In a message dated 98-07-03 16:42:43 EDT, you write: >In literature, there are many different proves of the >impossibility of a non-manipulatable election method. > >All these proves have the same structure: > >1) Take some axioms, such that a tie is possible. > That means: Take some criteria, such that it is possible > that A > B > C > A or in other words such that > a) Candidate A would have been elected, if candidate C > hadn't run for office. > b) Candidate B would have been elected, if candidate A > hadn't run for office. > c) Candidate C would have been elected, if candidate B > hadn't run for office. > >2) Assume, that there is a tie. In a rated (as opposed to ranked) voting system, each candidate receives "votes" according to some method which allows them to be tallied. (Think of Olympic scoring as a simple example.) After the votes for each candidate is tallied, each candidate then receives a resulting "score". One of several methods can then be used to determine a winner: -Under some methods, the candidate with the highest score is automatically deemed the winner -Under another possible method, any and all candidates (if any) who receive a score above some pre-set threshold is declared the winner. Note that this method can possibly result in multiple winners, or possibly result on "no winner". This might be more applicable for parliamentary situations where the set of choices is unbounded. In either case, note that a "circular result" e.g. A > B > C > A cannot occur. Therefore such a voting method is not subject to the same style of "impossibility proof" as are other voting systems. (The above conclusion applies for the situation where each candidate is voted upon in an "accurate" manner - meaning that the addition of newer candidates will not result in a change in the votes for previous candidates. Such an "objective" voting system is still a difficult design problem - but perhaps not impossible. Plus it would be necessary to make sure that there were no incentives to exaggerate or lie. So it is by no means a trivial problem to solve. I suspect it requires an "open ended" system with no fixed maximum vote value - this is a difficult area. But at least it cannot be proven impossible from the start as is apparently the case with all ranked voting systems.) Mike Saari
