Population paradox

[Joe Weinstein]

Many thanks to Joe Malkevich (Archive Message 10835) for the web reference  
(http://www.aps.org/apsnews/0401/040117.html) to Young’s very readable and 
useful summary paper on apportionment methods.

Again - and as a caveat to some conclusions one might draw from the paper - 
there are various viewpoints on just which criteria and measures thereof are 
most important to optimize.

For some of us, what counts is fairness to and among persons, more than to 
and among states.  For me, the preferred apportionment should maximize, for 
one’s chosen convex utility function, the sum over all persons of each 
person’s utility value for her per-cap representation level.  So, other 
things being equal, it is likely better to under-represent a few people (at 
a given level of per-cap representation) than to under-represent (at the 
same level) many people.

Conventional criteria featured in Young’s paper, however, directly address 
the issue of fairness to and among states rather than to and among persons.  
(Typically, each state, or each pair of states, gets equal weight in an 
objective function to be maximized or minimized.)  These criteria include 
house or population monotonicities, and lack of bias as between small vs 
large states.

So, to take the case of population monotonicity, in my view in some cases 
this concept may and should be violated in an optimal reapportionment.  
Namely, suppose house size is fixed, a given state A gains population share, 
and other states meanwhile also shift their shares.  The reapportionment may 
conceivably quite legitimately penalize A in order to achieve optimal 
representation overall.

Joe Weinstein
Long Beach CA USA


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