Collective Intelligence: Why groups get smart, strange and stuck

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A French aristocrat proved that majorities converge on the truth. The proof needs one condition, and he spent his life building the very things that destroy it.

In this episode

• The jury theorem built from scratch, on three people, with no equations
• Why 101 jurors reach 98 per cent while a referendum reaches nothing at all
• What thirty per cent correlation does to a crowd of a hundred
• The theorem running in reverse — below fifty per cent competence, large groups become reliably wrong
• Krishna Ladha's repair: correlation as a budget rather than a veto
• Franz Dietrich's objection, which is that the premises are never justified at the same time
• Why the theorem's best case looks like Galton's queue in Plymouth and nothing like an election

Sources

The paper

• Condorcet, marquis de (1785). Essai sur l'application de l'analyse à la probabilité des décisions rendues à la pluralité des voix. Paris: Imprimerie Royale. https://archive.org/stream/bub_gb_RzAVAAAAQAAJ/bub_gb_RzAVAAAAQAAJ_djvu.txt

The modern reading, and the objections

• Paulson, L. (2023). A brief history of collective intelligence, democracy, and governance. In Boucher, Hallin & Paulson (eds.), The Routledge Handbook of Collective Intelligence for Democracy and Governance. Routledge.
• Ladha, K. K. (1992). The Condorcet jury theorem, free speech, and correlated votes. American Journal of Political Science 36(3), 617–634.
• Dietrich, F. (2008). The premises of Condorcet's jury theorem are not simultaneously justified. Episteme. https://www.cambridge.org/core/journals/episteme/article/abs/premises-of-condorcets-jury-theorem-are-not-simultaneously-justified/066FBBE781B9E25B2F8A2D3075121C6D

Condorcet himself

• Condorcet (1781, as 'Joachim Schwartz'). Réflexions sur l'esclavage des nègres. https://classiques.uqam.ca/classiques/condorcet/reflexions_esclavage_negres/reflexions_esclavage_negres.html
• Condorcet (1790). Sur l'admission des femmes au droit de cité. https://blog.univ-angers.fr/dictionnairefeministes/2017/01/30/condorcet-jean-antoine-nicolas-caritat-marquis-de/
• Encyclopaedia Britannica, Marquis de Condorcet. https://www.britannica.com/biography/Marie-Jean-Antoine-Nicolas-de-Caritat-marquis-de-Condorcet

Credits

Written and presented by Niccolò Pescetelli. A PSi production. Sources for every episode are in the show notes.

Got something to say to this podcast? Send a voicemail, and you might hear yourself on the next episode!

A crowd guessed the weight of an ox and got it almost exactly right. The man who collected the guesses did not think much of crowds, and the condition he wrote down has been dropped from the story ever since.

In this episode

• Why the famous result is arithmetic rather than wisdom, and why 787 thermometers would do the same job
• The word Galton actually used — mediocrity — and where it came from
• What a correlation of one per cent between people's errors does to a crowd of 787 (it leaves about 89)
• The statistician who challenged Galton in print weeks later, and the number Galton gave in reply
• Pooled radiologists reading mammograms: what happens when you combine judgements from people who never met
• Why a hundred thousand people agreeing is often one piece of evidence, repeated

Sources

The paper

• Galton, F. (1907). Vox populi. Nature 75, 450–451. https://www.nature.com/articles/075450a0

The argument that followed, weeks later in the same journal

• Hooker, R. H. (1907). Mean or median. Nature 75, 487–488.
• Galton, F. (1907). The ballot-box. Nature 75, 509–510. https://www.nature.com/articles/075509f0
• Wallis, K. F. (2014). Revisiting Francis Galton's forecasting competition. Statistical Science 29(3). https://arxiv.org/pdf/1410.3989

Galton himself

• Galton, F. (1886). Regression towards mediocrity in hereditary stature. Journal of the Anthropological Institute 15, 246–263. https://galton.org/bib/JournalItem.aspx_action=view_id=157
• Galton's anthropometric laboratory, International Health Exhibition, South Kensington, 1884. https://wellcomecollection.org/works/deej6y5g
• Clayton, A. (2021). Bernoulli's Fallacy: Statistical Illogic and the Crisis of Modern Science. Columbia University Press. https://cup.columbia.edu/book/bernoullis-fallacy/9780231199957/
• Coyne, J. (2022). The ideologues: why we can't use statistics any more. Why Evolution Is True, 27 November. https://whyevolutionistrue.com/2022/11/27/the-ideologues-why-we-cant-use-statistics-any-more/

The modern test

• Kurvers, R. H. J. M., et al. (2016). Boosting medical diagnostics by pooling independent judgments. PNAS 113(31), 8777–8782. https://pmc.ncbi.nlm.nih.gov/articles/PMC4978286/

Mentioned

• Wisdom of the Crowd (2026), BBC One, created by Dean Nabarro and Andy Auerbach, hosted by John Bishop.

Credits

Written and presented by Niccolò Pescetelli. A PSi production. Sources for every episode are in the show notes.