>Venzke: >There is another scenario of interest to me, where you can only break a >tie between two candidates, but it isn't certain which two candidates they >will be, at the time you're voting. > If we'll always be limited to two frontrunners, then I'm not all that >interested in reform.
--Well, in major elections, we usually have a pretty good idea who A & B are. If we genuinely had no idea and the V-1 other votes were totally random, then probably in the V=huge limit best Condorcet strategy would be honesty (though I've never seen a proof) and best range strategy is mean-utility-as-threshold approval voting. If all voters do that, then compare system 16 vs system 2 here http://www.math.temple.edu/~wds/homepage/voFdata E.g regrets using random-normal utilities & 200 voters: system|2 canddts 3 canddts 4 canddts 5 canddts ------+--------- --------- --------- --------- Cond| 1.61631 2.18396 2.43847 2.57293 Appv| 1.61631 1.85211 2.40181 2.83800 so in this experiment approval voting does better than Condorcet with N=3,4 candidates; Condorcet does better with N=5; and both same with N=2. >> 5. In a monotone Condorcet method (such as Schulze, Tideman > ranked > pairs, etc) you cannot go wrong by ranking A top and B > bottom (both of > which, in general, will be dishonest, but this is always > strategically > correct). >Venzke: What assumptions are you making? This doesn't seem to be demonstrated. --it is just the monotonicity and the asumption only A & B can win. If you think some other vote is more strategic, then fine, use it, then I will raise A to top, which never hurts me due to monotonicity assumption, and drop B to bottom, same argument, thus proving my vote is at least as strategic as yours. So for the rest let us assume voters will cast votes with A,B top & bottom (or reverse) only, due to them being strategically wise and also due to them wanting to simplify their lives if they can (and they can, here). -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step) and math.temple.edu/~wds/homepage/works.html ---- Election-Methods mailing list - see http://electorama.com/em for list info
