Algorithmic Asset Voting: Difference between revisions

D and D2 would be the winners in regular [[Sequentially Spent Score|SSS]], [[Sequential Monroe|SMV]], and [[Reweighted Range Voting|RRV]] because they each have the highest scores in their respective Hare Quotas. But the Smith Set here is all winner sets with at least 1 candidate from (A, B, C) and at least 1 candidate from (A2, B2, C2) since 12 voters prefer each of them over 8 voters for D and D2 each, which means D and D2 must not win in order for the winner set to satisfy the Smith criterion (this can be discovered using a combinatorics calculator such as https://www.mathsisfun.com/combinatorics/combinations-permutations-calculator.html). Therefore, one way of applying SSS here would be to run SSS but first eliminate D and D2 to ensure they can't win, making one of B or B2 tie for the first seat. WLOG supposing B won, then A and C must be eliminated, because if one of them were to win the second seat, then it'd be impossible for 1 of (A2, B2, C2) to win, violating the Smith criterion. Then B2 wins the second seat, making the final winner set (B, B2). In the single-winner case, using cardinal PR methods to select from the Smith Set is equivalent to using [[Smith//Approval]] or [[Smith//Score]]. If a method such as [[STV]] is used to decide the winning set among the Smith winner sets, then it may even be necessary at times to prevent the elimination of a candidate who, if eliminated, would guarantee that a non-Smith winner set would be the final result.