[EM] Truncation

[Bart Ingles]

Adam Tarr wrote:
> 
> Bart Ingles wrote:
> 
> > > > Adam Tarr wrote:
> > > There's no sense in talking about uncertainty and ties; it only
> > > confuses the issue.
> >
> >Sorry to spoil your clarity.  Having never seen an election where the
> >exact vote count is known in advance (except possibly in a couple of
> >counties in Florida), I would say that uncertainty IS important.  Also,
> >my example wasn't really intended to show a tie, so much as it was to
> >show no clear winner before the election.
> 
> You're missing my point.  In this case, why wonder what indecision does,
> when we know that either outcome (my side has more votes, or my side has
> less votes) both point to the same conclusion (I should not truncate)?  Let
> me say that again, since that was pretty wordy:
> 
> In the example you gave, if it turns out that your side has less votes,
> then you should not truncate.  If it turns out that your side has more
> votes, then you have no need to truncate.  If it's unclear whether your
> side has less or more votes, then you should either not truncate, or not
> worry about truncating, depending on which is true.  Both of which suggest
> that you should not truncate.  So don't truncate.

But if both A and C camps truncate, B is removed as the likely winner. 
So whichever of A or C eventually wins is definitely better off for
truncating-- they won instead of B.  The losing camp is slightly worse
off (the opposite won instead of B), but that was part the gamble.

I agree that if either side is fairly certain of losing, or views B as a
reasonable compromise, then it should not truncate.  In which case the
opposing side gains nothing by truncating, as you point out.  But the
two sides don't necessarily know how many of the opposite voters will
truncate.  Since truncation makes no difference if the opposing side
doesn't do it, the approach should be to assume the opposing side _will_
truncate, and then make your decision based on polls and utilities.


> 
> >In the above example the probability of either A or C winning an A/C
> >pairing is 0.5, therefore those candidates' voters are better off
> >truncating whenever their perceived utility for B is less than 0.5.
> >Similarly, if the probabilities for A and C in an A/C pairing were
> >70/30, then the A voters would want to truncate whenever their utility
> >for B was < 0.7, and the C voters would want to truncate whenever their
> >perceived utility for B was < 0.3.
> 
> This is not the case.  Your conclusions about who wins in each case
> (depending on truncation or no truncation) were wrong.  See my previous
> message.

This seems to contradict your earlier example:

> 46 ABC
> 5 BAC
> 5 BCA
> 44 CBA
> 
> Pairwise votes are:
> 
> B 56 > C 44
> B 54 > A 46
> A 51 > C 49
> 
> In this case, B is the Condorcet winner.
> 
> If both sides truncate we get
> 
> 46 A
> 5 BAC
> 5 BCA
> 44 C
> 
> Pairwise votes are:
> 
> A 51 > C 49
> A 46 > B 10
> C 44 > B 10
> 
> Now A wins the election in either winning votes or margins (don't stop the presses yet).


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.  But it wouldn't have been known in
advance whether A or C would have more votes; if instead it had been 44
A and 46 C, then truncation would have caused C to win.  So it still
seems plausible that in advance of the election, both sides could easily
have sufficient incentive to truncate.

Bart

----
For more information about this list (subscribe, unsubscribe, FAQ, etc), 
please see http://www.eskimo.com/~robla/em