[EM] Friendly Voting

[Forest Simmons]

Friendly Voting is a form of Generalized Median Voting (GMV) adapted to
Ranked Choice Ballots.

GMV methods elect the candidate whose total distance to the ballots is
minimal. Friendly Voting gauges the distance from a candidate X to a ballot
B as the number of steps in the shortest beatpath from X to ballot B's
first place favorite f(B).

Example: Consider the ballot set profile...

x ABC
y BCA
Z CAB

The cyclic beat order is ABCA.

So the total distance from A to the ballot set is ...
x×d(A,A)+y×d(A,B)+z×d(A,C),
which simplifies to
0+y+2z.
Similarly, the total distance from B to the ballot set is
2x+0+z,
and the total distance from C to the ballot set is
x+2y+0

If we subtract x+y+z from each of these totals, the respective scores
become ...
z-x, x-y, and y-z.

Candidate A wins if z-x is the smallest of these, i.e. if fpC-fpA is
smallest, i.e. if ...
fpA-fpC is largest, i.e. larger than both fpB-fpA and foC-fpB.

So this seems to be the appropriate generalization of the fpA-fpC method
that Kristofer has persisted in pestering Kevin and me about for about half
a decade!

Thanks, Kristofer !!!! Bullseye🎯

-Forest
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