Comparative risk attitude and the aggregation of single-crossing

TL;DR

This paper explores the relationship between risk attitudes and the mathematical property of signed-ratio monotonicity, linking economic notions of risk aversion with theoretical conditions for aggregation of preferences.

Contribution

It establishes a novel connection between the concept of 'less risk-averse than' and signed-ratio monotonicity, advancing the theoretical understanding of preference aggregation.

Findings

Linked 'less risk-averse than' with signed-ratio monotonicity

Characterized conditions for aggregation of single-crossing functions

Extended theoretical framework for risk attitude comparison

Abstract

In choice under risk, there is a standard notion of 'less risk-averse than', due to Yaari (1969). In the theory of comparative statics, the single-crossing property is satisfied by all weighted averages of a family of single-crossing functions if and only if the family satisfies a property called signed-ratio monotonicity (Quah & Strulovici, 2012). We establish a close link between 'less risk-averse than' and signed-ratio monotonicity.