### Abstract

We define a binary relation (qualitative uncertainty assessment) that describes the shared likelihood assessments of decision makers with diverse ambiguity attitudes. Ambiguity renders this binary relation incomplete. Our axioms yield a representation according to which A is more likely than B if and only if a capacity, called uncertainty measure, assigns a higher value to A than to B and a higher value to B-complement than to A-complement. Agents combine this uncertainty perception with their uncertainty attitude to form a complete ranking of bets. We provide a representation theorem for this extended model, show that its parameters are uniquely identified and characterize a new measure of comparative ambiguity aversion. For general acts, we modify Machina and Schmeidler's (1992) sophistication axiom to allow for ambiguity and analyze three nested extensions: first, we axiomatize a minimal extension which reduces to expected utility when there is no ambiguity; the second and third extensions show how non-expected utility theories can be accommodated in our framework.

Original language | English (US) |
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Article number | 105016 |

Journal | Journal of Economic Theory |

Volume | 188 |

DOIs | |

State | Published - Jul 2020 |

### All Science Journal Classification (ASJC) codes

- Economics and Econometrics

### Keywords

- Ambiguity
- Ambiguity measure
- Separation of ambiguity perception and ambiguity attitude