Population paradox

Joe Weinstein jweins123 at hotmail.com
Tue Feb 4 14:51:29 PST 2003

Thanks to Joe Malkevich and Josh Narins for correcting hazy recollections 
(mine - and maybe others' as well).

I wouldn't go so far as to say that MEP is unquestionably 'the fairest' of 
all possible methods.  As far as I know, each of the standard (and each of 
many nonstandard) House Apportionment methods can be got as the solution to 
maximizing a weighted average of individual citizens' utilities - using a 
suitable utility function - of the citizen's 'representation share'.  
Here,(1) a citizen's 'representation share' may be defined as her state's 
apportioned number of seats divided by her state's population; and (2) a 
suitable utility function is in general convex, i.e., twice the 'rep share' 
does not yield twice the utility (or, put another way, utility as a function 
of rep. share follows a law of diminishing returns).

Even given agreement on a suitable utility function, some weighting schemes 
are fairer than others.  I would weight all citizens equally, but in effect 
some schemes instead give equal weight to each of the states (so that a 
given shortchanging in rep share of the average citizen of Montana is 
equated to the same shortchanging of the average citizen of California).

So, what's 'fairest' depends on which utility function you deem to be 
'fairest' or most apropos, and what scheme you deem 'fairest' for weighting 
different citizens.

Joe Weinstein
Long Beach CA USA

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