Adding Risks: Samuelson's Fallacy of Large Numbers Revisited

Abstract

Samuelson called accepting a sequence of independent positive mean bets that are individually unacceptable a fallacy of large numbers, and subsequent researchers have extended Samuelson's condition on utility functions to assure that they would not allow this fallacy. By contrast, some behavioralists, arguing the merits of diversification, believe that it is simply wrong headed to refuse a long series of independent “good” bets out of a misguided faith in expected utility theory. Contrary to what one might infer from the literature, this paper shows that accepting sequences of good bets is both consistent with expected utility theory and quite usual.