[EM] reply clarifications. Interesting project.

[MIKE OSSIPOFF]

EM list--

First, let me correct something that I missed in this letter:


>>then with
>>
>>N1 AB N2
>>N3 BC N4
>>N5 AC N6
>>
>>the N numbers must all be rather close for "you" (i.e. John/Mary Q. voter)
>>by
>>yourself (without any other devious voters) to change the results 
>>sincerely
>>or insincerely.

No. In any 1 particular situation there need only be _one_
pairwise defeat that's close enough for us to change, or one
pair of pairwise defeats whose magnitudes are close enough for
us to tip the balance. Sure, there could be more than one such
way that we could change the outcome in a particular situation--
but, given a situation where we can change the outcome, the
chance that there'd be two ways we could change it is negligibly
small. So always we just look at the situations where there's
one way that we could influence the outcome.

***

In my reply to David, I got it right in the 2nd to last paragraph,
and in the last paragraph,
but, because I said it misleadingly througout the rest of the
letter, I should clarify it better here:

When we have no knowledge about the other voters, it isn't
that we _assume_ that all the situations have equal probability--
they _do_ have equal probability from our point of view.

So the fact that we have no information about the other voters
is itself a piece of information from which we know probabilities,
by which we can calculate how various pair-orderings that we
vote would affect our utility expectation.

***

Of course one reason why this topic is of interest is for the
practical purpose of calculating strategy in an actual election.
Also, it's interesting to find out what utility-maximization would
have us do, with various methods, with various utilities.

But maybe, for the purpose of looking at methods in this way,
an interesting to find out would be the utility expectation that
goes with voting sincerely with various methods and various
candidate utilities. We could compare in that way Condorcet,
Margins, IRV, Plurality, & Approval. If it turned out that Margins
excelled in that respect, that would tend toward weighing against
its problems in other areas, somewhat, especially if the good
results continued when various kinds of probability information
are available.

***

Voting sincerely in Approval with 0-info seems naturally to mean
using Approval's strategy of voting for all the above-mean
candidates. Though it's a mathematical strategy, it's one that
doesn't require any calculations to implement, and it sounds
sincere to me.

***

But speaking of utility, it's been pointed out that if we're
considering elections in the future, and we don't know which
voter in the example we'll be, then it's in our best interest
to want a voting system that maximizes the voters' average
utility in the outcome. One that maximizes the sum of the
utilities for all the voters. One that maximizes the "social
utility" of the outcome.

If the distribution of the voters is even, or if its density
increases with decreasing distance from the mean & median position,
then a candidate at the voter median will also be the one who
maximizes social utility. The candidate at the voter median
is the SCW too. So if a method does well at picking SCWs, then
we can expect it do do excellently by social utility.

I don't think anyone's denied that Condorcet does better at
picking SCWs than Margins does, and better than IRV does.

Therefore, Condorcet does the best job of maximizing your utility
expectation for some election in the future after Condorcet is
adopted, when you don't know what the example will be or which
voter in the example you'll be.

Approval, like any method, picks the SCW if voters have complete
information about eachother. With 0-info, it does a good job
of picking the voter median candidate (and therefore a good
job of maximizing social utility) to the extent that the
mean position of the candidates coincides with the voter median.
That condition can't be guaranteed, though candidates will
quickly move toward that position & cluster around it when
a better method like Approval is in use. But even if it isn't
exactly so, it's a condition that will be approached reasonably
well.

Mike Ossipoff

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