Multi-Apartment Rent Division: Fairness in Choosing Apartments and Assigning Rooms and Rents

Core Concepts

The authors introduce rearrangeable envy-freeness as a solution to the multi-apartment rent division problem, ensuring fairness in choosing apartments and assigning rooms and rents. They prove its existence, optimality, and polynomial-time computability.

Abstract

The paper addresses the challenge of fair rent division across multiple apartments by introducing rearrangeable envy-freeness. It extends traditional envy-freeness to consider consensus among roommates when selecting an apartment. The authors provide theoretical proofs, examples, and algorithms to support their claims.
Key points include:

Introduction of the multi-apartment rent division problem.
Generalization of envy-freeness to rearrangeable envy-freeness for fair assignment of rooms and rents.
Definition of universal envy-freeness and probabilistic analysis under random valuations.
Comparison with related work on fair division mechanisms.
Construction of trades to achieve consensus among roommates on apartment selection.
Formalization of rearrangeable envy-freeness properties like Pareto optimality and individual rationality.
Proof of existence for solutions satisfying rearrangeable envy-freeness in polynomial time optimization.
The study provides insights into fair decision-making processes among roommates when selecting apartments, offering practical implications for real-world scenarios involving shared living spaces.

Stats

A solution (A, P ∗, j∗) satisfies rearrangeable envy-freeness if it maximizes the minimum utility over all players subject to this fairness notion.
For any player i, Xi = Q({Aj(i)}m j=1) - P({Aj(i)}m j=1).
The linear program for finding optimal price matrices P and Q under rearrangeable envy-freeness constraints is provided in the content.

Quotes

"The gold standard for fairness in rent division is envy-freeness."
"A new fairness notion is needed for the multi-apartment rent division problem."
"Perseverance will likely lead to a fair outcome."

Key Insights Distilled From

Multi-Apartment Rent Division

by Ariel D. Pro... at arxiv.org 03-14-2024

https://arxiv.org/pdf/2403.08051.pdf

Deeper Inquiries

How can the concept of rearrangeable envy-freeness be applied beyond rent division scenarios

The concept of rearrangeable envy-freeness can be applied beyond rent division scenarios in various shared resource allocation contexts. For example, it can be utilized in the assignment of office spaces within a co-working environment where multiple teams or individuals have different preferences for location, amenities, or workspace layout. By ensuring that each party is content with their assigned space and has no desire to switch with others based on perceived advantages, rearrangeable envy-freeness can help optimize overall satisfaction and productivity in the workplace.

What are potential drawbacks or limitations of relying solely on universal envy-free solutions

Relying solely on universal envy-free solutions may have drawbacks or limitations due to its stringent requirements. One potential limitation is the possibility of non-existence of universal envy-free solutions in certain scenarios, as highlighted in the paper. This could lead to deadlock situations where parties are unable to reach a consensus due to conflicting preferences or values. Additionally, achieving universal envy-freeness may not always result in an equitable distribution of resources among all parties involved, potentially leading to dissatisfaction or resentment among some individuals.

How might the findings in this paper impact decision-making processes in other shared resource allocation contexts

The findings presented in this paper regarding rearrangeable envy-freeness could significantly impact decision-making processes in other shared resource allocation contexts by providing a framework for fair and efficient division. In settings such as project team assignments, room allocations at events or conferences, or even task distributions within collaborative projects, incorporating principles of rearrangeable envy-freeness can help ensure that all participants feel fairly treated and satisfied with their respective roles or allocations. This approach could enhance collaboration, reduce conflicts over resource distribution, and ultimately improve overall outcomes through more harmonious interactions among stakeholders.