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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