[EM] Brams & Fishburn Condorcet definition

MIKE OSSIPOFF nkklrp at hotmail.com
Sun Feb 27 01:18:06 PST 2000

I'm going to quote Brams & Fishburn's definition of Condorcet,
because it shows the use of MaxMin to describe a procedure
that looks at all of a candidate's pair-comparisons, rather
than just at his pair-losses. If MaxMin is used in that way,
it's reasonable that MinMax can mean that too. It seems to
me that I've mostly only run across MaxMin definitions in
academic writing.

Brams & Fishburn's definition:

"Condorcet's procedure [Condorcet (1785), Black (1958)] is
a MaxMin procedure. [That would come as a surprise to Condorcet,
judging by the translations that I've seen--Mike]

Let v*(x) = min{v(x,y):y an element of X\{x}}. Then x an element
of F maximizes v*(x) over X.

v(x,y), I assume, is the number of people who voted x over y.
I assume that F is the set of winners.

I rendered the "an element of" symbol by words.

Their definition doesn't say anything about whether x beats
y or vice-versa.

Mike Ossipoff
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