🔗 St. Petersburg paradox

🔗 Economics 🔗 Statistics

The St. Petersburg paradox or St. Petersburg lottery is a paradox related to probability and decision theory in economics. It is based on a particular (theoretical) lottery game that leads to a random variable with infinite expected value (i.e., infinite expected payoff) but nevertheless seems to be worth only a very small amount to the participants. The St. Petersburg paradox is a situation where a naive decision criterion which takes only the expected value into account predicts a course of action that presumably no actual person would be willing to take. Several resolutions are possible.

The paradox takes its name from its resolution by Daniel Bernoulli, one-time resident of the eponymous Russian city, who published his arguments in the Commentaries of the Imperial Academy of Science of Saint Petersburg (Bernoulli 1738). However, the problem was invented by Daniel's cousin, Nicolas Bernoulli, who first stated it in a letter to Pierre Raymond de Montmort on September 9, 1713 (de Montmort 1713).