Hi all, I've revised the Definite Majority Choice page a bit. See if you like it (you may need to empty cache and refresh page to see latest changes):
http://wiki.electorama.com/wiki/Definite_Majority_Choice As I was going through my revised definition, I thought of a simple refinement that might be expanded on: ,----[ from http://wiki.electorama.com/wiki/Definite_Majority_Choice ] | We call a candidate definitively defeated when that candidate is | defeated in a head-to-head contest against any other candidate with | higher Approval score. This kind of defeat is also called an | Approval-consistent defeat. | | To find the DMC winner, the candidates are divided into two groups: | | 1. Definitively defeated candidates. | 2. Candidates that pairwise defeat all higher-approved | candidates. We call this group the definite majority set. | | The least-approved candidate in the definite majority set pairwise | defeats all higher-approved candidates, including all other members | of the definite majority set, and is the DMC winner. `---- James Green-Armytage is currently discussing strategy questions with both Mike Ossipoff and Chris Benham. I like the idea of getting better strategy resistance, but not at the expense of simplicity. So I've been attempting to think of some sieve-like approach to these ideas that is analogous to DMC. I think the main idea of ASM/AM/AWP is to exclude the DMC winner in some circumstances, and give more favor to approval. What might those circumstances be? Let's consider refining the definite majority set (Forest's P set) a little further. Say that you have some additional metric of defeat strength: Approval Margins, AWP's strong preference, what have you. With Approval Margins, the smaller the margin, the stronger the defeat. The P set is ordered pairwise from least-approved to highest-approved. Define the upward strength of a P-set candidate as the strength of its victory over the next-higher-approved P-set candidate. Then eliminate any P-set candidate whose upward strength is weaker than its defeat from below by a definitively-defeated candidate. Whatever metric you use, you have pruned away alternatives that can't escape their pursuers. You're left with a stronger set of candidates that are well separated in strength from the rest, and have strong beatpaths (approval + extra metric) to any other candidate that defeats them directly. Ted -- araucaria dot araucana at gmail dot com ---- Election-methods mailing list - see http://electorama.com/em for list info