Independence of irrelevant alternatives

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Independence of irrelevant alternatives (IIA) is an axiom of decision theory which codifies the intuition that a choice between ${\displaystyle A}$ and ${\displaystyle B}$ (which are both related) should not depend on the quality of a third, unrelated outcome ${\textstyle C}$. There are several different variations of this axiom, which are generally equivalent under mild conditions. As a result of its importance, the axiom has been independently rediscovered in various forms across a wide variety of fields, including economics,^[1] cognitive science, social choice,^[1] fair division, rational choice, artificial intelligence, probability,^[2] and game theory. It is closely tied to many of the most important theorems in these fields, including Arrow's impossibility theorem, the Balinski–Young theorem, and the money pump arguments.

In behavioral economics, failures of IIA (caused by irrationality) are called menu effects or menu dependence.^[3]