Ordinal Utility and Preference Reversal Phenomenon

Chapter 1 described that decision-making phenomena are broadly divisible into those under certaintyCertainty, those under riskRisk, and others under uncertaintyUncertainty. Chapter 2 described that preference relationPreference relation can be represented by set theorySet theory. This chapter first introduces the concept of utilityUtility (numerical representation) used to explain such decision-making phenomena and briefly presents the idea of traditional ordinal utility theoryOrdinal utility theory. Ordinal utility theoryOrdinal utility theory is assumed in many theories in economics. However, it includes some phenomena that constitute counterexamples that cannot be justified from the perspective of behavioral decision theoryBehavioral decision theory. Among such cases, this chapter presents specific examination of a case in which the transitivityTransitivity premised on ordinal utilityOrdinal utility is not satisfied, and presents a phenomenon known as preference reversalPreference reversal. Transitivity refers to a relation between two alternativesAlternatives, which is a consistent attributeAttribute of preference relationPreference relation that, for instance, if oranges are preferred to bananas and apples are preferred to oranges, then apples are preferred to bananas. In addition, preference reversal is regarded as a phenomenon that deviates from the procedural invarianceProcedural invariance that preference cannot be reversed by the preferencePreference revelation procedures. In this type of case, for instance, when making a purchase decision, although Brand A is said to be more desirable than Brand B when their values (e.g., the prices considered reasonable) are assessed independently, Brand B is chosen if the two are actually compared.