[EM] puzzle

[Warren Smith]

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