[EM] A Decisive, Landau Efficient, Generalized Median, Single Winner Method

[Forest Simmons]

The median X of a finite set of distinct points arranged along a straight
line segment will always minimize the sum of distances from it to the other
points. [If the points are not distinct, a weighted sum does the job.]

Consequently one way to generalize the concept of "median" in a general
metric space is by minimization of (weighted) sums of distances.

Thus, the Kemeny-Young method chooses the "finish order" that minimizes its
sum of distances to the ballots, i.e to their respective rank orders.

In this context, the distance from a ballot order to a potential finish
order is their Kendall-tau distance, the total number of basic order
reversals necessary to convert one order into the other.

There are two unnecessary difficulties associated with Kemeny-Young:
 (1) The number of finish orders that need to be checked grows
exponentially with the number of candidates,  even when all we need is the
winner of a single winner election.
(2) The method is clone dependent ... a fatal flaw in the context of
electoral politics. The basic spoiler problem that sparked election method
reform in the first place was a failure of clone independence. Even IRV
with all of its other problems, is clone independent.

The method we propose is both clone independent and computationally
efficient.

The key innovation is that we gauge the distance from ballot B to a
potential winner X by the cost of the least expensive beatpath from X to
the candidate f(B) that is favored above all others on ballot B.

I'm going to break here to let this idea sink in a little before filling in
the few remaining details.

To be continued...
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