Modified STAR for countering Vote Management strategies in cardinal PR

Vote Management is when a minority party splits its voters up strategically in such a way that they win a majority of the seats.

A counter would be to run a modified version of STAR for the final seat if no candidate gets a Hare Quota of points: choose the highest-scored candidate for the first spot in the runoff, then use Vote Unitarity to remove the points the voters gave to that candidate from their ballots. Then take the next-highest scored candidate as the second spot. This means B3 wins in the example above because they were scored higher than A3 by a majority.
This is immune to cloning; if there was an A4 candidate that the 16 A3 voters also max-scored, the Vote Unitarity modification to STAR ensures that only one of A3 or A4 makes the runoff, because the A ballots are then exhausted, allowing B3 to get the second spot in the runoff.
The one complication is that in a non-Vote Management scenario (there was legitimately no candidate with a Hare Quota), this could potentially give the majority one more seat than they deserve, though I can’t think of any scenarios where this could happen.

Edit: I have found a bunch of scenarios where the majority takes an additional seat. I will think about solutions.


OK, a simple solution is to keep track of whether any candidates were elected without a Hare Quota before the final seat, and only if that is the case is Vote Unitarity STAR run. In the example above, STAR would only be triggered because the first two Party A winners both got elected without using full Hare Quotas; in an example with 100 voters, 5 seats, Party A 31 votes and Party B 69 votes, and no Vote Management, no runoff is triggered for the final seat because everyone up until then has won with a Hare Quota, so the minority can (justifiably) win the final seat by virtue of deserving it more, 11 votes to 9. Does anyone see any other issues with this idea?

In fact, you can check after each seat is elected by the method whether a full Hare Quota has been “lost” because so many candidates won with significantly less than a Hare Quota. If that is the case, you can just run Vote Unitarity STAR on the very next seat, and then keep checking. In the example above, we could add in 100 ballots that bullet vote for 20 different candidates separately, meaning none of the individual candidates has a chance of winning, but raises the Hare Quota from 20 votes to 40. In that case, Party B actually spends an entire Quota electing just one candidate, meaning that Party A can take all four of the seats. But checking for “lost/unmade up” Hare Quotas shows that the first two Party A candidates collectively lost a Hare Quota between them, so then VU-STAR elects a Party B candidate on the 4th seat and takes the utility from Party B voters’ ballots. The final seat then has its runoff triggered because there is still “unmade up” utility left over from when the two Party A candidates got elected with collectively less than one Hare Quota, so the Party B candidate wins the final seat, and Party B gets 3 seats to A’s 2. This can be gamed if Party A makes sure it spends just a little more than a Hare Quota collectively between the first two elected Party A candidates, ensuring the runoff doesn’t trigger for seat #4, giving Party A 3 seats.
It might be necessary to just institute a “one non-Hare Quota-filled seat is immediately followed by a VU-STAR runoff for the next seat” principle. Seat #1 always goes to Party B, so if seat #2 goes to Party A and isn’t filled by a Hare Quota, then seat #3 triggers the runoff and goes to Party B. After that, it’s regular business for seat #4 which elects Party A, but now the final seat notices the non-Hare Quota seat #4 and the ensuing runoff picks Party A.