Score voting (also known as range voting) is not a very good system to use in a real election because there's a huge risk that, on a scale of 1 to 10, the extremists will all give their candidate a score of 10 and everyone else 1, whereas the moderates will score their candidates, say, 7 or 8 and score the ones they don't like 3 or 4. The extremists could thus prevail despite being significantly outnumbered by moderates.

Or in other words, it's not safe to vote honestly in a score voting system because you're throwing your voting influence away. The rational thing is to maximize all your votes to be 1 or 10 and nothing in between.

Approval voting is just that. Basically it avoids the problem by forcing everyone to vote tactically.

STAR voting approaches it differently, by using score voting to select the top two, and then doing a runoff with the votes maximized. (Under STAR there's a risk that you might have two extremist ideological clones that make it to the runoff.)

I think plain score voting could work reasonably well in a primary.

>whereas the moderates will score their candidates, say, 7 or 8 and score the ones they don't like 3 or 4

Indeed, you should use whole available range. But there's still incentive to differentiate more than max/min, because otherwise you don't get any influence to choose between other candidates. For example with candidates: A-best, B-lesser evil, C-evil; instead of scoring max/0/0 it would be more reasonable to vote max/something/0. Voting system cannot give you result reflecting your preferences if you don't provide them!

Maybe another way to look at this: there's only so much influence single ballot has, and you can spend it to either push A above B/C, or A/B above C. It's a tradeoff, but score voting allows you to dial in the ratio you want. Falling back to approval is strictly less expressive.

> The rational thing is to maximize all your votes to be 1 or 10 and nothing in between.

Can't you just scale everyone's votes to the same range?

You could. That would be a reasonable thing to do.

I suppose you could even do an iterative process: rescale, remove the lowest-scoring candidate, rescale, remove the lowest-scoring candidate, and so on until there's a winner. That'd be like STAR but with multiple runoffs instead of one.

What's the added complexity of STAR?

STAR is phase 1: sort(sum(candidates))[:2] (almost identical to score/approval/FPTP. We'd just take argmax instead of top two) and phase 2: eliminate other candidates, argmax(sum(candidates)) (identical to score/approval/FPTP).

On the other hand RCV is a multi-round system with a while loop. In practice it almost never has fewer than 2 rounds (requires overwhelming majority, which almost never happens with more than 3 candidates).

From an algorithms perspective RCV is more complex.

I mean the added complexity of STAR compared to score. It irks me that it basically adds second election using different system, that happens to sneakily reuse the same ballot.

It's not a different system, it's the exact same algorithm. In both rounds it is argmax(sum(candidates)) (identical to FPTP btw) but the first round you take two elements instead of 1 and second round you use one hot vectors restricted to the top 2. That's it.

> From an algorithms perspective RCV is more complex.

Perhaps, but people aren't computers.

It's admittedly difficult to score this objectively, but I find RCV much easier to understand.

Much easier to understand from the voter perspective of the tallier perspective? From the voter perspective I find them fairly equivalent and both are frequently used in the everyday world (scoring might be even more considering 5 star reviews). But from a tallying perspective I think it is very hard to argue that RCV is substantially easier. Again, the score/approval algorithm is identical to the FPTP algorithm (which is trivial). It is simply argmax(sum(candidates)). Just sum the totals in an excel file and pick the largest number. I don't know a single person that has a hard time understanding this and I suspect if they did they would have an even harder time understanding how to tally RCV.

With STAR, it's harder to understand the affect of your vote.

RCV means: "I'd like this candidate, but if he can't win, I'll take this candidate instead." (And so on down the list of candidates.) Most people understand the concept of runoff elections. And, it's very very obvious that adding second and third choice candidates will never make your first choice less likely to win (on your individual ballot).

Under STAR, the effect of your ratings are less clear.

I think you're over complicating it in your head and that's making it difficult for you to see. You need a different perspective. Instead the perspective you need is that you rate each of the candidates and then put that into the system. The system will look at all the ratings and determine which has the highest agreeability as a whole. If you're too focused on your own individual "should" then maybe this is hard. You'll over think how you should play the strategy and game the system to make your preference dominate. But the entire point of cardinal systems is to take this out because we don't want people gaming the system. We just want to find people's preferences and elect candidates that are most representative of the people.

You're having a hard time figuring out "the effect of your vote" because the entire point is for you to not be able to game the system. Obviously no system is immune to strategies and there very much are some here. But they don't have huge effects on the whole election. I mean we don't want to violate the monotonicity criteria.

As a practical consideration, the runoff in STAR does offer a legal advantage in some districts where a runoff is legally mandated.