[EM] Complex Preferences

[wclark at xoom.org]

> I'd think *that* should allow for preferences as complex as you'd like to
> make them, expressing any sort of strategy concerns or ambiguities you
> can dream up.  It also strikes me as a straight-forward generalization
> of the simpler preferences expressed by a single ranking.

Actually, I think it might also be a generalization of the Dyadic Approval
method, if we use rankings-of-outcomes as a ballot format.

Traditional ranked preferences (or ballots) can be created by using just
the singleton and empty sets from our 26-member set of possible
rankings/outcomes.  If our primary preference (i.e. first choice for the
election outcome, out of all 26 possibilities) is:

A>B>C

Then this can be represented by ranking:

[A]>[B]>[C]

If we want to express something like:

A>B>>C

We could use:

[A=B]>[A>B]>[A]>[B>A]>[B]>[C]

(or something similar).

Ambiguous preferences such as:

A>B>C>A

might now be represented as:

[A>B]=[B>C]=[C>A]

I think this new notation might prove convenient, not just for formalizing
some of the intuitive descriptions of voter motivation we've seen around
here, but also as an alternate method of evaluating election results
(alongside things like social utility maximization).

It might also be useful in generating complex strategies, either for
simulation purposes or as part of a DSV system.

-Bill Clark

-- 
Protest the 2-Party Duopoly:
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