An interesting property of choice procedures, called path independence, refers to the following problem. Let us say that you have to make a choice from a set A: Does it matter whether
(i) you make a choice from the entire set, or (ii)you fi?rst partition A into subsets A1and A2; then make a selection from among each of the sets, and ?finally make a choice from among elements you selected from A1 and A2?

(a) Formulate the path independence property.
(b) Show that the rational decision-maker does satisfy the property.
(c) Find exs of procedures of choice that do not satisfy this property.