Designing Census Sampling for
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.