There are these axioms in the theory of rational choice:

Rational choice theory makes two assumptions about individuals’ preferences for actions. First, is the assumption of completeness, that is that all actions can be ranked in an order of preference (indifference between two or more is possible). Second, is the transitivity, the assumption that if action a1 is preferred to a2, and action a2 is preferred to a3, then a1 is preferred to a3.

(Source: Wikipedia page http://en.wikipedia.org/wiki/Rational_choice_theory)

Focus on the second axiom. If you observe me choosing a1 over a2 whenever presented a choice between a1 and a2; and choosing a2 over a3, whenever presented a choice between a2 and a3, you conclude that I would prefer a1 over a3 whenever presented a choice between a1 and a3.

If instead, I choose a3, when presented a choice between a1 and a3, you conclude that I am irrational.

I. don’t. think. so.

Hint: Especially when a1, a2 and a3 are people, rather than inanimate things.

We had a long debate about it yesterday in the lab and I finally found an example. Later over dinner, my wife found many more examples — all involving people, though. Not inanimate things.

Let me not give out the examples right now, just to let your minds get tickled a bit..