...and residual approval weights Summary:
This method is like the previous one (K) excepted that the elimination order is definer by a ranked pair path instead of the number of 1st preference votes. It mixes IRV, Ranked Pairs and Approval methods. Explanation: The input is Demorep's preferential and approval ballot. We use ? to represent unranked candidates. Using the election-methods-list notation, we will use >> to indicate the approval limit. So acceptable candidates >> unacceptable candidates. For example: A > C > E >> D > B. We apply ranked pairs with relative margin. In case of equality, each ranking scenario is done, the final result is the average of the scenarios (well weighted). When the last candidate is eliminated, we check what is his residual approval rating. He receives one residual weight for each ballot where he is the last active candidate higher than >>. Elimination should not modify the ranked pair order. If the approval limit >> is not mentionned we suppose it could be added at the end. The winner is the candidate with the highest approval rating, not necessarily the latest eliminated. Example: 26: A > E > B >> C ? D 25: B > E >> A ? C ? D 24: >> C > E > A = B ? D (None ballots with lesser evil details) 23: D > E >> A ? B ? C 1: E >> A ? B ? C ? D 1: A ? B ? C ? D ? E (Blank ballot, a none ballot would start by >>) Locking produces: E>D (53/99) E>C (51/99) E>B (49/99) E>A (47/99) B>C (27/75) A>D (3/49) B>D (2/48) A>C (2/50) C>D (1/47) A>B (1/75) Resulting ranking: E > A > B > C > D. Elimination produces the weights: D => 0 residual approval. C => 0 residual approval. B => 0 residual approval. A => 0 residual approval. E => 75 residual approval. and 24 none ballots and 1 blank ballot. Final ranking: E(75) > A = B = C = D (0) E wins. Advantages: The method does not encourage cloning. Trying to identify a lesser of two evil cannot help elect it. The method has weights as output so it can be incorporated into a fully proportional multiple-winners method. None and blank ballots can be differenciated, so they could have different consequences in a multiple-winners method. This methods guarantees the election of a Condorcet winner if it exists and is approved by all ballots. It resists well against vote-splitting because it is pairwise comparison based. Disadvantages: It is not monotonic. Previous explanations: http://groups.yahoo.com/group/Electoral_systems_designers/message/77 Steph. ---- For more information about this list (subscribe, unsubscribe, FAQ, etc), please see http://www.eskimo.com/~robla/em
