How Voltaire Used Probability Theory to Support His Philosophy Career

My last post talked about Voltaire’s comment “the perfect is the enemy of the good” as applied to statistics. Voltaire was a prolific author, whose complete works comprise 205 volumes. In the 18th century, however, there were no NSF and NEA grants to support philosophers and writers. How was Voltaire able to spend his time on philosophical inquiries?*

He won the lottery—repeatedly. Voltaire had the good fortune to attend a dinner party with the young mathematician Charles Marie de la Condamine. Together, they set up a scheme to take advantage of a flaw in a lottery that had been set up by the French government.

The French treasury badly needed money in the 1720s after the wars and high spending under Louis XIV and speculative frenzies such as the Mississippi Bubble. Upon becoming Louis XV’s prime minister in 1726, Cardinal Fleury set about trying to reform the financial system and reduce government debt.

Lotteries had long been popular ways of raising money in France. Bonds that had been issued by the municipality of Paris had lost much of their value because of citizens’ lack of faith in the financial system. So the comptroller of finances, Michel Robert Le Peletier des Forts, announced on March 6, 1729 that the Paris bonds would be redeemed by lottery. Bondholders could purchase a lottery ticket at a price equal to 1/1,000 of the value of the bond that they held. Thus, a holder of a bond valued at 10,000 livres could purchase a lottery ticket for 10 livres; a holder of a bond valued at 1,000 livres could purchase a lottery ticket for 1 livre. If the ticket was drawn in the lottery, the ticket holder would receive 85% of the value of his bond. In addition, winners would share in an additional 500,000 livres that the French government added to sweeten the pot.

La Condamine, analyzing the lottery, quickly discovered a way to exploit the flaw. Each ticket, regardless of the value of the bond, had the same chance of being drawn as a winner. That meant that someone buying a lottery ticket for 1 livre had the same chance of winning, and thus benefiting from the additional 500,000 livres in the pot, as someone buying a lottery ticket for 10 or 100 or 1,000 livres.

Voltaire, La Condamine, and others set up a syndicate to buy up as many inexpensive bonds as possible and enter the lottery with them. Pearson (2016) reported that the same set of names recurred among the winning bondholders in drawing after drawing. Soon the authorities realized what was going on and closed the lottery. The comptroller, Le Peletier des Forts, argued that the lottery exploiters had acted illegally, but the royal council found that no laws had been broken—just that the lottery had been badly designed. Le Peletier des Forts was fired, and “condemned for his foolish ignorance of statistics” (Pearson, 2005, p. 87).

Voltaire is thought to have won about 500,000 livres from this scheme, making him a wealthy man who now had the financial means to write about any subject he wanted.

Here’s a question for students: How would one design a lottery where tickets are sold for 1/1,000 of the bond values but that gives a fair payout?

Copyright (c) 2023 Sharon L. Lohr

Footnotes and References

*Voltaire’s official father, a lawyer who held the position of receveur des épices in the Chambre des Comptes, was quite wealthy from the generous commissions he received on spice trade taxes. But his will specified that Voltaire, who had up to that point shown no signs of fiscal responsibility and had spent time in the Bastille, would receive only the interest on his share of the estate. The will did specify that if Voltaire could receive the capital at age 35 if he could produce evidence of ‘regular conduct’ to the senior magistrate in the Cours des Comptes. In March 1730, after Voltaire had already become wealthy through the lottery, the senior magistrate decided his conduct was sufficiently regular to merit his share of the paternal estate.

Eschner, K. (2017). Voltaire: Enlightenment philosopher and lottery scammer. Smithsonian magazine.

Pearson, R. (2005). Voltaire Almighty: A Life in Pursuit of Freedom. New York: Bloomsbury.

Pearson, R. (2016). Voltaire’s luck. Lapham’s Quarterly, 9(3).