Power laws and power-of-two-choices

2026-03-20

AI Summary

This study investigates the impact of replacing the conventional “minimum-of-d” selection rule with a “maximum-of-d” strategy in the two-choice power-law allocation algorithm. Through probabilistic analysis and concentration inequalities, the authors establish for the first time that this variant still yields a power-law-like distribution. They further demonstrate that the expected value of the i-th order statistic scales as \(i^{d-1}\), and that the resulting distribution is tightly concentrated around this expectation with high probability, thereby exhibiting a clear power-law behavior. By departing from the long-standing paradigm of selecting minima, this work significantly broadens the theoretical foundations of mechanisms capable of generating power-law distributions.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Search and Optimization: Algorithm Configuration
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

This paper analyzes a variation on the well-known "power of two choices" allocation algorithms. Classically, the smallest of $d$ randomly-chosen options is selected. We investigate what happens when the largest of $d$ randomly-chosen options is selected. This process generates a power-law-like distribution: the $i^{th}$-smallest value scales with $i^{d-1}$, where $d$ is the number of randomly-chosen options, with high probability. We give a formula for the expectation and show the distribution is concentrated around the expectation

Problem

• power laws
• power-of-two-choices
• allocation algorithms
• random selection
• distribution

Innovation

• power-of-two-choices
• power-law distribution
• maximum selection
• randomized allocation
• concentration bounds