Adding risks: Samuelson's fallacy of large numbers revisited

Samuelson called accepting a sequence of independent positive mean bets tha t are individually unacceptable a fallacy of large numbers, and subsequent researchers have extended Samuelson's condition on utility functions to ass ure that they would not allow this fallacy. By contrast, some behavioralist s, arguing the merits of diversification, believe that it is simply wrong h eaded 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 th e literature, this paper shows that accepting sequences of good bets is bot h consistent with expected utility theory and quite usual.