It is demonstrated, using transportation theory, that controlled selection can be used to solve the following sampling problem. Sample primary sampling units (PSUs) are to be selected with probability proportional to size for two designs, both one PSU per stratum, denoted as D1 and D2. The universe of PSUs is the same for each design but the stratifications are different. The goal of the problem is to simultaneously select the sample PSUs for the two designs in a manner which maximizes the expected number of PSUs that are in both samples. This procedure differs from previous overlap procedures in that it yields a better overlap, but is only applicable when the two samples can be selected simultaneously. An important special case occurs when the probability of selection for each PSU in D1 does not exceed its probability of selection in D2. The procedure can then guarantee that the D1 sample PSUs are a subset of the D2 sample PSUs. A proposed, but since cancelled, expansion of the Current Population Survey would have been a potential application of this special case, which is discussed. Variance formulas for estimators of total under the controlled selection procedure are also presented.

Revised (1993-03-15)