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.
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.
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.