree with that? Or is it just that you are confident that the noise greatly exceeds the signal in typical cases? (Or some other option I haven't thought of?)