[EM] Truncation

[Adam Tarr]

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
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