On Jan 15, 2008, at 18:22 , Steve Eppley wrote: > Daniel Radetsky wrote:
>> Whatever >> you think of range voting, it is a voting system and GST, AT, >> etc., do not >> apply to it. > > (Arrow's theorem can be written to apply to Range Voting and Approval > and all methods. From the perspective of a math purist, to whom a > "framework" is a non-standard way to express axioms, that's a > better way > to write it. Arrow's theorem is also more powerful when rewritten to > cover any method that chooses a winner, rather than just methods that > return a social ordering of the alternatives. That's how I present > Arrow's theorem in my webpages at > http://www.alumni.caltech.edu/~seppley, along with a proof.) One explanation to Range and Arrow's theorem: - social preference orderings may be cyclic - one may arrange Range (or Approval) elections in this situation - Range will not measure number of voters preferring X to Y (although this can be derived from the ballots) - strategic Range (and Approval) voters however need to decide how to vote when there is a cycle in the social preference ordering - let's say there is a loop A>B>C>A (preferences are e.g. 33: A>B>C, 33: B>C>A, 33: C>A>B) - if A wins, some voters with preference B>C>A and who approved / gave full points only to B will regret using that strategy - also voters with preference C>A>B and who approved / gave full points to C and A will regret if C was second Juho ---- Election-Methods mailing list - see http://electorama.com/em for list info
