Combining Utilitarianism and Proportionality in PR via Ballot Checkboxes

What if, in sequential score PR methods where the highest-scored candidate in each round wins, each voter had a checkbox they could tick on the ballot allowing their favorite to win based on having the most points within a Hare Quota of the voters who ticked the box, even though some other candidate is more high-utility overall? In an example where Green Party voters are unsure of whether they are a Hare Quota or not, and so must decide whether to help the lesser evil Democrats get an additional seat or risk it all to elect a Green and potentially get no representation, they could all tick that checkbox and give a few points to the Democrat; if they are a Hare Quota, then the algorithm would see that the Democrat, who is leading in points overall, has less points than the Green Party candidates within the quota, and would elect a Green and allocate or reweight the Green ballots.

This probably fails a bunch of criteria, but it might be a useful method for private organizations. Certainly it seems a good way to give fully proportional representation and utilitarian PR at the same time in a way voters can choose between. And, by observing the percentage of voters who check the box, how they vote vs. those who don’t, etc., this may yield valuable insight into how proportional voters want PR to be.

The idea for this comes from Utilitarian Sum vs Monroe Selection. A huge inspiration for this was “Score Then Optional Runoff”, which allows majoritarian voters to vote in a way closer to their own values without losing ballot power or preventing more utilitarian voters from having their say in single-winner elections.