Not obviously manipulable allotment rules

TL;DR

This paper introduces a class of allocation rules called 'simple' rules for single-peaked preferences that are efficient, not obviously manipulable, and fair, expanding the set of feasible rules under limited strategic reasoning.

Contribution

It characterizes a large family of simple, efficient, and NOM-compliant allocation rules for single-peaked preferences, and shows their maximal domain applicability.

Findings

Simple rules fully satiate agents with low peaks in excess demand economies.

In excess supply economies, simple rules are symmetric and assign allocations between equal division and peaks.

The maximal domain for these rules remains the single-plateaued preferences domain.

Abstract

In the problem of allocating a single non-disposable commodity among agents whose preferences are single-peaked, we study a weakening of strategy-proofness called not obvious manipulability (NOM). If agents are cognitively limited, then NOM is sufficient to describe their strategic behavior. We characterize a large family of own-peak-only rules that satisfy efficiency, NOM, and a minimal fairness condition. We call these rules "simple". In economies with excess demand, simple rules fully satiate agents whose peak amount is less than or equal to equal division and assign, to each remaining agent, an amount between equal division and his peak. In economies with excess supply, simple rules are defined symmetrically. These rules can be thought of as a two-step procedure that involves solving a claims problem. We also show that the single-plateaued domain is maximal for the characterizing properties of simple rules. Therefore, even though replacing strategy-proofness with NOM greatly expands the family of admissible rules, the maximal domain of preferences involved remains basically unaltered.