Title:

An empirical evaluation of Prelec's compound invariant functions as models of probability weighting in prospect theory

Prospect theory, which proposes both referencedependent utilityand probability
weighting, has proved to be the most successful ofseveral approaches to
generalising nonnative expected utility theory. It has been widely adopted in the
social sciences to explain risk behaviour, with applications ranging from
infrahuman, preindustrial, financial, corporate and political decisionmaking.
This wide, and growing, range of applications demands effective econometric
analysis ofthe prospect theoretical framework.
A major advance has been Prelec's approach using a weak consistency condition
known as compound invariance (Cn as an axiomatic basis for developing
exponential functions that describe probability weighting. Combined .with a
standardly adopted constant relative risk aversion (CRRA) utility function this
leads to a CI+CRRA model.
Prelec proposl?s two versions ofthis model, one in which probability weighting is
described by two (a probability sensitivity and a probability attractiveness)
parameter and a oneparameter version in which the probability attractiveness
parameter is axiomatically eliminated. One mathematical convenience ofthis
version ofthe model is that it may be linearised via a double log transfonnation to
provide risk decision descriptive parameters from the plot's intercept ~d gradient
of certainty equivalence ~aluations.
The research uses standard laboratory gambles (under  , varied incentive and
problem presentation conditions) as the basis oftesting this model and the
predictions ofprospect theory relating to risk attitude, pattern ofprobability
weighting, gainloss risk attitude reflection, fourfold inversion ofrisk attitude,
loss aversion and framing effects.
The research, involving over 12,000 individual prospect valuations generally finds
strongly for prospect theory predictions. However, the twoparameter version of the CI+CRRA model performs far better as a predictor ofsubjects' prospect
valuation than the oneparameter version. This is largely due to the increasing
subadditivity ofvaluation as outcome value increases. Consequently the results
draw into question the multiplicative assumption in prospect theory that outcome
value and probability weighting are psychometrically independent. The
dissertation concludes with considerations on how the model might be developed
and applied to ecological risk decisionmaking studies in the future.
