The probability triangle (also called the Marschak-Machina triangle) allows for compact and intuitive depictions of risk preferences. Here, we develop an analogous tool for choice under uncertainty - the ambiguity triangle - and show that indifference curves in this triangle capture preferences for unknown probabilities. In particular, the ambiguity triangle allows us to examine whether subjects adhere to the generalized axiom of revealed preference (GARP) and satisfy a non-parametric test for constant ambiguity attitudes. We find that more than 95% of subjects adhere to GARP and that about 60% satisfy our test for a constant ambiguity attitude. Yet, among these 60% of subjects there is substantial preference heterogeneity. We characterize this heterogeneity with finite-mixture estimates of a one-parameter extension of Expected Utility Theory wherein 48% of subjects are ambiguity averse, 22% are ambiguity seeking, and 30% are close to ambiguity neutral. The ambiguity triangle also highlights how variable ambiguity attitudes arise mainly because indifference curves are 'fanning-in' across the triangle. This fanning-in property implies that aversion to ambiguity increases as the likelihood of receiving a good outcome increases. We capture this behavior with a simple parametric model that also allows for finite mixture characterizations of preference heterogeneity for these subjects. We show that for a substantial share of these subjects (43%) their fanning-in is so strong that, although they are initially ambiguity seeking, they become strongly ambiguity averse as the likelihood of receiving a good outcome increases.

Burghart, Daniel R; Epper, Thomas; Fehr, Ernst (2015). *The ambiguity triangle: uncovering fundamental patterns of behavior under uncertainty.* Working paper series / Department of Economics 196, University of Zurich.

## Abstract

The probability triangle (also called the Marschak-Machina triangle) allows for compact and intuitive depictions of risk preferences. Here, we develop an analogous tool for choice under uncertainty - the ambiguity triangle - and show that indifference curves in this triangle capture preferences for unknown probabilities. In particular, the ambiguity triangle allows us to examine whether subjects adhere to the generalized axiom of revealed preference (GARP) and satisfy a non-parametric test for constant ambiguity attitudes. We find that more than 95% of subjects adhere to GARP and that about 60% satisfy our test for a constant ambiguity attitude. Yet, among these 60% of subjects there is substantial preference heterogeneity. We characterize this heterogeneity with finite-mixture estimates of a one-parameter extension of Expected Utility Theory wherein 48% of subjects are ambiguity averse, 22% are ambiguity seeking, and 30% are close to ambiguity neutral. The ambiguity triangle also highlights how variable ambiguity attitudes arise mainly because indifference curves are 'fanning-in' across the triangle. This fanning-in property implies that aversion to ambiguity increases as the likelihood of receiving a good outcome increases. We capture this behavior with a simple parametric model that also allows for finite mixture characterizations of preference heterogeneity for these subjects. We show that for a substantial share of these subjects (43%) their fanning-in is so strong that, although they are initially ambiguity seeking, they become strongly ambiguity averse as the likelihood of receiving a good outcome increases.

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## Additional indexing

Item Type: | Working Paper |
---|---|

Communities & Collections: | 03 Faculty of Economics > Department of Economics
Working Paper Series > Department of Economics |

Dewey Decimal Classification: | 330 Economics |

JEL Classification: | D81, C91 |

Uncontrolled Keywords: | Behavior under uncertainty, ambiguity preferences, heterogeneity, probability triangle, ambiguity triangle |

Language: | English |

Date: | June 2015 |

Deposited On: | 01 Jul 2015 10:15 |

Last Modified: | 05 Apr 2016 19:18 |

Series Name: | Working paper series / Department of Economics |

Number of Pages: | 59 |

ISSN: | 1664-7041 |

Official URL: | http://www.econ.uzh.ch/static/wp/econwp196.pdf |

Related URLs: | http://www.econ.uzh.ch/static/workingpapers.php |

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