I was at a boring retreat over the weekend and had the time to ponder two ideas:
The most important one is that strong FBC becomes easier to satisfy if we allow truncation. The condition is no longer that the voters never derive advantage from betraying their favorite. It instead becomes that favorite betrayal never give an outcome preferable to that obtained by sincere truncation (listing favorite and no others in a 3-way race). This might not make strong FBC possible, but it seems to improve the odds somewhat. Second, although this isn't particularly significant, I realized that plurality voting can be derived from a symmetry condition when voters are limited in the amount of info they can provide. I started by thinking of a situation where instead of 6 dimensions (for 6 types of ballots in a 3-way race, or 9 types with truncation) we work in some lower-dimensional space, to try and make my geometric idea easier to visualize. By symmetry, such a space can only have 3 dimensions (or zero, in a dictatorship). Furthermore, by constraining the number of voters in each category to add up to a predetermined number, we find ourselves working in a triangle. Finally, the symmetry condition for making the election method unbiased forces us to divide the triangle into three equal regions corresponding exactly to plurality voting. OK, so plurality voting is a no-brainer. I just thought it was cute that I could derive it as the only possible ranked method for a 3-way race when we limit the amount of info voters can provide. Anyway, it tells me that the geometric idea might actually be useful for providing insight into harder problems than pluralityl. Just felt like sharing. Alex ---- For more information about this list (subscribe, unsubscribe, FAQ, etc), please see http://www.eskimo.com/~robla/em
