Independence of irrelevant alternatives (IIA) is an axiom of decision theory which codifies the intuition that a choice between
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.
"IIA rules out this kind of arbitrary behavior, by stating that:In economics, the axiom is connected to the theory of revealed preferences.
Economists often invoke IIA when building descriptive (positive) models of to ensure agents have well-defined preferences that can be used for making testable predictions.
Often, the axiom is justified by arguing that any irrational agent will be money pumped until going bankrupt, making their preferences unobservable or irrelevant to the rest of the economy.
Behavioral economics introduces models that weaken or remove many assumptions of consumer rationality, including IIA.
This provides greater accuracy, at the cost of making the model more complex and more difficult to falsify.
In social choice theory, independence of irrelevant alternatives is often stated as "if one candidate (
Arrow's impossibility theorem shows that no reasonable (non-random, non-dictatorial) ranked voting system can satisfy IIA.
Methods that unconditionally pass IIA include sortition and random dictatorship.
Balinski and Laraki disputed that any interpersonal comparisons are required for rated voting rules to pass IIA.
They argue the availability of a common language with verbal grades is sufficient for IIA by allowing voters to give consistent responses to questions about candidate quality.
[5][page needed] Arguments have been made that IIA is itself an undesirable and/or unrealistic criteria.
Allowing either of these conditions alone causes approval and range voting to fail IIA.
Amartya Sen argued that seemingly independent alternatives could provide context for individual choice, and thus that menu dependence might not be irrational.