About Scott Ritchie's "feel alike vote same FAVS" criterion that all members of a feel-alike group should want to vote the same.
FAVS is falsified by IRV if incomplete information: either A or B need 5 more votes to surpass the hated C and/or the 50% mark (but you do not know which) and your group has 10 votes. So split them. I am not sure whether FAVS is satisfied by IRV in complete information scenarios. FAVS also is satisfied by Approval and Range and Plurality Voting in complete information scenarios. That is because, the group decides what is the best candidate they can make win, and then they can always make him win by voting for him max and the rest get min. Juho Laatu pointed out that FAVS is falsified by Condorcet methods (at least in incomplete information scenarios) because the group may wish to create a cycle. This can rule out the opponents being Condorcet Winners but leave that still possible for their favorite. A similar technique can be made to show FAVS falsity for the Copeland (which is a Condorcet) method even in a complete info scenario. FAVS also is falsified by plain old approval voting in incomplete information scenarios. See http://rangevoting.org/RVstrat1.html#examples and scale up the example appropriately. I also claim FAVS is falsified by every vector-additive method where the allowed vote-vectors form a discrete set (e.g. Borda, Plurality) in incomplete information scenarios. To prove that, we set up a situation where the "best" vote is not allowed by the rules of the voting system but is attainable as a convex linear combination of two or more allowed kinds of votes. (The same thing was happening in the approval example last paragraph). In some vector-additive methods, FAVS can also be falsified in this way even in complete information scenarios. For example, in vote-for-and-against voting if the current totals are Good 10 Lousy 15 Cruddy 15 then 4 more voters can elect Good by voting (+1,0,-1) twice and (+1,-1,0) twice but any unified 4 votes will not do the job. This same example also works against Borda voting because it is equivalent to vote-for-and-against in the 3-candidate case. CONCLUSION: so far, all the prototypical methods (Condorcet; Weighted Positional including Approval, Plurality, Borda; and IRV) have falsified FAVS in incomplete info scenarios. But RANGE VOTING obeys FAVS in both complete & incomplete info scenarios. Proof: suppose I lied. Then just take the vector-average of all the votes in your "optimal" group-strategy, and cast them. Q.E.D. So once again this is a property of range voting that no voting method based on discrete votes can match. Warren D. Smith http://rangevoting.org ---- election-methods mailing list - see http://electorama.com/em for list info
