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
