Economics 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. If agents' behavior or preferences are allowed to change depending on irrelevant circumstances, any model could be made
unfalsifiable by claiming some irrelevant circumstance must have changed when repeating the experiment. 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 While economists must often make do with assuming IIA for reasons of
computation or to make sure they are addressing a
well-posed problem,
experimental economists have shown that real human decisions often violate IIA. For example, the
decoy effect shows that inserting a $5 medium soda between a $3 small and $5.10 large can make customers perceive the large as a better deal (because it's "only 10 cents more than the medium").
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.
Social choice In
social choice theory, independence of irrelevant alternatives is often stated as "if one candidate (X) would win an election without a new candidate (Y), and Y is added to the ballot, then either X or Y should win the election."
Arrow's impossibility theorem shows that no reasonable (non-random, non-
dictatorial)
ranked voting system can satisfy IIA. However, Arrow's theorem does not apply to
rated voting methods. These can pass IIA under certain assumptions, but fail it if they are not met. Specific candidates that change the outcome without winning are called
spoilers. Methods that unconditionally pass IIA include
sortition and
random dictatorship.
Common voting methods Deterministic voting methods that behave like majority rule when there are only two candidates can be shown to fail IIA by the use of a
Condorcet cycle: Consider a scenario in which there are three candidates A, B, and C, and the voters' preferences are as follows: : 25% of the voters prefer A over B, and B over C. (A > B > C) : 40% of the voters prefer B over C, and C over A. (B > C > A) : 35% of the voters prefer C over A, and A over B. (C > A > B) (These are preferences, not votes, and thus are independent of the voting method.) 75% prefer C over A, 65% prefer B over C, and 60% prefer A over B. The presence of this societal
intransitivity is the
voting paradox. Regardless of the voting method and the actual votes, there are only three cases to consider: • Case 1: A is elected. IIA is violated because the 75% who prefer C over A would elect C if B were not a candidate. • Case 2: B is elected. IIA is violated because the 60% who prefer A over B would elect A if C were not a candidate. • Case 3: C is elected. IIA is violated because the 65% who prefer B over C would elect B if A were not a candidate. For particular voting methods, the following results hold: •
Instant-runoff voting, the
Kemeny–Young method, the
Minimax Condorcet method,
Ranked Pairs,
top-two runoff,
First-past-the-post, and the
Schulze method all elect B in the scenario above, and thus fail IIA after C is removed. • The
Borda count and
Bucklin voting both elect C in the scenario above, and thus fail IIA after A is removed. •
Copeland's method returns a three-way tie, but can be shown to fail IIA by going in the opposite direction. If A were not a candidate, then B would win outright. Introducing A changes the outcome into a three-way tie. So the introduction of A makes C no longer a loser, which is a failure.
Rated methods Generalizations of
Arrow's impossibility theorem show that if the voters change their rating scales depending on the candidates who are running, the outcome of cardinal voting may still be affected by the presence of non-winning candidates.
Approval voting,
score voting, and
median voting may satisfy the IIA criterion if it is assumed that voters rate candidates individually and independently of knowing the available alternatives in the election, using their own absolute scale. If voters do not behave in accordance with this assumption, then those methods also fail the IIA criterion.
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. In other words, they argue most voters will not change their beliefs about whether a candidate is "good", "bad", or "neutral" simply because another candidate joins or drops out of a race. == Criticism of IIA ==