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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.
References
Barzilai, J.; "Game
Theory Foundational Errors - Part I," Technical Report, Dept. of
Industrial Engineering, Dalhousie University, pp. 1-2, 2007.
[554]
Barzilai, J.; "Preference
Modeling in Engineering Design," in Decision Making in Engineering
Design, K.E. Lewis, W. Chen and L.C. Schmidt (Eds.), ASME Press
ISBN 0791802469, pp. 43-47, 2006.
Barzilai, J.; "On the
Mathematical Modelling of Measurement,", pp. 1-4, 2006. [555]
Barzilai, J.; "Measurement and
Preference Function Modelling," International Transactions in
Operational Research, Vol. 12, pp. 173-183, 2005.
Barzilai, J.;
“Notes on Utility Theory,” Proceedings of the IEEE International
Conference on Systems, Man, and Cybernetics, pp. 1000—1005,
2004.
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