The Barzilai paradox is a concept in mathematics which claims to show that utility theory is not the correct framework for measuring preference. It was proposed by Jonathan Barzilai.
Utility theory does not impose constraints on the values of preference scales for prizes, but the interpretation of the utility operation in terms of lotteries is required in the construction of these scales and this interpretation constrains the values of utility scales for lotteries. The theory permits lotteries that are prizes and this leads to a contradiction since an object may be both a prize, which is not constrained, and a lottery which is constrained. In other words, utility theory has one rule for assigning values to prizes and a different, conflicting, rule for assigning values to lotteries. Since a prize may be a lottery ticket, the conflicting rules are contradictory.
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