A122916 Minimum number of n-candidate full-rank-order ballots required to instantiate any tournament on n nodes (where A beats B in the tournament if and only if it does so in a majority of the ballots and we forbid pairwise ties).

1, 3, 3, 3, 3

Offset: 1

Author

Warren D. Smith, Sep 19 2006

Keywords

• hard
• more
• nonn

Comments

Every entry is an odd number. a(n) <= a(n+1) <= a(n)+4. For all large enough n we know Cn/log(n) < a(n) < Kn/log(n) for suitable constants 0= 5.

Links

• P. Erdos and L. Moser, On the representation of directed graphs as unions of orderings, Publ. Math. Inst. Hungar. Acad. Sci. 9 (1964) 125-132; also reprinted in Paul Erdos: The art of counting, Selected writings (ed. Joel Spencer) MIT Press 1973, pp. 79-86.
• Warren D. Smith, Answer to puzzle 28 (surveys the problem)
• Richard Stearns, The voting problem, Amer. Math. Monthly 66 (1959) 761-763. Warning: Erdos, Moser and Stearns actually consider a slightly different problem definition, where ties are allowed. That would define a different sequence which would upper-bound this one and is related to it, but the present sequence seems to be a little more pleasant.