[EM] Truncation

[Bart Ingles]

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