BnC    CnB    BaC    Two-sided  Misc  Manipulable

                Burial   Just comprmise Two-sided  Misc  Manipulable

A follow-up on the last post; here are some stats for the different simple fpA-fpC generalizations ("IFPP-like", fpA-max fpC, and fpA-sum fpC). I haven't implemented Friendly Cover yet. What's surprising is that fpA-max fpC is better than fpA-sum fpC, but after thinking a bit about it, I think I get it. The heuristic says that whether A wins instead of B shouldn't depend on A>C (to the degree we can do so). Suppose A is beaten by C and beats B and D. Then if we have fpA-sum fpC, we can always perturb A's score by reversing the A>D defeat. But under fpA-max fpC, we can only do so if D has more first preferences than C. That's my hunch, at least. (I used to prefer fpA - sum fpC because it's more naturally cloneproof. But IIRC, Kevin Venzke preferred fpA - max fpC because it had fewer Plurality failures. Guess I was wrong and Kevin was right, in a sense :-) Anyway, the stat categories denote the fraction of elections where a particular strategy is possible. The strategies are: "Burial, no compromise" (BnC): Burial is possible but compromising isn't. "Compromise, no burial" (CnB): Compromise is possible but burial isn't. "Burial and compromise" (BaC): Either works. "Two-sided" (2S): Neither of the above, but putting the candidate you want to win first and the current winner last (simultaneous burial and compromise) works. "Other coalition strats" (Misc): None of the above, but brute-forcing a coalitional strategy works. There are a max of three coalitions, i.e. each strategist may employ any of up to three different ballots. "Manipulable": Some strategy worked 97 voters, 4 candidates, impartial culture. 50k elections per method, 512 coalitional strategy tests per election. BnC CnB BaC Two-sided Misc Manipulable Smith,IFPP-like 0.234 0.130 0.024 0.507 0 0.895 Smith,fpA-sum fpC 0.354 0.095 0.070 0.374 0 0.893 Smith,fpA-max fpC 0.132 0.148 0.015 0.395 0 0.691 Smith,IFPP 0.091 0.170 0.006 0.015 0.05 0.331 Smith,IRV 0.056 0.174 0 4e-05 0.05 0.280 or collapsing the burial types: Burial Just comprmise Two-sided Misc Manipulable Smith,IFPP-like 0.2582 0.1296 0.5073 0 0.8950 Smith,fpA-sum fpC 0.4232 0.0954 0.3744 0 0.8930 Smith,fpA-max fpC 0.1477 0.1480 0.3950 0 0.6906 Smith,IFPP 0.0969 0.1700 0.0148 0.05 0.3310 Smith,IRV 0.0560 0.1738 4e-05 0.05 0.2799 Note that the test system may underestimate the nonmonotone methods' burial rates because the burial strategy just tries to put the current winner at the bottom; these methods may reward lowering the candidates some of the way but not all the way to the bottom. But any such underestimates should be captured by "Misc".