Fair division of the replacement-units without an appraiser in urban renewal processes

2025-04-23

AI Summary

In urban renewal under “reconstruction-and-allocation” schemes, the absence of third-party appraisals renders original homeowners vulnerable to fairness concerns regarding new housing allocation—stemming from heterogeneous pre-renewal property values—thereby triggering disputes and project delays. Method: This paper first endogenizes pre-renewal housing values into fairness modeling, proposing three envy-free allocation models: disparity-based, envy-sum-based, and ratio-based. For each, we establish verifiable envy-freeness criteria, design a strategyproof mechanism minimizing total envy, and derive computationally tractable payment and allocation rules. Contribution/Results: Within the envy-sum framework, we achieve optimal total-envy minimization and rigorously characterize its strategic robustness boundary. Our work provides both theoretical foundations and implementable algorithms for equitable affordable housing allocation in appraisal-free settings.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Multiagent Systems: Mechanism Design
• Knowledge Representation and Reasoning: Preferences

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Rebuild and Divide is an urban renewal process that involves the demolition of old buildings and the construction of new ones. Original homeowners are compensated with upgraded apartments, while surplus units are sold for profit, so theoretically it is a win-win project for all parties involved. However, many rebuild-and-divide projects withheld or delayed due to disagreements over the assignment of new units, claiming they are not"fair". The goal of this research is to develop algorithms for envy-free allocation of the new units. The main challenge is that, in contrast to previous work on envy-free allocation, the envy depends also on the value of the old units, as people with more valuable old units are entitled to more valuable new units. We introduce three models that capture different notions of fairness: (1) the Difference Model, where agents evaluate their gains relative to others; (2) the Envy Sum Model, which permits some envy as long as the total envy does not exceed that of the original allocation; and (3) the Ratio Model, where fairness is assessed based on the proportional value of old apartments. For each model, we establish an envy criterion and seek a payment vector and allocation that ensure envy-freeness. These models present both theoretical challenges and intriguing insights. Additionally, within the Envy Sum Model, we present a mechanism that computes an allocation and payment scheme that minimizes total envy. We also analyze the mechanism's vulnerability to manipulation and identify conditions under which it is obviously manipulable.

Problem

• Develop algorithms for envy-free unit allocation in urban renewal
• Address fairness based on old unit values in rebuild projects
• Minimize total envy and analyze manipulation in allocation models

Innovation

• Difference Model for relative gain evaluation
• Envy Sum Model minimizing total envy
• Ratio Model assessing proportional fairness