Irrational choice
We cannot directly see people’s thought processes when they choose, but we can observe the choices they make and see if these are consistent with rationality and the independence axiom. Imagine that you are given a choice between an apple and an orange, and you choose the apple. Now imagine that you are offered the choice of an apple, an orange, and a peach. The independence axiom assumes that you might choose the apple again, or the peach, but you would not choose the orange because the addition of the peach cannot change your preference for apples over oranges.