[EM] Simpson-Kramer definition

[Markus Schulze]

Hallo,

Mike Ossipoff wrote (14 April 2005):
> If you don't believe that Condorcet himself proposed PC,
> then accept the fact that a number of authors have called
> PC "Condorcet" in journal articles. I believe that Fishburn
> is one of those, for instance.

I have added Fishburn's (Peter C. Fishburn, "Condorcet Social
Choice Functions", SIAM Journal on Applied Mathematics, vol. 33,
pp. 469--489, 1977) description of "Condorcet's function".

Also Fishburn restricts his consideration to situations where
each voter casts a complete ranking of all candidates.

Also Fishburn uses the term "minimax".

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Page 470:
> For expositional simplicity it will be assumed throughout that
> all voters have linear preference orders on the candidates or
> alternatives so that individual indifference between distinct
> candidates does not arise.

Page 471:
> For any situation (A, p) and alternatives x, y e A, we shall let
> p(x,y) be the number of terms in p that have x preferred to y.
> Hence if p = (p1,p2,...,pn) then p(x,y)+p(y,x) = n when x <> y.

Page 471:
> f(x,A,p) = min { p(x,y) | y e A\{x} }.

Page 472:
> C6: Condorcet's function. (Also minimax function.)
> C6(A,p) = { x e A: f(x,A,p) >= f(y,A,p) for all y e A }.

Markus Schulze