# Wisdom of Crowds Through Myopic Self-Confidence Adaptation

arXiv: https://arxiv.org/abs/2506.18195 · HTML: https://mlsanity.com/paper/2506.18195/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 26 references that are in the map.
- First posted on arXiv 22 Jun 2025.

## Builds on (most cited first, 7 of 7)

- [Opinion Dynamics of Online Social Network Users: A Micro-Level Analysis](https://mlsanity.com/paper/2011.00864/) (2020)
- [Robustness of large-scale stochastic matrices to localized perturbations](https://mlsanity.com/paper/1309.0158/) (2013)
- [From local averaging to emergent global behaviors: the fundamental role of network interconnections](https://mlsanity.com/paper/1509.08572/) (2015)
- [Finite-time influence systems and the Wisdom of Crowd effect](https://mlsanity.com/paper/1902.03827/) (2019)
- [On a Centrality Maximization Game](https://mlsanity.com/paper/1911.06737/) (2019)
- [Reaching optimal distributed estimation through myopic self-confidence adaptation](https://mlsanity.com/paper/2207.01384/) (2022)
- [On a Network Centrality Maximization Game](https://mlsanity.com/paper/2211.03685/) (2022)

## Abstract (arXiv)

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.