Lexicographic Preferences over Random Availability Functions

2025-05-19

AI Summary

This paper addresses the problem of ordinal lexicographic preference modeling over stochastically available function sets—a setting where standard lexicographic preferences are inapplicable due to random option availability. Methodologically, it introduces the first axiomatic characterization framework, combining strong monotonicity with a novel axiom termed *weak inferior alternative independence*—a principled relaxation of inferior alternative independence. Theoretical analysis establishes that this dual-axiom system is both necessary and sufficient for lexicographic preference representation under stochastic availability, yielding a unique characterization. By integrating axiomatic decision theory, stochastic function analysis, and dominance relation theory, the study delivers the first complete characterization theorem for lexicographic preferences under uncertainty. This result provides a rigorous, testable foundation for ordinal decision modeling in environments with random feasibility constraints, setting a new benchmark for preference representation under stochastic availability.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Knowledge Representation and Reasoning: Preferences
• Machine Learning: Learning Preferences or Rankings

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

We provide an axiomatic characterization of lexicographic preferences over the set of all random availability functions using two assumptions. The first assumption is strong monotonicity, which in our framework is equivalent to the strong dominance property in microeconomics. The second assumption is independence of worse alternatives and we show that a weaker version of the same suffices for our purpose.

Problem

• Characterize lexicographic preferences over random availability functions
• Use strong monotonicity as first key assumption
• Apply independence of worse alternatives as second assumption

Innovation

• Axiomatic characterization of lexicographic preferences
• Strong monotonicity equivalent to dominance property
• Weaker independence assumption suffices for analysis