[EM] Condorcet Flavored PR Methods

[Forest Simmons]

A "Condorcet Flavored PR Method" is an M-winner election method that

(1) compares candidate subsets of cardinality M head-to-head, and

(2) does the comparison in such a way that the winning combination of any
head-to-head comparison provides better PR representation than the loser
subset, and

(3) gives the win to the "beats-all" combination if there is such a
subset.

Every Condorcet Flavored PR Method (CFPRM) generates a pairwise comparison
matrix which has one entry for each ordered pair of candidate subsets of
size M.

If there are N candidates and M winners, then there C = N!/M!/(N-M)!
possible candidate combinations (i.e. subsets) of cardinality M, and there
are C*(C-1) ordered pairs of such combinations, so the pairwise comparison
matrices suffer from a "combinatorial explosion" of size.

Nevertheless, if N and M are not too large, the calculations can be done,
and the results have practical as well as theoretical value.

If the method yields a "beats all" combination, then that combination is
by definition better than any other combination according to whatever
standard of "better PR representation" is being used in item (2) above.

To be continued ...

Forest

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