One possible way of combining AV + STV is to allow equal ranks. This method becomes a method that is very similar to approval in the single winner case.
When determining if a candidate is elected, all candidates at the rank share the remaining vote strength, but when determining if a candidate should be eliminated, the candidates at the rank get the full strength of the ballot, like in approval. A feature of STV is that the proportionality for solid coalitions criterion isn't affected by the elimination ordering, so you can use any rule that you want. This assumes that candidates who exceed the quota are elected (and elected candidates are immune from elimination). Assuming there was a ballot: A: 1 B: 1 C: 2 D: 2 E: 3 F: 3 In round 1, the ballot would count as For electing: A: 0.5 B: 0.5 Others: 0 For eliminating A: 1 B: 1 Others: 0 So, the vote is shared when determining if someone has reached the quota, but is full strength when determining who to eliminate. If a candidate has more than a quota of "electing" votes, he is deemed elected. Otherwise, the candidate with the lowest "eliminating" votes is eliminated. If B was eliminated and A was elected with 133.3% of the quota (so 75% of the voting strength consumed), then the ballot would count as: For electing: A: 0.75 B: 0 (eliminated) C: 0.125 D: 0.125 To eliminate A: 0.75 (irrelevant since already elected) B: 0.75 (irrelevant since already eliminated) C: 0.25 D: 0.25 Others: 0 This means that if all party supporters vote for party members as ranks 1 and 2, then the party is guaranteed to gets its share of the seats. This follows from the solid coalition criterion. However, when determining the intra-party ordering, rank 1 candidates are considered approved and rank 2 candidates are disapproved. The most approved party candidates (up to the limited number of seats the party gets) are the last to be eliminated, so they will be the ones elected. Standard PR-STV becomes IRV in the single seat case. However, this system becomes a method that is very similar to approval in the single seat case. This means that for parties that get 1 seat, the intra-party decision is made by IRV, but with this method, the intra-party decision is made by approval (or at least an approval-like method). Assuming Meek's method for the transfers, then the rules are For both vote types (for election and for elimination) Vote strength passed to the next rank - the amount that would be passed to the next rank if all candidates at the current rank were ranked in order - This is the product of (1 - keep factor) for all candidates at the current rank times the vote passed into this rank - Nothing is passed to the next rank unless all candidates at the current rank are elected or eliminated Sharing (for election) - vote strength not passed to the next rank is shared between candidates at the current rank in proportion to their keep factors Sharing (for elimination) - vote strength not passed to the next rank is given at full strength to all candidates at the current rank ---- Election-Methods mailing list - see http://electorama.com/em for list info
