On Nov 16, 2009, at 4:58 PM, Raph Frank wrote: > The theorem states (from wiki) that there is no method which has the > following properties: > > * If every voter prefers X over Y, then the group prefers X over Y. > * If every voter prefers X over Y, then adding Z to the slate > won't change the group's preference of X over Y. > * There is no dictator. > > All 3 of those conditions are met for range. The only problem is that > adding Z could cause renormalisation changes in how people vote.
The problem in applying the theorem to range isn't in the properties; it's in the formal definition of the method and the proof. http://en.wikipedia.org/wiki/Arrow%27s_impossibility_theorem#Formal_statement_of_the_theorem The proof applies to strict social welfare functions, defined as functions mapping a set of linear orderings (by voters) to a social ordering. While a range ballot (without ties) can be interpreted as a linear ordering, the range counting rule is not a function of that ordering, but rather of the cardinal values on the ballot. Different range ballots could have the same ordering but lead to a different result. ---- Election-Methods mailing list - see http://electorama.com/em for list info
