JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Biometrika Trust is collaborating with JSTOR to digitize, preserve and extend access to Biometrika. SUMMARY An asymptotic approximation is given to the expectation of the size of a selected subset from a set of t objects, where the design is a balanced paired comparison experiment of n replicates. The paper also contains an excerpt (Table 4) of a table of expected sizes of the selected subset, expressed as proportions of t. The complete set of tables, which may be obtained by writing to the author, includes entries for combinations of t = 3(1) 20, n = 1(1) 20 (5) 50(10) 100 and preference probabilities p = 0-60(0410) 1 00 at each level of selection P* = 0 75, 0 90, 0 95, 0 975, 0 99. Examples of applications are directed towards an optimization of designs for selection.