A Proportional Approval Voting where your ballot is allocated to the weakest (fewest votes) quota-meeting candidates you approved first

Starting from Party List Voting, one can add the generalization that a voter can approve as many party lists or independent candidates as they want (and a voter might be guaranteed the ability to write in up to 3 or 4 independent candidates). Among the approved lists and candidates, you could apportion a voter’s ballots to the weakest candidate or party list (the one with the fewest votes) they approved that got a Droop/Hare Quota of votes (because our best guess would be that the candidate with the fewest votes is presumably the voter’s favorite i.e. so unique that they only appeal to that voter and the fewest other voters.) You can use fractional surplus handling to then apportion the ballot to the next-weakest candidate/party list, and so on.

This might create an inverse incentive where candidates and parties attempt to produce the weakest consensus possible, but a Proportional Approval Voting which apportions a voter’s ballot to the strongest candidate/party that they approved first would essentially shut down any independent candidate (because they presumably have less opportunity to receive votes as the bigger parties do.) Perhaps a voter who only approves parties/candidates with multiple quotas of votes would have the opposite happen to their ballot i.e. their ballot goes to the strongest candidate/party, while a voter who approves only candidates/parties with a quota or less of votes has their ballot apportioned to the weakest one with a quota.

In order to make this method meet ULC though, it’d probably have to apportion your ballot to the strongest quota-meeting candidate first.