### Abstract

Original language | English |
---|---|

Pages (from-to) | 83-116 |

Journal | Journal of Risk and Uncertainty |

Volume | 56 |

Issue number | 1 |

DOIs | |

Publication status | Published - Feb 2018 |

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### Keywords

- ambiguity
- reference dependence
- certainty independence
- prospect theory
- loss aversion

### Cite this

*Journal of Risk and Uncertainty*,

*56*(1), 83-116. https://doi.org/10.1007/s11166-018-9273-7

}

*Journal of Risk and Uncertainty*, vol. 56, no. 1, pp. 83-116. https://doi.org/10.1007/s11166-018-9273-7

**Making the Anscombe-Aumann approach to ambiguity suitable for descriptive applications.** / Trautmann, Stefan; Wakker, P.P.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - Making the Anscombe-Aumann approach to ambiguity suitable for descriptive applications

AU - Trautmann, Stefan

AU - Wakker, P.P.

PY - 2018/2

Y1 - 2018/2

N2 - The Anscombe-Aumann (AA) model, originally introduced to give a normative basis to expected utility, is nowadays mostly used for another purpose: to analyze deviations from expected utility due to ambiguity (unknown probabilities). The AA model makes two ancillary assumptions that do not refer to ambiguity: expected utility for risk and backward induction. These assumptions, even if normatively appropriate, fail descriptively. This paper relaxes these ancillary assumptions to avoid the descriptive violations, while maintaining AA’s convenient mixture operation. Thus, it becomes possible to test and apply all AA-based ambiguity theories descriptively while avoiding confounds due to violated ancillary assumptions. The resulting tests use only simple stimuli, avoiding noise due to complexity. We demonstrate the latter in a simple experiment where we find that three assumptions about ambiguity, commonly made in AA theories, are violated: reference independence, universal ambiguity aversion, and weak certainty independence. The second, theoretical, part of the paper accommodates the violations found for the first ambiguity theory in the AA model—Schmeidler’s CEU theory—by introducing and axiomatizing a reference dependent generalization. That is, we extend the AA ambiguity model to prospect theory.

AB - The Anscombe-Aumann (AA) model, originally introduced to give a normative basis to expected utility, is nowadays mostly used for another purpose: to analyze deviations from expected utility due to ambiguity (unknown probabilities). The AA model makes two ancillary assumptions that do not refer to ambiguity: expected utility for risk and backward induction. These assumptions, even if normatively appropriate, fail descriptively. This paper relaxes these ancillary assumptions to avoid the descriptive violations, while maintaining AA’s convenient mixture operation. Thus, it becomes possible to test and apply all AA-based ambiguity theories descriptively while avoiding confounds due to violated ancillary assumptions. The resulting tests use only simple stimuli, avoiding noise due to complexity. We demonstrate the latter in a simple experiment where we find that three assumptions about ambiguity, commonly made in AA theories, are violated: reference independence, universal ambiguity aversion, and weak certainty independence. The second, theoretical, part of the paper accommodates the violations found for the first ambiguity theory in the AA model—Schmeidler’s CEU theory—by introducing and axiomatizing a reference dependent generalization. That is, we extend the AA ambiguity model to prospect theory.

KW - ambiguity

KW - reference dependence

KW - certainty independence

KW - prospect theory

KW - loss aversion

U2 - 10.1007/s11166-018-9273-7

DO - 10.1007/s11166-018-9273-7

M3 - Article

VL - 56

SP - 83

EP - 116

JO - Journal of Risk and Uncertainty

JF - Journal of Risk and Uncertainty

SN - 0895-5645

IS - 1

ER -