%I A122916
%S A122916 1,3,3,3,3
%N 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).
%C A122916 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<C<K. Additional entries should be within the reach of computers. 
               a(19) >= 5.
%D A122916 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.
%D A122916 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.
%H A122916 Warren D. Smith, <a href="http://rangevoting.org/PuzzHowManyBallots.html">
               Answer to puzzle 28</a> (surveys the problem)
%Y A122916 Sequence in context: A082127 A031354 A033700 this_sequence A132973 A107760 
               A138070
%Y A122916 Adjacent sequences: A122913 A122914 A122915 this_sequence A122917 A122918 
               A122919
%K A122916 hard,more,nonn
%O A122916 1,2
%A A122916 Warren D. Smith (warren.wds(AT)gmail.com), Sep 19 2006