Better-Than-Expectation strategy, for Approval says to vote for every candidate
who is better than
your expectation for the election.
The other Approval strategies are special cases of Better-Than-Expectation.
If you know who the frontrunners will be, and that the winner will be one of
those two, one strategy
says to vote for the better of those two, and for everyone who is better than
that.
But, if you know that the winner will be one of those two, then your
expectation is somewhere between
the utilities of those two candidates, and so Better-Than-Expectation says to
vote for the better frontrunner
and for everyone who is better.
Of course, strictly speaking, since your expectation has some specific value
between the two frontrunners' utilities,
you should also vote for whatever other candidates are better than that
inbetween point. So you aren't
just voting for the best frontrunner and everyone better--you're also voting
for some candidates whose
merit is between those of the two frontrunners.
That's what is recommended in a Best-Frontrunner strategy suggested by Brams,
Fishburn, or both.
As a practical matter, of course it isn't instrumentally important which, if
any, inbetween candidates you vote for,
since you know that the winner will be one of the two frontrunners. But voting
for a candidate shows
your support for that candidate, shows how many people like that candidate.
That's why you certainly
want to vote for everyone better than the best frontrunner. And also for the
inbetween candidates who
are better than that inbetween cutoff point that is your expectation, if you
know where it is. But maybe you
only know who the frontrunners are; you might not have the information needed
to find that inbetween
cutoff.
Now, suppose it's a u/a election (there are completely unacceptable candidates
who could win).
The following isn't rigorous, but sounds compelling:
The unacceptables have arbitrarily immense negative magnitude for their
utility, though they have
a finite probability of winning. That means that, inevitably, they pull your
expectation below the
utilities of any of the acceptable candidates.
Similarly, because the acceptables are similarly immensely better than the
unacceptables, and have
a finite chance of winning, they likewise pull your expectatation to better
than any of the
unacceptables. So your expectation is somewhere between the utilities of the
acceptables and
the unacceptables. Hence you should vote for all of the acceptables, and for
none of the
unacceptables.
So, whether or not the election is u/a, and whichever of the abovementioned
strategies you're using,
you're voting (only) for the Better-Than-Expectation candidates.
In a non u/a election, maybe you know who the frontrunners will be. But maybe
not. But then,
maybe you still have a feel for how good you expect the election result to be,
and so you
can judge which candidates are better than what you expect from the election.
You might want to ask yourself, regarding each candidate: Shall I appoint hir
president, or shall
I conduct the election. If the answer is "Appoint hir president", then vote for
hir.
Because, in all these strategies, you're voting for the Better-Than-Expectation
candidates, then,
whichever of these strategies the various voters might be using, they're all
voting for the
candidates better than what they expect for the election.
So the winner will be the candidate who is, for the most voters, better than
what the voter expects
from the election.
The winner will be the candidate who maximizes the number of voters who are
pleasantly-surprised
by the outcome.
Of course that's true in Score-Voting too, if voters are voting in their best
interest, by giving maximum
rating to the candidates they'd vote for in Approval, and minimum points to the
candidates they
wouldn't vote for in Approval.
The fact that Score-Voting affords that opportunity makes it one of the best
voting systems.
There's a good chance that Score-Voting's great familiarity could make it the
most winnable
voting system reform.
In fact, to propose Approval, you should first suggest Score-Voting, and then
suggest the "Yes/No",
"Acceptable/Unacceptable", or "one point/zero points" version of
Score-Voting--Score-Voting's
simplest version: Approval.
Introducing Approval as a Score-Voting version means that it benefits from the
great familiarity
of being asked to cardinally rate things or people (from 1 to 10, for example).
And it avoids the erroneous criticism of Approval that claims that it violates
"one-person-one-vote":
Approval, as a Score-Voting version, lets each voter rate each candidate (one
point or zero points, yes or no).
Each voter equally only has one vote for rating any particular candidate.
No one could seriously try to claim that Score-Voting violates 1-person-1-vote.
Mike Ossipoff
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