# Weighted Envy-Freeness in House Allocation

Source: [Weighted Envy-Freeness in House Allocation](<https://www.sota2.com/research/paper/68fa74921e209131cea6294c>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-26T03:13:35.838Z

Authors: Sijia Dai, Yankai Chen, Xiaowei Wu, Yicheng Xu, Yong Zhang

Published: 2024-08-22T16:26:47.000Z

## Abstract

The classic house allocation problem involves assigning $m$ houses to $n$ agents based on their utility functions, ensuring each agent receives exactly one house. A key criterion in these problems is satisfying fairness constraints such as envy-freeness. We extend this problem by considering agents with arbitrary weights, focusing on the concept of weighted envy-freeness, which has been extensively studied in fair division. We present a polynomial-time algorithm to determine whether weighted envy-free allocations exist and, if so, to compute one. Since weighted envy-free allocations do not always exist, we also investigate the potential of achieving such allocations through the use of subsidies. We provide several characterizations for weighted envy-freeable allocations (allocations that can be turned weighted envy-free by introducing subsidies) and show that they do not always exist, which is different from the unweighted setting. Furthermore, we explore the existence of weighted envy-freeable allocations in specific scenarios and outline the conditions under which they exist.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Envy-Free House Allocation on House Allocation 0/1 preferences](<https://www.sota2.com/research/sota/envy-free-house-allocation-on-house-allocation-0-1-preferences.md>): Envy-Free House Allocation; House Allocation 0/1 preferences; Sum Score: not recorded.

- [Envy-Free House Allocation on House Allocation Identical preferences](<https://www.sota2.com/research/sota/envy-free-house-allocation-on-house-allocation-identical-preferences.md>): Envy-Free House Allocation; House Allocation Identical preferences; Sum: not recorded.

- [Envy-Free House Allocation on House Allocation Additive Monotonic preferences](<https://www.sota2.com/research/sota/envy-free-house-allocation-on-house-allocation-additive-monotonic-preferences.md>): Envy-Free House Allocation; House Allocation Additive Monotonic preferences; Sum Utility: not recorded.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2408.12523>)

[PDF](<https://arxiv.org/pdf/2408.12523.pdf>)