Least-squares -- Is This Just A Complicated Restatement Of Score Voting?
Let each voter submit a Score-style ballot. Assume normalization from -1 to 0. Then define the square of a score as the pain that voter will experience should that candidate be elected. For each candidate, calculate the sum over the pains experienced by the voters should that candidate win. Elect the least painful candidate.
Yes, this is just Score with the elements of the range being expressed in a strange notation. But maybe an extension of a least-squares idea to the multiwinner context can get you multiwinner-cognoscenti (among whom I don't include myself) somewhere interesting.
@jack-waugh I don't think this would work for PR, not in its current guise anyway. It wouldn't be proportional for party voting. If everyone scored 0 to candidates of their favourite party and -1 to everyone else, then a voter's pain for each candidate is just 0 or 1. The most popular party would win all the seats.