Re: Population paradox

[Joseph Malkevitch]

Dear Josh,


The way the so called 5 divisor methods work is that each has an objective function which works with regards to pairs of states. One can think of the seats up to 435 being handed out one at a time (beyond the 50 that the constitution assigns automatically). At each stage one gives the next seat to that state which is most entitled to it as measured by the objective function. At the end some states get more than their quota and some get less. (With real data its not very likely a state will get exactly its quota.) The issue of bias is whether or not over a period of time "small" vs. "large" states (as measured by population) are under or over represented. In 1980 Huntington-Hill gave Montana more seats than it "deserved" and in 1990 and 2000 it gave Montana fewer seats than it deserved. But in the last two cases had it been given 2 seats rather than 1 some other state would have been treated even worse, with respect to the Huntington-Hill measure of fairness.

Balinksi and Youngs "chart" about this is available at the web site below. The different numbers of seats for all the censuses is available in the second editon of their book.


http://www.aps.org/apsnews/0401/040117.html


Best wishes,

Joe


--
Joseph Malkevitch
Department of Mathematics
York College (CUNY)
Jamaica, New York 11451


Phone: 718-262-2551
Web page: http://www.york.cuny.edu/~malk

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