> I hadn't noticed that you think of ordinal preferences as what voters fundamentally have

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.)