Re: 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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