# Single-crossing dominance: A preference lattice

## TL;DR

This paper explores the mathematical structure of single-crossing dominance in preferences, providing foundational theorems and applying them to collective choice, uncertainty, and decision-making models.

## Contribution

It characterizes the lattice structure of single-crossing dominance, establishing existence and uniqueness results, and applies these to various economic and decision-theoretic contexts.

## Key findings

- Proved the lattice structure of single-crossing dominance.
- Derived new comparative statics theorems for collective choice.
- Characterized a 'maxmin' class of uncertainty-averse preferences.

## Abstract

Most comparisons of preferences are instances of single-crossing dominance. We examine the lattice structure of single-crossing dominance, proving characterisation, existence and uniqueness results for minimum upper bounds of arbitrary sets of preferences. We apply these theorems to derive new comparative statics theorems for collective choice and under analyst uncertainty, and to characterise a general 'maxmin' class of uncertainty-averse preferences over Savage acts.