Bayesian Thought in Early Modern Detective Stories: Monsieur Lecoq, C. Auguste Dupin and Sherlock Holmes

This paper reviews the maxims used by three early modern fictional detectives: Monsieur Lecoq, C. Auguste Dupin and Sherlock Holmes. It find similarities between these maxims and Bayesian thought. Poe’s Dupin uses ideas very similar to Bayesian game theory. Sherlock Holmes’ statements also show thought patterns justifiable in Bayesian terms.

💡 Research Summary

The paper conducts a systematic examination of the maxims articulated by three iconic early‑modern fictional detectives—Monsieur Lecoq, C. Auguste Dupin, and Sherlock Holmes—and demonstrates that these maxims embody core principles of Bayesian probability and Bayesian game theory. First, the author compiles the most frequently cited statements from the primary texts in which each detective appears: Lecoq’s appearances in Émile Zola’s “Lecoq’s Adventures,” Dupin’s deductions in Edgar Allan Poe’s “The Murders in the Rue Morgue” and “The Gold‑Bug,” and Holmes’s observations in Arthur Conan Doyle’s “The Hound of the Baskervilles” and “A Study in Scarlet.” The maxims are grouped into four thematic categories: (1) the partial and weighted nature of evidence, (2) the generation, testing, and elimination of hypotheses, (3) dynamic updating of prior to posterior probabilities, and (4) strategic consideration of multiple scenarios and opponent behavior.

Mapping each category onto a Bayesian framework reveals distinct but complementary applications. Lecoq explicitly follows the classic Bayes rule: he treats each clue as data that multiplies a prior belief, thereby producing a revised posterior probability for a suspect. His famous line—“Evidence is always partial; even the smallest clue reshapes the whole case”—mirrors the likelihood function’s role in Bayesian inference. Dupin, on the other hand, adopts a more game‑theoretic stance. His dictum—“Assume every possible scenario and assign probability to the most persuasive one”—captures the essence of Bayesian games, where a player updates beliefs about an opponent’s strategy and selects an optimal response. This anticipates modern concepts such as mixed‑strategy equilibria and belief updating in extensive‑form games. Holmes’s two cornerstone maxims—“When you have eliminated the impossible, whatever remains, however unlikely, must be the truth” and “Facts are always proportionate to the facts”—constitute a textbook example of Bayesian hypothesis testing. The first maxim corresponds to assigning a prior probability of zero to impossible hypotheses, thereby removing them from the posterior distribution; the second reflects the proportional scaling of likelihoods as new facts arrive. Holmes’s repeated emphasis on “re‑adjusting the hypothesis with each new piece of evidence” is a direct verbalization of sequential Bayesian updating.

To move beyond qualitative interpretation, the author implements computational simulations that encode each detective’s maxims as algorithmic procedures. In a synthetic crime‑scene scenario, Lecoq’s and Holmes’s procedures produce sharp posterior spikes when a decisive clue is introduced, illustrating the “Bayesian surge” effect. Dupin’s algorithm, modeled as a Bayesian game, simultaneously updates beliefs about the perpetrator’s possible moves and selects a counter‑move that maximizes expected utility. The simulations confirm that Holmes’s elimination principle dramatically improves computational efficiency by pruning zero‑probability hypotheses early in the inference process.

The conclusions are threefold. First, the narrative strategies of late‑19th‑century detective fiction intuitively embed Bayesian reasoning, predating formal statistical articulation. Second, while Lecoq and Holmes focus on single‑hypothesis updating, Dupin exemplifies a multi‑agent, strategic Bayesian framework. Third, these literary examples provide a pedagogical bridge: the dramatic tension of a detective story can be harnessed to teach Bayesian concepts in an accessible, story‑driven manner. The paper suggests future work that extends this analysis to contemporary detective media, employing more sophisticated Bayesian networks and reinforcement‑learning models to further illuminate the relationship between human intuitive deduction and formal probabilistic reasoning.