2010/11/8 <[email protected]> > A few years ago Jobst invented Total Approval Chain Climbing or TACC for > short. > > At the time I was too young (not yet sixty) to really appreciate how good > it was. It is a monotonic. clone > free, Condorcet Efficinet method which always elects from the "Banks Set," > a nice subset of the Smith > Set (if not the entire Smith Set). > > It is easy to describe: > > (1) Initialize the variable S as the empty set S = { }. > > (2) While some alternative beats every member of S pairwise, augment the > list S with the lowest > approval alternative that does so. > > (3) Elect the last alternative added to S, i.e. the member of S with the > greatest approval. > > That's it. > > Obviously the method will elect the CW when there is one. > > If the Smith set consists of a cycle of three alternatives, say A beats B > beats C beats A,, then this > method (TACC) will will elect either the member of this cycle with the > greatest approval or the one with > the second greatest approval, depending on whether or not the cyclic order > goes up or down the approval > list. > > What I didn't appreciate in my younger days was how beautifully resistant > the method is to strategic > manipulation. > > Scenario 1: > > 49 C > 27 A>B > 24 B (sincere is B>A) > > The sincere CW is A, but the B faction creats an ABCA cycle by rruncation. > > Assuming that "approval" is the same as "ranked" in each of the factions, > the approva order is (from > greatest to least) B, C, A . Since this is in the same cyclic order as > the cycle, C wins. If the B voters > are rational, they will not truncate A! > > Now look at the burial temptation scenario: > > 49 A>B (sincere is A>C) > 27 B>C > 24 C>A > > The sincere CW is C. > > Now suppose that the A faction buries C as indicated above: > > TACC will elect B. whether or not the A faction approves B. >
But if the A faction votes A>B>C (ie, if they approve C), then C wins. So I think that this method would work best with only 3 rating levels (only 2 approval levels) available. > > Forest > > ---- > Election-Methods mailing list - see http://electorama.com/em for list info >
---- Election-Methods mailing list - see http://electorama.com/em for list info
