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In game theory, Bayesian regret is the average difference between the utility of a strategy and an ideal utility where desired outcomes are maximized.

The term Bayesian refers to Thomas Bayes (1702–1761), who proved a special case of what is now called Bayes' theorem, who provided the first mathematical treatment of a non-trivial problem of statistical data analysis using what is now known as Bayesian inference.


Social choice theoryEdit

In social choice theory, Bayesian regret is the average difference in social utility between the chosen candidate and the best candidate. It is only measurable if it is possible to know the voters' true numerical utility for each candidate – that is, in Monte Carlo simulations of virtual elections. The term Bayesian is somewhat a misnomer, really meaning only "average probabilistic"; there is no standard or objective way to create distributions of voters and candidates.[citation needed]

The Bayesian regret concept was recognized as useful (and used) for comparing single-winner voting systems by Bordley and Merrill, and it also was invented independently by R. J. Weber.[citation needed] Bordley attributed it (and the whole idea of the usefulness of "social" utility, that is, summed over all people in the population) to John Harsanyi in 1955.[citation needed]


This term has been used to compare a random buy-and-hold strategy to professional traders' records. This same concept has received numerous different names, as the New York Times notes:

"In 1957, for example, a statistician named James Hanna called his theorem Bayesian Regret. He had been preceded by David Blackwell, also a statistician, who called his theorem Controlled Random Walks. Other, later papers had titles like 'On Pseudo Games', 'How to Play an Unknown Game', 'Universal Coding' and 'Universal Portfolios'".[1]

See alsoEdit


  1. ^ Kolata, Gina (2006-02-05). "Pity the Scientist Who Discovers the Discovered". The New York Times. ISSN 0362-4331. Retrieved 2017-02-27.