What Is Voter Satisfaction Efficiency?

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.)

That said, if we adopted something like score or STAR I don't think there would be any problem with parties, nor would they be destroyed. You still get the advantages of pooling resources. Have a strong preference for members of the hippo party? You can donate and campaign for them even while you hash out which candidate best represents the coalition of people at the time. Think the hippo party played dirty and kicked out your favorite candidate Salamander-Gibbon Yack but really don't like the opposing party Tree Trunks? You can still vote your favorite person and not have any determent (system is monotonic). This actually gives less power for the hippo party to determine for you which is your preferred candidate.

Better yet, you get a lot of information! So even if the hippo party's leading candidate wins but you find that Salamander-Gibbon Yack was an extremely close second then the hippo party will have to update their policies (hopefully). By rating, instead of ranking, candidates you have a substantially more expressive ballot and we can data mine and learn from it through this expressiveness. We live in the age of big data and yet in politics we compress data to a point that is almost meaningless.

Cardinal systems won't destroy political parties, but they prevent them from controlling and manipulating the elections.

You have 3 candidates that you like in preferential order. A > B > C. But you like A only a little more than B and REALLY dislike C. Ordinal systems do not allow you to express this. When you score, you can say A: 5, B:4, C:0. Approval is just the same thing but with a smaller range and is easy to integrate into existing tools (I don't think that's a great argument though because we should rebuild these tools anyways considering massive security flaws we've consistently found).

From wiki

> Arrow originally rejected cardinal utility as a meaningful tool for expressing social welfare, and so focused his theorem on preference rankings, but later stated that a cardinal score system with three or four classes "is probably the best".

Again note that he's talking about social welfare and not voting.