Designing Census Sampling for Reapportionment

Joseph B. Kadane


This paper proposes a design criterion for sampling in conjunction with the Censuses of 2000 and beyond. Since reapportionment of Congress is the constitutional basis of the Census, the loss function used here minimizes apportionment errors in a certain sense. This leads to a stochastic modification of the Hill (equal proportions) method of apportionment now used. If the sampling in the census is designed to achieve minimum constant coefficient of variation of state shares of the national population, the use of the proposed ``single-number'' census will result in the same apportionment as would have been obtained using the proposed loss function.