Optimal? not

Mike Ositoff ntk at netcom.com
Wed Jul 15 14:37:50 PDT 1998

> In a message dated 98-07-11 20:16:05 EDT, you write:

I reply a few paragraphs down:

> >And
> >if you chose A & B for voting a ratings difference, then why
> >vote a small one??
> ...
> >So that's the strategy to maximize your utility expectation: 
> >If the sum in the previous paragraph is positive for i, then
> >give maximum votes to i. If the sum is negative for i, then
> >give i the minimum possible vote (even if that's negative).
> >
> >***
> >
> >I don't claim that that's rigorous, but hopefully it demonstrates
> >why it's best to give all or nothing in direct point-assignment
> >methods ("cardinal measure methods").
> A more realistic assumption is that you do NOT have a reliable advance
> predictor of the outcome or the likely ties.  What is the best strategy where
> you really have no good predictor as to the likelihood of a tie between any
> given set of candidates?
> I claim it is a "spread vote" which matches as closely as possible to your
> "real" feelings.  What do you think?

If you don't know anything about the tie-probabilities, then, in
Plurality you vote sincerely, for your favorite, the one with most
utility for you. In Approval you vote for every candidate whose
utility is above the mean. In -100 to 100 you give 100 to every
candidate whose utility is above the mean, and -100 to every
candidate whose utililty is below the mean.

So then, when you don't know the tie-probabilities, the difference
is that you go by utility instead of strategic value (as I defined
it earlier).

If we don't know the tie-probabilities, if you gave, in your
example, those inbetween scores to most of the members of that
preferred set of candidates, then you aren't fully voting them
over the ones you gave -100 to, and you aren't fully voting them
under the one you gave 100 to. Well, if, for instance, the utility
difference is greatest between one of those preferred candidates
and the -100 ones, than between that preferred candidate and
your favorite, and if all ties are equally likely, then you're
gaining more to give maximum vote difference to the pair for which
you have the biggest utility difference, even though it means giving
no vote difference to the pair for which you have less utility

What it amounts to overall is to give maximum to the ones
with positive strategic value (if you know the tie-probabilities)
or to the ones with utility above the average (if you don't know
the tie-probabilities). And minimum points to everyone else.

But I don't agree with your statement that we don't usually have
information about tie-probabilities. Why did so many people tell
me they were voting for Clinton as a lesser-evil? Voting sincerely,
without tie-probability information, they'd have voted for their
favorites. They felt that Clinton had the highest strategic value.
They felt that the only likely tie for 1st was between Clinton &
Dole, which automatically means that their favaorite of those
2 has the highest strategic value.

So in -100 to 100, they'd have given 100 to Clinton & everyone they
like more, and -100 to everyone else.

If there's someone else who's their real favorite, then he has
a positive utility difference with respect to all the others, and
so, however low his probability of being in a tie for 1st with
the others, and however consequently low his strategic value, that
strategic value will be positive, and so he gets 100.

Voters vote strategically, based on their beliefs about the
tie-probabilities, usually believing that only 2 have any
significant likelihood of a tie for 1st.

Mike Ossipoff

> Mike S

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