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Population Paradox

The population paradox is an apportionment method paradox in which one state loses a seat to another state even though the first state's population has grown faster. An apportionment method that cannot exhibit this behavior is called population monotone.

The Balinski-Young impossibility theorem shows that no apportionment method for four or more states can always satisfy the quota rule and also avoid the population paradox.

See also

Alabama Paradox, Apportionment Method, Balinski-Young Impossibility Theorem, New-States Paradox

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References

Balinski, M. L. and Young, H. P. Fair Representation: Meeting the Ideal of One Man, One Vote, 2nd ed. Washington, DC: Brookings Institution Press, 2001.Bogomolny, A. "The Constitution and Paradoxes." https://cut-the-knot.org/ctk/Democracy.shtml.

Cite this as:

Weisstein, Eric W. "Population Paradox." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PopulationParadox.html

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