STAR but with weak votes in the runoff (when voters don't give their favorite candidate the top score)

Suppose the highest score a voter gives any candidate is a 3 out of 5. Arguably, instead of giving this voter 100% of a vote in the runoff, they would likely only want 3/5ths (60%) of a vote.

This is still compatible with precinct-summability: either, if finding the pairwise matrix, weight it so that only 0.6 of a vote goes to the voter’s preference in each matchup, or if doing a second round of counting for the runoff, check the highest score filled in on each ballot and then report that the voter wanted 0.6 votes to go to their preferred candidate in the runoff.

Why would any voter willingly want their vote power reduced?

Suppose a voter has a very weak preference between the running candidates. That voter might feel that in a ranked method, it’d be best for them to rank all the candidates equally (so as not to overrule someone else’s preference) or not vote. Given that they’d be willing to cast no vote in that situation, it’d be sensible for that same voter to give less than a full vote if given the opportunity in a cardinal method. With Score voting, for example, you could choose to give nobody a score higher than a 1 out of 5, and the method counts it that way.

Well, this is either just score voting (with honest voters) or plain STAR (with strategic voters)

Either do a simple, automatic runoff (STAR), or just cut out the runoff entirely (plain score)

It’s somewhat of a hybrid, since you can have a few voters who honestly want little influence in the runoff, while others want maximal influence.

Example:

2 A:1 D:5
3 A:5
6 B:4

Scores are A 17 B 24 D 10, with B pairwise beating A 6 to 5. So the Score and STAR winner is B. But taking into account that those who preferred B over A all have their favorite a maximum of a 4 out of 5, if we weight their runoff votes at 80%, then now B loses the runoff 4.8 to 5. So A wins under modified STAR.

Wouldn’t this just negate the point of the run-off? If you’re using the scores the voters have given the candidates as their weights in the run-off, wouldn’t it just be score voting?

I suppose you’re probably reducing to zero the score they gave the other candidate, but this seems a bit contrived and I’m not sure it’s something to pursue.

I should’ve phrased it better as “the highest score the voter gives to any candidate”. In other words, if there are 3 candidates, I prefer one in the runoff over the other, but the highest score I gave to any of the 3 was a 4 out of 5, then my runoff vote is weighted at 80%.

This might make sense in the SMV context as well: only let a voter’s ballot count so far in filling out a candidate’s quota of ballots as they supported their favorite candidate. So, for example, if a Hare quota of voters gave their favorite, a no-hoper, a 50% rating, and the SMV round winner a 25% rating, it’d be possible to count them as only half of a quota total.