IMPRECISE PROBABILITIES AND THEIR APPLICATIONS

30 June - 2 July 1999

** Abstract **

We explore a generalization of Ellsberg's paradox (2-color scenario) to the Vague-Vague (V-V) case, in which neither of the probabilities (urns) is specified precisely, but one urn is always more precise than the other. One hundred and seven undergraduate students compared 63 pairs of urns involving positive outcomes. The paradox is as prevalent in the V-V case, as in the standard Precise-Vague (P-V) case. The paradox occurs more often when differences between ranges of vagueness are large and occurs less often with extreme midpoints. The urn with more vagueness was avoided for moderate to high expected probabilities and preferred for low expected probabilities in P-V cases, and the opposite pattern was found for the V-V cases. Models that capture adequately the relationships between the prevalence of vagueness avoidance and the lotteries' parameters (e.g. differences between the two ranges) were fitted for the P-V and V-V cases.

** Keywords. ** Vagueness, ambiguity, imprecise probabilities, Ellsberg's paradox.

The paper is available in the following formats and sites:

- Gzipped pdf file (Granada - Spain)
- pdf file (Granada - Spain)
- pdf file (Sau Paulo - Brasil)
- pdf file (Gent - Belgium)

Department of Psychology

University of Illinois

603 E. Daniel St.

Champaign IL, 61820

USA

** E-mail addresses: **

Karen M. Kramer | kkramer@uiuc.edu |

David V. Budescu | dbudescu@uiuc.edu |

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