Simmons, Forest wrote:
>Here's a version that is both clone proof and monotonic: > >The winner is the alternative A with the smallest number of ballots on which >alternatives that beat A pairwise are ranked in first place. [shared first >place slots are counted fractionally] > >That's it. > >This method satisfies the Smith Criterion, Monotonicity, and Clone >Independence. > More not-so-good news for this Simmons method: it fails mono-raise (aka Monotonicity). 31: A>B 02: A>C 32: B>C 35: C>A C>A>B>C. "Simmons" scores: A35, B33, C32. C has the lowest score and wins. But if we raise C on the two A>C ballots, changing them to C>A, then we get: 31: A>B 32: B>C 37: C>A (2 of these were A>C) C>A>B>C. "Simmons" scores: A37, B31, C32. Now B has the lowest score and wins. So raising C on some ballots without changing the relative ranking of any of the other candidates has caused C to lose, a failure of mono-raise. Interestingly in both cases the method gave the same result as IRV. In fact it is starting to look as though in the 3-candidate case "Schwartz//Simmons" is equivalent to Schwartz,IRV! Say sincere is: 48: A 27: B>A 25: C>B B is the CW, and in this case both methods (even without the "Schwartz" component) elect B. And both methods are vulnerable to the same Pushover strategy. If from 3 to 20 of the 48 A supporters change their vote to C>A or C or even C>B, then both methods will elect A. 45: A 03: C>A (sincere is A) 27: B>A 25: C>B B>A>C>B "Simmons" scores: A27, B28, C45. A has the lowest score and so wins. IRV eliminates B and likewise elects A. 28: A 27: B>A 45: C>B (20 of these are sincere A!) B>A>C>B "Simmons" scores: A27, B45, C28. A has the lowest score and so wins. IRV eliminates B and likewise elects A. Chris Benham ---- election-methods mailing list - see http://electorama.com/em for list info
