Why adding a third option can fundamentally change your original choice

Ideas & Philosophy · Published 18 October 2026 Swipe more like this →

In short: If you prefer apple pie to blueberry, does the sudden arrival of cherry pie change your mind? In decision theory, this is known as the Independence of Irrelevant Alternatives. While logically sound, this principle is frequently violated by both human psychology and the very voting systems we use to govern.

The Independence of Irrelevant Alternatives (IIA) is an axiom suggesting that a preference between two options should remain unchanged if a third, unrelated option is introduced. In economics, this principle helps create testable models of revealed preferences. Without it, a model could become unfalsifiable by claiming that any change in experimental results was simply due to an unobserved, irrelevant shift in the environment. Economists often justify this axiom by arguing that any irrational agent would eventually be subjected to a money pump until they are bankrupt.

However, human behavior often exhibits 'menu effects' or 'menu dependence.' A classic example is the decoy effect, where adding a medium soda priced at $5 between a $3 small and a $5.10 large makes the large appear to be a better deal. Similarly, the philosopher Sidney Morgenbesser famously illustrated the violation of IIA with a joke: after choosing apple pie over blueberry, the introduction of cherry pie caused him to switch his preference to blueberry. This phenomenon is also studied in behavioral economics, where such failures of the axiom are referred to as menu dependence.

In social choice theory, the stakes are even higher. Arrow's impossibility theorem demonstrates that no reasonable, non-dictatorial ranked voting system can satisfy IIA. This leads to the 'spoiler effect,' where a third candidate alters the election outcome without winning. While some methods like sortition or random dictatorship pass the test, they are often considered undesirable. Even rated voting methods, such as approval or range voting, face scrutiny; they may only satisfy IIA if we assume voters rate candidates independently of the available alternatives—an assumption many argue is unrealistic. In certain scenarios, a Condorcet cycle can occur, where a group of voters prefers candidate A to B, B to C, and C to A. Furthermore, Amartya Sen has suggested that such context-dependent choices might not be irrational, noting that a third option can provide necessary context for an individual's decision.

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