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FIRST INTERNATIONAL
SYMPOSIUM ON

IMPRECISE PROBABILITIES AND THEIR APPLICATIONS

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Ghent, Belgium

30 June - 2 July 1999

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** ELECTRONIC PROCEEDINGS **

## Karen M. Kramer and David V. Budescu

# Modeling Ellsberg's Paradox in Vague-Vague Cases

** 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:

** Authors addresses: **

Department of Psychology

University of Illinois

603 E. Daniel St.

Champaign IL, 61820

USA

** E-mail addresses: **

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