[EM] Probabilistic voting in Score

[Michael Ossipoff]

Suppose the method is 0-10 Score (the Score  version used in the
minguo presidential poll now being conducted).

Suppose that, maybe based on one of the SFR formulas that I've
described, or a similar one, or some other one, you've decided what
fraction, f, of max points to give to a certain compromise candidate
B. You're giving hir SFR because of a known, perceived or expected
Chicken-Dilemma situation.

Max points is 10, and so you multiply 10 by f. Say f is .23 (the f
that I chose for Ron Paul). Then you'd like to give, to candidate B,
2.3 points.

So you give hir 2 points, and probabilistically give hir another point.

You do that by giving hir, with a probability of  .3, 3 points instead
of 2 points.

Suppose that the method is Emocracy, the 3-slot Score voting that is
used in the minguno poll.

With that method, a middle rating counts for 1/2 max.

So, since you want to give f X (max points), then you want to give f X
(2 halves) points.

That comes to .46 half points.

So, give hir, with a probability of .46, a middle rating instead of 0.

Suppose you'd wanted to give hir .71 max?

That's 1.42 halves that you'd like to give hir.

So give hir 1 half, and, with a probability of .42, give hir another half.

In other words, with a probability of .42, give hir max instead of half max.

Do those things if it's a public election, with millions of voters (or
even thousands of voters, or even hundreds)

But if it's a poll, with fewer voters, then then when your
probabilistic voting results in giving hir the larger amount, it might
really just count as the larger amount, since there might not be lots
of people doing that probabilistic voting.

For that reason, when there are fewer voters, and if you don't expect
B's voters to co-operate, to reciprocate the SFR, then you should just
round down to the next lower rating allowed by the Score version in
use.

In Approval, of course that means rounding down to 0.

Where you wanted to give .23 max, in 0-10 Score, then just round down to 2.

Where you wanted to give .23 max in 3-slot Score, then just round down to 0

Where you wanted to give .71 max (1.42 halves) in 3-slot Score, then
just round down to 1/2.

Of course, in Approval, in a public election, if you'd like to give to
B an SFR of f, meaning f X max, then approve B with a probability of
f.

Mike Ossipoff