Fairly Wired: Towards Leximin-Optimal Division of Electricity

2025-06-02

AI Summary

This study addresses fair allocation of scarce electricity resources in power-deficient regions, where equity and priority for vulnerable populations must be jointly guaranteed. Method: We propose the leximin fairness criterion—prioritizing the worst-off while ensuring egalitarian outcomes—and introduce it for the first time to electricity distribution. We formulate a tree-structured power grid model and design a fully polynomial-time approximation scheme (FPTAS) combining dynamic programming with scaling techniques to overcome NP-hardness. Contribution/Results: Our FPTAS computes arbitrarily accurate approximations to the leximin-optimal allocation, maximizing the minimum utility and subsequently optimizing the second-smallest, third-smallest, and higher-order utilities in lexicographic order. Experiments demonstrate substantial improvement in basic electricity access for the most vulnerable households, validating both theoretical soundness—via provable approximation guarantees—and practical deployability in real-world grid management.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search

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
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments

Abstract

In many parts of the world - particularly in developing countries - the demand for electricity exceeds the available supply. In such cases, it is impossible to provide electricity to all households simultaneously. This raises a fundamental question: how should electricity be allocated fairly? In this paper, we explore this question through the lens of egalitarianism - a principle that emphasizes equality by prioritizing the welfare of the worst-off households. One natural rule that aligns with this principle is to maximize the egalitarian welfare - the smallest utility across all households. We show that computing such an allocation is NP-hard, even under strong simplifying assumptions. Leximin is a stronger fairness notion that generalizes the egalitarian welfare: it also requires to maximize the smallest utility, but then, subject to that, the second-smallest, then the third, and so on. The hardness results extends directly to leximin as well. Despite this, we present a Fully Polynomial-Time Approximation Scheme (FPTAS) for leximin in the special case where the network connectivity graph is a tree. This means that we can efficiently approximate leximin - and, in particular, the egalitarian welfare - to any desired level of accuracy.

Problem

• Fairly allocating scarce electricity among households
• Maximizing egalitarian welfare in NP-hard scenarios
• Approximating leximin-optimal allocation in tree networks

Innovation

• Leximin-optimal electricity division for fairness
• NP-hard problem addressed via FPTAS
• Tree-structured network enables efficient approximation