Independence of irrelevant alternatives

The independence of irrelevant alternatives (IIA), also known as binary independence or the independence axiom, is an axiom of decision theory and the social sciences that describes a necessary condition for rational behavior. The axiom says that adding "pointless" (rejected) options should not affect behavior. This is sometimes explained with a short story by philosopher Sidney Morgenbesser:

Morgenbesser, ordering dessert, is told by a waitress that he can choose between blueberry or apple pie. He orders apple. Soon the waitress comes back and explains cherry pie is also an option. Morgenbesser replies "In that case, I'll have blueberry."

Independence of irrelevant alternatives rules out this kind of arbitrary behavior, by stating that:

If A(pple) is chosen over B(lueberry) in the choice set {A, B}, introducing a third option C(herry) must not result in B being chosen over A.

The axiom is deeply connected to several of the most important results in social choice theory, welfare economics, ethics, and rational choice theory; among these are Arrow's Impossibility theorem, the Von Neumann–Morgenstern utility theorem, Harsanyi's utilitarian theorem, and the Dutch book theorems.