>in major elections, we usually have a pretty good idea who the frotrunners 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. --Let me elaborate a bit on this: The above regret numbers were for basic Condorcet. If you change to other Condorcet methods like Black or Schulze, you will get somewhat different numbers, but you pretty much always find that approval is better than Condorcet for N=3, they are about the same for N=4, and for N>=5 Condorcet starts being superior, increasing advantage at larger N. But what is the number of candidates N? See, really, N is not the number of candidates -- really it is better to regard N as the cardinality of the subset of candidates that the public thinks have a chance of winning. Because they are going to vote strategically about that subset. In (say) an 18-candidate election, usually we are not completely clueless. We usually have a lot of reason to believe it is going to be A or B. Or maybe we only feel confident narrowing it to a 3- or 4- or 5-candidate subset. I personally have never experienced any election (which I voted in) in which I felt unable to narrow it down to 5-or-fewer frontrunners where I had high confidence the winner would be in that set. Indeed, I don't think I've ever needed to go above 3. Elections with effectiveN>5 are, I think, very rare. So if we believe in the "Venzke model" that the "effective N-value" is <=5, then we conclude approval is better than Condorcet if N=3, about same if N=4, and worse if N=5, but they're pretty close in all three cases. -- 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
