# Balanced House Allocation

arXiv: https://arxiv.org/abs/2109.01992 · HTML: https://mlsanity.com/paper/2109.01992/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Sep 2021.

## Built on by (most cited first, 1 of 1)

- [Preference Reasoning under Indeterminacy in Large Language Models](https://mlsanity.com/paper/2608.18631/) (2026)

## Abstract (arXiv)

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.