INTRODUCTION: One of the most important decisions that an animal has to make in its life is choosing a mate. Although most studies in sexual selection assume that mate choice is rational, this assumption has not been tested seriously. A crucial component of rationality is that animals exhibit transitive choices: if an individual prefers option A over B, and B over C, then it also prefers A over C. RESULTS: We assessed transitivity in mate choice: 40 female convict cichlids had to make a series of binary choices between males of varying size. Ninety percent of females showed transitive choices. The mean preference index was significantly higher when a female chose between their most preferred and least preferred male (male 1 vs. male 3) compared to when they chose between males of adjacent ranks (1 vs. 2 or 2 vs. 3). The results are consistent with a simple underlying preference function leading to transitive choice: females preferred males about one third larger than themselves. This rule of thumb correctly predicted which male was preferred in 67% of the cases and the ordering in binary choices in 78% of cases. CONCLUSIONS: This study provides the first evidence for strong stochastic transitivity in a context of mate choice. The females exhibited ordinal preferences and the direction and magnitude of these preferences could be predicted from a simple rule. The females do not necessarily compare two males to choose the best; it is sufficient to use a self-referent evaluation. Such a simple decision rule has important implications for the evolution of the mating strategies and it is consistent with patterns of assortative mating repeatedly observed at population level.