Studies exist which have been taken to show that values are additive, and that linear utility scales are appropriate to represent social, economic or aesthetic choices. The predictions of an alternative value model based on set theory differ in choice situations where identical replications appear in the stimuli. 30Ss making preference rankings of replicated picture postcards (a) comparing different degrees of replication of the same picture and (b) comparing different pictures with the same degree of replication for each picture, yielded results which significantly failed to confirm (p<.025) the linear scale or the set theory predictions, but could be accounted for by a lexicographic variant of the set theory model. Relevant axioms or properties of the value models are given, requirements which an adequate theory must meet are indicated.