Ordinality in Random Allocation

TL;DR

This paper explores the role of ordinal rules in lottery-based allocations, showing that certain desirable properties imply the use of ordinal methods in three-agent problems.

Contribution

It provides an axiomatic justification for ordinal rules in three-agent lottery allocations based on efficiency, strategy-proofness, non-bossiness, and continuity.

Findings

Ordinal rules are implied by key axioms in three-agent settings.

Efficiency and strategy-proofness together lead to ordinality.

The results justify the common use of ordinal rules under certain conditions.

Abstract

In allocating objects via lotteries, it is common to consider ordinal rules that rely solely on how agents rank degenerate lotteries. While ordinality is often imposed due to cognitive or informational constraints, we provide another justification from an axiomatic perspective: for three-agent problems, the combination of efficiency, strategy-proofness, non-bossiness, and a weak form of continuity collectively implies ordinality.