Bayesian beliefs with stochastic monotonicity: An extension of Machina and Schmeidler |
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| Authors: | Simon Grant Ben Polak |
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| Institution: | aDepartment of Economics, Baker Hall, Rice University, MS 22, PO Box 1892, Houston, TX 77251-1892, USA;bSchool of Economics, Faculty of Economics & Commerce, Australian National University, ACT 0200, Australia;cDepartment of Economics, Yale University, USA |
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| Abstract: | Machina and Schmeidler show that the probabilistic sophistication can be obtained in an Anscombe–Aumann setting without imposing expected utility by maintaining stochastic monotonicity and adding a new axiom loosely analogous to Savage's P4. This analogous axiom, however, is very strong. In this note, we obtain probabilistic sophistication using a weaker (and more natural) analog of Savage's P4. Stochastic monotonicity is sufficient to bridge the gap, where Anscombe and Aumman use independence twice, we use stochastic monotonicity twice. |
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| Keywords: | Subjective probability Stochastic monotonicity Independence Horse/roulette lotteries Anscombe– Aumann |
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