I'm basically looking at the inputs and outputs, and ignoring what goes on in between as irrelavent. Adam seems to be taking the opposite approach, which I suspect is more difficult.
The reason I am comparing only the diagonal (T/T vs. NT/NT) is that the A and C sides can't know which they are in advance of the election (in other words, which is the majority faction). So whatever strategy applies to one applies to both; in fact there is no way for the two sides to distinguish themselves on your matrix in advance of the election. In effect, the two sides combine as a "pool" of votes, and don't know which side they are on until after the election. In fact by truncating they are voting for an AC lottery over a probable B win. Another approach, using utilities: Assuming a utility for a side's own candidate of 1.0, and the opposite side's of 0.0, and a roughly equal (0.5) chance of being on the majority side, bilateral truncation yields an expected utility of outcome of 0.5 for each side by guaranteeing the winner will be either A or C. If neither side truncates, the expected utility of outcome would be the same as each sides' utility for B. If no truncation, I would expect this to be something greater than 0.5; if truncation, then something less than 0.5 (as a source of incentive to truncate). Bart Adam Tarr wrote: > > Bart, you've got it wrong. You're jumping to bad conclusions here, > because you're not looking at all four cases. Look back at my > original analysis, or at least look at this, the final decision matrix > for winning votes (ABC voters' choices on top, CBA voters' choices on > left): > > xxx| T | NT | > ---|---|----| > T | A | A | > ---|---|----| > NT | B | B | > ------------- > > You were comparing the top left and bottom right squares, and drawing > conclusions about the A faction's incentives from this. This is > totally invalid. Do the analysis. You will see that truncating never > helps you. If you are the faction with the majority (decisions on the > top row) then whether you truncate makes no difference. If you are > the faction with less votes (decisions on the left column) then > truncation HURTS you, every time. > > > In your example, if neither truncates, B wins. If both truncate, A > > wins. Clearly the A voters were better off with both sides > > truncating, > > while the C voters were worse off. > > Sure, but the A voters do just as well if they fully vote and the C > voters truncate. So the truncation of the A voters didn't help them. > Rather, the truncation carried out by the C voters HURT the C voters, > and helped the A voters. If the C voters had voted their full > preferences, they would have gotten B elected in stead. > > And of course, the same is true if the C faction turns out to be > stronger (ABC voters' choices on top, CBA voters' choices on left): > > xxx| T | NT | > ---|---|----| > T | C | B | > ---|---|----| > NT | C | B | > ------------- > > Now, the C faction's choice makes no difference, while the A faction > does better if they do not truncate. So, given that there is some > uncertainty whether the results will follow this box or the previous > box, both factions have a strong incentive to not truncate. > > In this example, truncation never helps the faction that truncates. > > -Adam ---- For more information about this list (subscribe, unsubscribe, FAQ, etc), please see http://www.eskimo.com/~robla/em
