- Existence of ANR+PO Rules in the Total Order Case
- Project Year:
2025
- REU Student (s):
Kyle Lee | University of Michigan-Ann Arbor MI
- Student 1 Institution:
University of Michigan-Ann Arbor
- Project Mentor:
Lirong Xia
- Project Mentor Area:
DIMACS
- Project Abstract:
This paper addresses the compatibility of four fundamental axioms in social choice theory: anonymity (A), neutrality (N), resolvability (R), and Pareto optimality (PO). Building upon the seminal characterization of Bubboloni and Gori, which completely determines when an anonymous, neutral, and resolute (ANR) social choice rule exists on the domain of total orders, we examine whether Pareto efficiency introduces additional constraints. We show that the divisibility condition identified by Bubboloni and Gori - namely, that the number of alternatives m must be strictly smaller than the smallest nontrivial divisor d of the number of voters N - is both necessary and sufficient for the existence of a rule satisfying all four properties simultaneously. Our argument demonstrates that Pareto optimality can be accommodated without further restrictions, and that in the feasible case any voter's ranking can serve as the social outcome while preserving all desired axioms. We conclude by discussing the theoretical significance of this finding, its relation to symmetry considerations in social choice, and how the result may extend to domains beyond total orders, including partial orders and restricted preference classes.
