[EM] Approval Voting vs Instant Runoff Voting:

[MIKE OSSIPOFF]

>>I'll combine my responses to Richard's three previous messages;
>
>Richard wrote:
>
> >Although I think you are looking for a mathematical solution, and I do
> >believe one is
> >possible, I don't think one is needed (though it would be an interesting
> >derivation).
> >I would vote A only without the need to refer to any math. The
>
>I'm not necessarily looking for a mathematical solution.  The point is 
>that,
>even given a significant amount of information on which to base one's vote,
>it is still difficult to divine how to vote in approval.

First of all, let's not exaggerate the importance of that need to
calculate Approval strategy. Approval strategy is no more mathematically 
demanding or complicated than Plurality strategy.
In a meaningful sense it's less of a problem, because it takes twice
as many mistaken compromisers to give away an election.

I don't care what strategy you use in that election. What I care about
is, no matter what your strategy is, you'll vote for your favorite,
and won't vote anyone else over him. Maybe you'll just estimate which
candidate is your needed lesser-evil, and vote for him/her, as in
Plurality, except that you'll also vote for everyone whom you like
more, including your favorite. Or maybe you'll use mathematical
strategy. Either way, you won't dump your favorite by voting someone
else over him/her.

About the mathematical strategy, if that's what you choose to use:

If your polling information is from one of the usual pollsters, like
the one that was caught falsifying their data, then that poll isn't
a significant amount of information. It's really a zero-info election.
Your A voter, with his utilities, should vote only for A in a zero-info
election. That's because A is the only candidate with above-average
utility for you.

Of course a crooked pollster would tend to understate the support of
the best candidate, the honest one, and so you might also vote for
A only, for that reason too--because you expect that A has been
understed by the pollster.

But maybe the poll is done by an organization that the A voters trust,
people who share the goals of the A voters, and their fear of their
last choice. And maybe the candidate lineup is a 1-dimensional one,
like Nader, Gore, & Bush, and so the responses to the Approval poll
mean something. Then it isn't difficult to devine how to vote, if
someone among the A voters does the strategy calculation. Don't suppose
that every A voter must work the mathematical strategy out for himself/
herself. All it takes is one voter to do that.

Of course the only difficult part is calculating the frontrunner
probabilities. That can probably be done, based on your poll result,
by assuming that the probability distributions are normal, and that
they're similar for the various candidates. One person can do that,
and make the information available to the other voters.

One person does that, and then various groups, with different
utilities, use those Pij to calculate their strategy, by
calculating the strategic values of the candidates, as I've described
here on previous occasions.

Maybe the A voters are one group with one set of utilities, or maybe
there are subgroups with different utilities. In the latter case,
each subgroup would need only one person to calculate the optimal
voting strategy. Remember that it only takes on person in the whole
election to calculate the Pij, and the subgroups can use those Pij
to calculate their own voting strategy.

  So far, two
>people, both highly intelligent and with a thorough understanding of voting
>systems, have decided to vote in two separate ways, given the same
>information, preferences and expected utility outcomes.  I suspect the rest
>of the list would be similarly divided, if not the populace as a whole.
>
> >If the scenario happens under approval voting, I don't think that it
>happens
> >for the wrong reasons. The result happens because enough voters felt the
> >utility gap between their favorite candidate and their second favorite 
>(or
> >their second and third, or whatever) was small enough to include that
> >additional choice, while the utility gap to their next choice was larger.
>In
> >other words, approval is tending to maximize voter utility.
>

>If people, given exactly the same utilities, cast totally different 
>approval
>ballots, then I don't see how Approval can maximise voter utility in any
>even handed manner.

Remember, Craig, that we don't have the Pij yet. People are only
guessing now. And of course different people on this list might have
made different assumptions about the trustworthiness of the pollster.
You didn't say if it was a typical unreliable one, or some organization
that the A voters trust.

Don't say the situation doesn't have an answer. Someone can
estimate the Pij from your polling data

Anyway, _any_ estimate of Pij will maximize your utility expectation
if that estimate, however unreliable it is, is your best estimate.

Don't expect everyone on EM to vote the same, when we now only have
our own guesses about Pij. If your guess is different from mine, then
we'll vote differently, but we'll both maximize our utility expectation
based on our guesses. Your Pij estimates needn't be "right" in some
absolute sense, whatever that would mean. They need only be _your_
best estimates.

And, as has been previously pointed out here by people other than me,
it's just as valid to estimate which candidates to vote for as to
estimate Pij, and then calculate which candidates to vote for based
on that Pij estimate. The voters are maximizing their utility just
as Plurality voters now do, when they judge whom to vote for without
estimating Pij and doing the calculation. The Plurality voters, when
asked why they vote as they do, are obviously trying to maximize their
utility expectation, though they don't calculate strategy mathematically.

Any utility (in a broader sense) advantage Approval has
>over Condorcet is more than countenanced by the fact that it doesn't give
>votes equal power.

Nonsense. Any voter has the power to cancel out any other voter.
Everyone has the same voting options. But I'm glad that you're
making it explicit that you're comparing Approval to Condorcet.

This is also true, of course, if someone votes
>insincerely (and non-strategically) or truncates their vote in a Condorcet
>election, but this inequality is the fault of the voter.  The inequality in
>Approval is the fault of the voting system.

Forgive Approval for not being Condorcet, unless you think you
can enact Condorcet, unless you think you can convince a sufficient
number of people about the best way to count rankings, in the
IRVie environment that we now have.


>
> >Approval counts more than one preference. If there are four candidates, 
>and
> >I vote AB, then I am expressing the following preferences:
> >
> >A > C
> >B > C
> >A > D
> >B > D
>
>If A is your favourite, B is your lesser of two evils candidate and C is 
>the
>greater of two evils candidate, you cannot express your A>B preference as
>well as your B>C preference.  You have to pick one, and if you make the
>wrong choice, your candidate can lose.  In a Condorcet election, there can
>be strategies involved, but they are complex and diffuse enough so that,
>without highly detailed information, it is safest to number all your
>preferences in sincere order.  The only choice you have to make in making
>your vote as effective as is possible, is who you like the best.
>

Sure, as I said, I like Condorcet's luxury of letting me vote all
my preferences, and counting them. Can we get the luxury model,
Condorcet? If not, let's accept the next best, Approval.

Mike Ossipoff

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