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Samuelson's Fallacy of Large Numbers With Decreasing Absolute Risk Aversion

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  • Whelan, Karl

Abstract

Samuelson (1963) conjectured that accepting multiple independent gambles you would reject on a stand-alone basis violated expected utility theory. Ross (1999) and others presented examples where expected utility maximizers would accept multiple gambles that would be rejected on a stand-alone basis once the number of gambles gets large enough. We show that a stronger result than Samuelson's conjecture applies for DARA preferences over wealth. Expected utility maximizers with DARA preferences have threshold levels of wealth such that those above the threshold will accept N positive expected value gambles while those below will not and these thresholds are increasing with N.

Suggested Citation

  • Whelan, Karl, 2024. "Samuelson's Fallacy of Large Numbers With Decreasing Absolute Risk Aversion," CEPR Discussion Papers 19319, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:19319
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    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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