Quota System
A generalization of simple majority voting in which a list of quotas 
specifies, according to thenumber of votes, how many votes an alternative needs to win (Taylor 1995). The quota system declares a tie unless for some
, there are exactly tie votes in the profile and one of the alternatives has at least 
votes, in which case thealternative is the choice.
Let 
be the number of quota systems for 
voters and 
the number of quota systems for which 
, so
where
is the A001405). It may be defined recursively by 
and
where
is a Catalan Number (Young et al. 1995). The function satisfies
for
(Young et al. 1995). satisfies the Quota Rule.See also Binomial Coefficient, Central Binomial Coefficient
References
Sloane, N. J. A. SequenceA001405/M0769in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995. Taylor, A. Mathematics and Politics: Strategy, Voting, Power, and Proof. New York: Springer-Verlag, 1995. Young, S. C.; Taylor, A. D.; and Zwicker, W. S. ``Counting Quota Systems: A Combinatorial Question from Social Choice Theory.'' Math. Mag. 68, 331-342, 1995.
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