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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