Re: Population paradox

[Joe Weinstein]

If I am not mistaken, Adam's 'Population paradox' has a venerable history in apportionment of the US House of Representatives, where at one point it was known as the 'Alabama paradox' (In 1840 or so, Alabama gained a larger proportion of the population, yet lost a seat.) It took a long while, but this paradox was a major impetus finally leading in the early 20th century to systematic 'scientific' house apportionment per Huntington. However, and please someone correct me, as far as I know none of the usual methods used or considered by the House (Webster, Hamilton, Jefferson - AND latterly Huntington) really reliably solve the 'population' paradox. To ensure a solution, you must deliberately design for 'population' consistency, or 'monotonicity', as for instance is done by the so-called 'quota method' of Balinski and Young. [By the way, though I no longer have the exact reference conveniently at hand, their paper in the Amer Math Monthly - late 70s, I believe - was one of the few that really got me interested academically in election methods.]

Joe Weinstein Long Beach CA USA


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