[EM] Truncation

[Adam Tarr]

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.

>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.

>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.

It was not, since they could not be hurt by fully expressing their preferences.

> > >  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.

Absolutely.  This ability to take candidate utility into account is a way 
that approval could be viewed as superior to Condorcet voting.  In the case 
of a close election, the "vote for everyone you like more than the 
front-runner, and vote for the front-runner if you like him/her more than 
the closest contender" strategy breaks down, and you are left voting based 
on expected probabilities and perceived utilities.

It's very hard to predict what would end up happening in cases like 
this.  Donald Saari sees this as a flaw in approval voting.  I'm not sure 
I'd go that far, but one thing is sure: if anyone other than B wins the 
election, then a lot of people are going to regret their votes.  That sort 
of large-scale uncertainty, and the potential that a large portion of the 
electorate will feel cheated afterward, is a bad scenario for approval, 
even if we can argue that a higher utility candidate was elected.  By 
comparison, a winning-votes based Condorcet election will be boring and 
stable and will produce virtually no regrets from the voters after the 
election.

Don't get me wrong, I think approval voting is a huge step forward.  But 
winning votes-based Condorcet's predictable results and lack of strategic 
demands make it the best choice in my book.

> > 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.

Well, real election results seem to suggest that even when the pertinent 
information is perfect (i.e, "you're not influencing the election unless 
you vote for either Bush or Gore") people will still vote in non-strategic 
fashions.  For this reason, I support voting methods that place the minimum 
strategic burden on the voter.  Approval is decent in this regard, but 
winning votes-based Condorcet is even better.  IRV, Borda, and to a lesser 
extent margins-based Condorcet, are much worse.

-Adam


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