There is an old joke that says that given the choice between eternal happiness and a ham sandwich, one should choose the ham sandwich. The proof is quite simple: (1) nothing is better than eternal happiness; (2) a ham sandwich is better than nothing; and therefore, it straightforwardly follows from (1) and (2) that (3) a ham sandwich is better than eternal happiness. So, given the choice, one should choose a ham sandwich. This article takes a slightly more serious view of transitive relationships, and their interpretation in the real world. The author contends that transitivity and intransitivity are fascinating concepts that relate both to mathematics and to the real world, and that lessons devoted to this topic are almost certain to interest and engage students of almost any age.