[EM] Truncation

[Bart Ingles]

Adam Tarr wrote:
> 
> Bart Ingles wrote:
> 
> > Adam Tarr wrote:
> > > Specifically, there is the remarkable fact that a voter in a
> > winning
> > > votes-based Condorcet voting system can NEVER be hurt by fully
> > expressing
> > > their preferences.  There are cases where fully voting your
> > preferences can
> > > fail to help you, but it can never actually hurt you.
> >
> > Never is a strong word.
> 
> True, and I lack a rigorous proof, but every empirical example I have
> seen supports this.  Your example is no different...
> 
> >  How about the following:
> >
> > (projected vote percentages shown; assumed accurate to within +/- 5
> > percentage points)
> >
> > 45%   A  B  C
> >  5%   B  A  C
> >  5%   B  C  A
> > 45%   C  B  A
> 
> 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.

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.

Obviously, when the election is complete and the votes are counted, you
can say that the losing voters would have been better off ranking
fully.  I don't think this would translate to 'regret', though, since
truncation was the best strategy available at the time of the election.



> In winning votes methods, truncation for the ABC voters makes no
> difference (i.e. does not hurt them, even if it fails to help them).
> In margins methods, truncating can prove costly for an ABC voter.
> This is neither here nor there for the purposes of my analysis; I can
> show you a counter-example where truncation can help in margins cases.
> 
> The point is, nowhere here do we get any suggestion that a voter in a
> winning votes method can be helped by truncation.  My initial
> contention still stands.
> 
> >  But then I don't see truncation as necessarily a bad thing. If
> > truncation can defeat a "hated middle" candidate, it addresses my
> > main misgiving about the Condorcet methods.
> 
> Much in the same way that we can't differentiate between the
> indifferent voter and the lazy voter, we cannot distinguish between
> the "respected (if unglamorous) compromise middle" and the "hated (yet
> still) compromise middle".  Smart CBA voters in an approval election
> will still approve B, to defeat A, anyway.

Substitute "low utility Condorcet winner" for "hated middle" if you
like.  The approval CBA voters who approve B are only smart if they are
relatively certain that A would win otherwise, or if they have an
extremely high opinion of B.


> What method would actually
> prevent B from winning when the voters act in a logical manner?  Even
> plurality and IRV encourage CBA voters to dump C for B if they have
> perfect information.

"Perfect information" being the key phrase here.  If perfect information
were available it wouldn't matter what we used.

Bart

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