2. Fairness and Apportionment
The Constitution does not specify what fairness criteria should be used in comparing two different proposed ways to solve an apportionment problem. From the beginning there were both political and equity considerations in choosing an apportionment system but there are some principles that one can call attention to in evaluating apportionment systems. One fairness idea is that each state should get either its lower quota or upper quota. A second approach to fairness is to look at pairwise equity between states. The empirically discovered Alabama paradox (one can get fewer seats in a larger house, with fixed population) called to the attention of politicians and others interested in apportionment that one had to worry about the fairness properties of the methods that one might use to solve the apportionment problem. However, little seems to have been done in a systematic way to see what the consequences for fairness were of adopting different apportionments. In the United States, what became a matter of concern was the perception that different methods of apportionment might display bias. The idea of bias is that a method might systematically reward states with specific characteristics or groups of such states. For example, were some methods more likely to give smaller states more than their fair share of seats, say, as measured by exact quota? One way to try to answer this question was to turn to statistics. It is not hard to see that the different methods of apportionment treat small and large states in different ways. This can be seen in contrived artificial examples as well as using data that has arisen from the censuses. However, there are many different ways of thinking and models for deciding what constitutes bias of an apportionment method. As just one example, the Constitution itself has a bias in favor of small states because it will give every state one seat regardless of how undeserving the state might be. In computing bias of a method, how should this "minimum of one seat" condition be taken into account?
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