Revealed Preference Analysis Under Nontransitive Preferences

This dissertation presents three chapters that examine revealed preference theory under the assumption that economic agents may have nontransitive preferences. The first chapter introduces the Random Preference Model (RPM), a framework similar to the Random Utility Model (RUM) designed to explain consumer choice behavior. Unlike RUM, which assumes transitive preferences often contradicted by behavioral economics, the RPM allows for nontransitive preferences. Its main application is modeling aggregate choice behavior in a population of heterogeneous individuals whose choices are consistent with the Weak Axiom of Revealed Preference. The empirical validation of RPM is based on the UK Family Expenditure Survey, which includes household expenditure, income, and socio-demographic characteristics. The analysis identifies different consumer profiles that support nontransitive behaviors and highlights the limitations of traditional rational choice models. The second chapter introduces a nonparametric method for deriving the income compensation function from finite price and quantity data satisfying the Weak Generalized Axiom of Revealed Preference (WGARP), a condition weaker than GARP. The framework accommodates minor measurement and optimization errors, providing an approximate rationalization of WGARP. This method extends Varian (1982)'s framework by offering deeper insights into choices that deviate from strict utility maximization. Using the revealed preference characterization of approximate WGARP, we establish robust welfare bounds on the income compensation function, improving the partial identification of both cost-of-living and standard-of-living indexes. The third chapter explores the empirical implications of consumer behavior when preferences are nontransitive and homothetic. We provide a rationalization of the pairwise homothetic axiom of revealed preference (PHARP), originally proposed by Varian (1982), that holds regardless of the number of goods. This rationalization is nonparametric, offering flexibility because it does not require assuming a specific mathematical form for consumers' underlying preferences. Rather than imposing a predetermined model, we let the data inform our analysis. Our work presents a direct parallel to Varian's theorem on nonparametric tests for homothetic utility maximization, adapted to PHARP. We then show that satisfying PHARP is equivalent to Laspeyres quantity and price indexes being at least as large as the corresponding Paasche indexes.

Name thesis:degree_name

Ph D

Discipline thesis:degree_discipline

Economics

Grantor dc:publisher

The University of Western Ontario

Year dc:date.issued

2025

Author dc:creator

• Youmbi Fotso, Wilfried

Advisor dc:contributor.advisor

• Aguiar, Victor

• Nontransitive preferences
• Weak Generalized Axiom of Revealed Preference
• Weak Axiom of Revealed Preference
• Random Preference Models
• Income Compensation Functions
• Pairwise Homothetic Axiom of Revealed Preference
• Preference Functions
• Homothetic Preference Functions
• Laspeyres and Paasche indexes
• and Fisher Ideal indexes.

Statement dc:rights

• Attribution-NoDerivatives 4.0 International

Language dc:language.iso

en

Handle dc:identifier.uri

https://hdl.handle.net/20.500.14721/39045

OAI identifier oai:identifier

oai:uwo.scholaris.ca:20.500.14721/39045