Balanced House Allocation

TL;DR

This paper introduces a fairness criterion called balancedness in house allocation, showing that, except for three agents, Top Trading Cycles is uniquely balanced, efficient, and strategy-proof.

Contribution

It formalizes the balancedness axiom and characterizes the Top Trading Cycles mechanism as the unique solution under this criterion for most cases.

Findings

Top Trading Cycles is the only balanced, efficient, and group strategy-proof mechanism for most cases.

Balancedness ensures equal treatment of agents at the mechanism's announcement stage.

The exception occurs in the three-agent case, where other mechanisms may exist.

Abstract

We introduce balancedness a fairness axiom in house allocation problems. It requires a mechanism to assign the top choice, the second top choice, and so on, on the same number of profiles for each agent. This axiom guarantees equal treatment of all agents at the stage in which the mechanism is announced when all preference profiles are equally likely. We show that, with an interesting exception for the three-agent case, Top Trading Cycles from individual endowments is the only mechanism that is balanced, efficient, and group strategy-proof.