Many Traditional Algebraic Analyses of preference and choice for a finite set of alternatives have been based on binary choices. They have assumed that the binary preference information given by a decision maker is transitive. However, there is considerable evidence that many relations that might occur as preference relations cannot be presented as transitive relations. To construct transitive binary comparisons from intransitive ones, we suggest the notion of superior set, which helps us to understand the structure of intransitive binary comparisons. We also provide a heuristic method to construct transitive binary comparisons. And some merits merits of the suggested method over the existing methods are also discussed.