Apportioned Cardinal Voting

Apportioned Cardinal Voting is a sequential Multi-Member System built on Score voting ballots.

Method
The algorithm:


 * 1) Find the Score winner as normal
 * 2) Find the Hare Quota ballots that contribute most† to the candidate being seated (Candidate X).‡
 * 3) Confirm that the Candidate X has the highest score for that Quota. If not, declare that the candidate with the highest score in that Quota (Candidate Y) is seated rather than Candidate X, put the Quota back in the pool at large, and Go To #2.
 * 4) Set that Quota aside as being Represented by that Candidate/Seat.
 * 5) Repeat until all seats are filled, considering only the scores on ballots that have not been set aside as having been "Represented"

‡ Obviously, there will be cases where there are multiple ballot types that return the same "Contribution" (eg, 5/3/4/2 vs 5/3/3/3). The two suggested methods are:
 * In increasing number of different scores for candidates still eligible to be seated (so, {3} before {2,3,4})
 * Proportional to their group size (ie, if you have X ballots of type A and 2X ballots of type B, then you set aside 2 B ballots for every one A ballot).