Wisdom of Crowds Through Myopic Self-Confidence Adaptation

2025-06-22

AI Summary

This paper investigates how agents in non-Bayesian social learning improve collective estimation accuracy by adaptively adjusting trust weights. Focusing on the French–DeGroot dynamics—where agents iteratively aggregate noisy private signals—the asymptotic estimation variance is shown to depend on the global weight matrix. The problem of designing optimal weights is formulated as a multi-objective game. The authors propose a novel distributed, self-interested weight adaptation mechanism, rigorously characterizing the relationship between the Pareto frontier and Nash equilibria. They prove that asynchronous best-response dynamics converge to a unique strict Nash equilibrium. Crucially, even when each agent solely minimizes its own estimation variance, the system self-organizes into a consensus structure that globally minimizes aggregate estimation variance. This reveals sufficient conditions for emergent, robust collective intelligence in distributed learning settings.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Adversarial Learning
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: Social networks and social learning
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

The wisdom of crowds is an umbrella term for phenomena suggesting that the collective judgment or decision of a large group can be more accurate than the individual judgments or decisions of the group members. A well-known example illustrating this concept is the competition at a country fair described by Galton, where the median value of the individual guesses about the weight of an ox resulted in an astonishingly accurate estimate of the actual weight. This phenomenon resembles classical results in probability theory and relies on independent decision-making. The accuracy of the group's final decision can be significantly reduced if the final agents' opinions are driven by a few influential agents. In this paper, we consider a group of agents who initially possess uncorrelated and unbiased noisy measurements of a common state of the world. Assume these agents iteratively update their estimates according to a simple non-Bayesian learning rule, commonly known in mathematical sociology as the French-DeGroot dynamics or iterative opinion pooling. As a result of this iterative distributed averaging process, each agent arrives at an asymptotic estimate of the state of the world, with the variance of this estimate determined by the matrix of weights the agents assign to each other. Every agent aims at minimizing the variance of her asymptotic estimate of the state of the world; however, such variance is also influenced by the weights allocated by other agents. To achieve the best possible estimate, the agents must then solve a game-theoretic, multi-objective optimization problem defined by the available sets of influence weights. We characterize both the Pareto frontier and the set of Nash equilibria in the resulting game. Additionally, we examine asynchronous best-response dynamics for the group of agents and prove their convergence to the set of strict Nash equilibria.

Problem

• How agents minimize variance in collective estimates through adaptation.
• Analyzing game-theoretic optimization in iterative opinion pooling dynamics.
• Characterizing Pareto frontier and Nash equilibria in influence weights.

Innovation

• Non-Bayesian learning rule for opinion updates
• Game-theoretic multi-objective optimization approach
• Asynchronous best-response dynamics convergence