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Quota Rule


A quota rule is the recurrence relation for the function Q(n,r) that counts quota systems for n voters with initial quota q_0=r+1,

 Q(n,r)=Q(n-1,r-1)+Q(n-1,r)

for integers n>=1 and |_n/2_|<=r<=n, where |_x_| is the floor function. The initial value is Q(0,0)=1, and Q(n,r)=0 for integers n>=0 and r outside |_n/2_|<=r<=n (Young et al. 1995). The restriction on r is needed for the recurrence relation. For example, Q(2,0)=0 whereas Q(1,-1)+Q(1,0)=1.


See also

Quota System, Recurrence Equation

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References

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. https://doi.org/10.1080/0025570X.1995.11996354.

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Quota Rule

Cite this as:

Weisstein, Eric W. "Quota Rule." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/QuotaRule.html

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