(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?)
I think that ordinal preferences are the objectively comparable thing that voters fundamentally have, relevant to the question of normal elections of candidates in public elections. That’s not all they have, and if we had an objective way to measure and an objectively correct way to aggregate expected experienced (dis)utility you could probably build a better public choice system around such a measure and aggregate than anything using ranked preference ballots. But we know from the research done in scoring/rating systems that the kind of things done in score/range voting or compressed-preference ballots like approval aren’t anything like a consistent measure of that, even before considering aggregation issues.
For lots of group choice situations that aren’t elections of candidates for public office, either approval or score style voting (and probably in some cases other compressed-preference systems besides approval) have concrete comparable meaning across different ballots and make sense, as I discussed with some examples upthread.[0]
> 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 is, across a population, in normal secret ballot, no personal consequence for the relation of ballot markings to actual winners, someone must win, elections for public office [1], because there is no consistent mapping to what people have beyond ranked preferences and how they do scoring of the type those ballots call for. There’s been fairly extensive research on this where it comes to rating systems. It’s one of the reasons rating systems have trended away from generic forms (though there is a lot of inertia!) to context-specific forms that focus on what has consistent meaning across respondents for the particular use being made of the rating. E.g., Facebook a while ago dropping 5-star ratings for “Would you recommend?”, media platforms like Netflix and others that had star ratings switching to just Up/Down, etc.
[0] including some public elections, e.g., modified approval makes sense — and is in effect used in California (though it isn’t called that) — for conflicting ballot measures, where in the event of fundamental conflict of measures in the same election, the “winning” measure if multiple get at least the minimum required to pass is the one with the most yes votes.
[1] But even for public office elections, if you weaken any of those constraints you can find situations where this changes. E.g., plain approval would make sense in candidate elections if you eliminate the “someone must win” condition, and instead it is an optional position, and if no candidate (even the one with the most approval ratings) got more than some threshold (say, approval by a majority of voters), then the seat would be unfilled. Then, the approval/disapproval choice would have a concrete meaning rather than just being an arbitrary compression of preferences. (Actually, that’s effectively the same system as the one discussed above used by California for competing ballot initiatives, which works because in any such set of initiatives, “None are psssed” is a valid final outcome.)
No, that's not it at all. I mean, now that you mention it, that sounds like something I would agree with, but its not either what I was saying here or particulary relevant to this discussion.
What I said here is about honest not dishonest votes. For ballots that do not ask a question with an objective mapping to preferences, honest ballots for the same preferences are a cultural variable. (This article implictly recognizes that honest ballots have no consistent meaning for approval, when testing it with two different consistent mathematical models, though that doesn’t really address the issue and it ignores the same issue for other methods to which it applies.)
For typical public elections, this problem occurs mostly with: ballots that ask the user to assign a score or rating to each candidate which is either more detailed than an unforced ranked preference ballot (a ranked preference ballot allowing ties) or less detailed than a forced preference ballot (a ranked preference ballot not allowing ties). Phrased another way, it applies to ballots that ask the user to assign scores or categories to candidates, where either the maximum number of distinct scores or categories is either more or less than the number of candidates.
There's fairly extensive literature on scoring systems (mostly outside of voting research, because they aren't widely implemented as voting systems), whether with a wide number (e.g., 0-100) or narrow range (5 stars) showing that without an objective touchstone, these are highly variable between individuals, in a way which strongly correlates with culture, in how they relate to what people actually think, on an absolute or relative scale, about the things rated, with the only consistent thing being that they tend to be consistent with ordered preferences, but the additional information (for score systems) or compression (for limited-categories) is inconsistent.
For that reason, approval/score/etc. ballots are, at best (that is, considering only personal variation and discounting any significance of the cultural correlations) just ranked preference ballots with either randomized noise or randomized compression, into which the associated tallying methods read false signficance.
EDIT: MORE that this applies to the use of these ballots in typical public elections of candidates. For other types of voting scenarios, the ballot markings involved may have concrete meanings that make these methods better, even ideal in some cases.
For instance, when planning a group activity for which you want maximum participation from the voter pool, approval where an “approve” mark is a binding commitment to participate if that option wins is an ideal method. Similarly, score voting where the assigned score is a binding commitment of that many units some scarce resource to the common project in the event of victory for the chosen option makes perfect sense.