4 hours ago
A 250-Year-Old Theorem Walks into a Courtroom
In their article, Tommy Andersson and Erik Angner examine how mathematics can help explain the reliability of jury decisions. They discuss research investigating whether increasing the number of jurors improves the probability of reaching a correct verdict. Although a recent study correctly calculated how majority accuracy changes with jury size, the authors point out that its central result had already been established in 1785 by the French mathematician and philosopher Marquis de Condorcet, through what is now known as Condorcet’s Jury Theorem.
The theorem states that when each juror independently has a probability greater than 50% of making the correct decision, the probability that the majority reaches the correct verdict increases as the jury grows. Conversely, if each juror is more likely to be wrong than right, adding more jurors makes the collective decision increasingly likely to be incorrect. The article connects this mathematical result to a much older philosophical debate between Plato, who was sceptical of collective decision-making, and Aristotle, who recognised that groups can benefit from combining the knowledge and judgement of their members.
The authors also explain how the development of probability theory, particularly the work of Jacob Bernoulli and his nephew Nicolaus Bernoulli, made it possible to analyse collective decisions mathematically rather than relying solely on philosophical arguments. The article illustrates the continuing relevance of classical mathematical results to modern research in law, political science and social choice. Its broader lesson is that mathematical knowledge can reveal when collective decisions are more reliable than individual judgements—but only when the underlying assumptions, especially the accuracy and independence of individual decisions, are satisfied.
Source: A 250-Year-Old Theorem Walks into a Courtroom.
In their article, Tommy Andersson and Erik Angner examine how mathematics can help explain the reliability of jury decisions. They discuss research investigating whether increasing the number of jurors improves the probability of reaching a correct verdict. Although a recent study correctly calculated how majority accuracy changes with jury size, the authors point out that its central result had already been established in 1785 by the French mathematician and philosopher Marquis de Condorcet, through what is now known as Condorcet’s Jury Theorem.
The theorem states that when each juror independently has a probability greater than 50% of making the correct decision, the probability that the majority reaches the correct verdict increases as the jury grows. Conversely, if each juror is more likely to be wrong than right, adding more jurors makes the collective decision increasingly likely to be incorrect. The article connects this mathematical result to a much older philosophical debate between Plato, who was sceptical of collective decision-making, and Aristotle, who recognised that groups can benefit from combining the knowledge and judgement of their members.
The authors also explain how the development of probability theory, particularly the work of Jacob Bernoulli and his nephew Nicolaus Bernoulli, made it possible to analyse collective decisions mathematically rather than relying solely on philosophical arguments. The article illustrates the continuing relevance of classical mathematical results to modern research in law, political science and social choice. Its broader lesson is that mathematical knowledge can reveal when collective decisions are more reliable than individual judgements—but only when the underlying assumptions, especially the accuracy and independence of individual decisions, are satisfied.
Source: A 250-Year-Old Theorem Walks into a Courtroom.
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