A generalization of simple majority voting in which a list of quotas 
specifies, according to the number 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 the alternative is the choice.
Let 
be the number of quota systems for
voters and 
the number of quota systems for which 
, so
 |
(1)
|
where 
is the floor function. This produces the sequence
of central binomial coefficients 1,
2, 3, 6, 10, 20, 35, 70, 126, ... (OEIS A001405).
It may be defined recursively by 
and
 |
(2)
|
where 
is a Catalan number (Young et al. 1995).
The function 
satisfies
 |
(3)
|
for 
(Young et al. 1995).
satisfies the quota
rule.
