A maximum overlap method for two-PSU-per-stratum designs is described in Ernst (1989, Sec. 3.1). The procedure requires identical primary sampling unit (PSU) definitions in the initial and final designs. This note outliner two modifications to the Ernst procedure to account for different PSU definitions in the two designs.

The first modification is a procedure for establishing a one-to-one correspondence between the PSUs in the initial and final designs when PSU definitions arc different in the two designs. The maximum overlap algorithm includes an ordering procedure for PSUs and pairs of PSUs that requires setting up a one-to-one correspondence between the initial and final PSUs. This correspondence can include dummy PSUs (artificial PSUs that have a zero probability of selection).

The second modification is a change in the calculation of the cost matrix to account for the possibility of several initial PSUs intersecting with one final PSU.