[2102.02666] The Wisdom of the Crowd and Higher-Order Beliefs Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Economics > Theoretical Economics arXiv:2102.02666 (econ) [Submitted on 4 Feb 2021 ( v1 ), last revised 28 Apr 2026 (this version, v3)] Title: The Wisdom of the Crowd and Higher-Order Beliefs Authors: Yi-Chun Chen , Manuel Mueller-Frank , Mallesh M Pai View a PDF of the paper titled The Wisdom of the Crowd and Higher-Order Beliefs, by Yi-Chun Chen and 1 other authors View PDF HTML (experimental) Abstract: We propose a new simple procedure called Population-Mean-Based Aggregation (PMBA) that enables a principal to "aggregate" information about an unknown state of the world from agents without understanding the information structure among them. PMBA only requires agents to communicate their beliefs about the state, and some agents to communicate their expectations of the population average belief. In a large population, for any finite number of possible states, and under weak assumptions on the information structure, allowing individual agents' beliefs to be misspecified, we show that PMBA infers the true state (in probability or almost surely under the stated conditions). We show how PMBA can be reinterpreted as a linear regression procedure, and how it can be used to aggregate information from a finite number of agents, allowing us to reuse existing results on inference in linear models. We conduct a novel experiment to show that the real-world performance of our procedure exceeds that of existing methods. Subjects: Theoretical Economics (econ.TH) ; Computer Science and Game Theory (cs.GT) Cite as: arXiv:2102.02666 [econ.TH] (or arXiv:2102.02666v3 [econ.TH] for this version) https://doi.org/10.48550/arXiv.2102.02666 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Mallesh Pai [ view email ] [v1] Thu, 4 Feb 2021 15:05:18 UTC (70 KB) [v2] Thu, 11 Nov 2021 16:40:46 UTC (45 KB) [v3] Tue, 28 Apr 2026 12:07:23 UTC (1,377 KB) Full-text links: Access Paper: View a PDF of the paper titled The Wisdom of the Crowd and Higher-Order Beliefs, by Yi-Chun Chen and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: econ.TH < prev | next > new | recent | 2021-02 Change to browse by: cs cs.GT econ References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from