PARTICIPATION FAILURE PROBABILITY --------------------------------- Call an election situation a "participation failure scenario" if there exists a vote Q, such that adding some number T>0 of honest Q-voters, will cause the election result to worsen in their view.
(This is a "no-show paradox" - these extra voters are better off staying home.) The "random election model" is V voters, V-->infinity, all independently casting random votes (all votes equally likely). IRV-3: I did some analysis and concluded the probability that a random 3-candidate IRV election is a participation failure scenario, is 16.2%. COND-4: I can prove the probability P than a random 4-candidate Condorcet election, is a participation failure scenario, is bounded below by a positive constant independent of which-flavor of Condorcet you use. For two particular Condorcet methods, I estimated P by monte-carlo and it is safe to say 0.5% < P < 5% and my best guess is 2.5%. (My program does not compute P exactly, it only finds high-confidence bounds on it. If I were less lazy I could tighten the bounds...) COOL OPEN QUESTIONS ------------------- I suspect: COND-INFINITY: Random C-candidate Condorcet elections are participation failure scenarios with probability-->1 when C is made large. IRV-INFINITY: Random C-candidate IRV elections are participation failure scenarios with probability-->1 when C is made large. I have not proven either. I have got something close to a proof for three particular Condorcet methods (Copeland, Simpson-Kramer MinMax, and basic Condorcet) although even in these cases my proof could be attacked as not really being a proof (argument is pretty convincing, but not fully a proof). For IRV, P is easily seen to be a non-decreasing function of C so it must approach a limit. IMPORTANCE: The (conjectured) fact that this pathology is 100% common if the number of candidates is made large, seems important... Warren D. Smith http://rangevoting.org ---- Election-Methods mailing list - see http://electorama.com/em for list info
