Let M(n) be the minimum number of rank-order ballot votes
(without truncation) that always suffice to create any
pairwise-beats-relationship configuration among n-candidates.
(Where A "beats" B if a majority of the votes say so.)
For example M(2)=1 since one candidate always beats the other,
which you can say with a single vote.
M(3)=M(4)=M(5)=3, i.e. any configuration of beats-relations among up to 5
candidates can be got using only 3 votes at most (and 3 can be required,
e.g. a 3-cycle). There is some discussion of M(n) in CRV's puzzle 28:
http://rangevoting.org/PuzzlePage.html
But anyhow, pathetically, I do not know:
what are the values of M(6), M(7), M(8), M(9)?
Warren D. Smith
http://RangeVoting.org <-- add your endorsement
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