Buying%20and%20Selling%20Prices%20under%20Risk,%20Ambiguity%20and%20Conflict

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Buying and Selling Prices under Risk, Ambiguity
and Conflict
Michael Smithson The Australian National
University Paul D. Campbell Australian Bureau
of Statistics
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• We report an empirical study of buying and
  selling prices for three kinds of gambles
• Risky (with known probabilities),
• Ambiguous (with lower and upper probabilities),
  and
• Conflictive (with disagreeing probability
  assessments).
• We infer preferences among gambles from peoples
  buying and selling prices in two ways
• Valuation Using the raw prices, and
• Relative valuation Comparison of a price for an
  ambiguous or conflictive gamble with the price
  for a risky gamble having an equivalent expected
  utility.

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Preference ordering hypothesis For mid-range
probabilities, Ellsberg (1961) and many others
since have found that people tend to prefer risk
to ambiguity. Smithson (1999) and Cabantous
(2007) found that people prefer ambiguity to
conflict. Hypothesis 1 For mid-range
probabilities, both valuation and relative
valuation will be lowest for conflictive gambles,
second lowest for ambiguous gambles, and highest
for risky gambles.
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Correlated orientations hypothesis Several
researchers have investigated whether attitudes
towards risk and ambiguity are correlated. An
early study by Curley et al. (1986) found no
significant correlation, but later more nuanced
investigations by Lauiola and his colleagues did
find a positive correlation (2001, 2007).
Pushkarskaya et al. (2009) found no correlation
between orientations towards conflictive gambles
and orientations towards the other two kinds.
Hypothesis 2 Valuation and relative valuation
of risky and ambiguous gambles will be positively
correlated, but neither will be correlated with
valuation of conflictive gambles.
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Endowment effect hypothesis In a well-known
violation of subjective expected utility known as
the endowment effect, people tend to offer higher
selling than buying prices for risky gambles.
The standard betting interpretation of lower and
upper probabilities also stipulates a higher
selling than buying price for ambiguous gambles.
However, there appears to be no similar standard
interpretation for conflictive gambles. Hypothesi
s 3 For mid-range probabilities, the difference
between buying and selling prices will be higher
for ambiguous and conflictive gambles than for
risky gambles.
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• Method
• Experimental Design
• 88 volunteers randomly assigned to one of two
  conditions
• Vendor, asked for a minimum selling price for
  each gamble, or
• Purchaser, asked for a maximum buying price.
• Card Games (comparable to Ellsbergs 1961
  2-colour task)
• Risky gambles. Proportions of winning cards were
  .25, .4, .5, .6, and .75.
• Ambiguous gambles. Proportions were
  interval-valued .3, .7 , .15, .85, and 0,
  1.
• Conflictive gambles. Proportions were given by
  two equally credible sources .4, .6 , .3, .7
  , and .2, .8.

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Method Expected utilities for all ambiguous and
conflictive gambles were 0.510. The variance
of the probabilities associated with each
conflictive gamble was approximately equal to
the variance in a corresponding ambiguous
gamble. All of the valuations were analyzed with
a 2-level choice model (see poster). The model
was estimated via Bayesian MCMC.
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Valuation Results Hypothesis 1 receives only
partial support. The risky gambles are valued
more highly than the ambiguous and conflictive
gambles, but the ambiguous and conflictive
valuation means do not significantly
differ. Hypothesis 3 is well-supported. There are
greater differences between buying and selling
prices (i.e., the endowment effect) for the
ambiguous and conflictive gambles than for risky
gambles. The effect of variance in the
probabilities on valuation was negative for
valuation of conflictive gambles. However, this
effect did not emerge for ambiguous gambles.
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Relative Valuation Results Hypothesis 1 is
contradicted. The conflictive gambles are valued
more than the ambiguous gambles, relative to
EU-equivalent risky gambles. Hypothesis 2
receives partial support. There were no
discernible differences in the strength of
correlations between the different types of
gambles. Hypothesis 2 was further tested by
examining correlations between random-effects
parameter estimates in the choice model. These
results contradict Hypothesis 2.
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Conclusions Conflictive and ambiguous gambles
were valued less than expected-utility-equivalent
risky gambles, but relative valuation favoured
conflictive over ambiguous gambles. This latter
finding conflicts with Smithson (1999) and
Cabantous (2007) and is difficult to explain.
The endowment effect was decidedly stronger for
conflictive and ambiguous gambles than for risky
ones. However, the standard betting
interpretation of lower and upper probabilities
does not seem to explain this effect. The
endowment effect is enhanced equally for
ambiguous and conflictive gambles. Respondents
appear to devalue both types of gamble as if they
perceive a feature that makes both of them
inferior to gambles with known probabilities.
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• Four Suggestions for Future Research
• Include alternative response modes (forced choice
  versus direct comparison versus rating or
  pricing), to look for preference effects or even
  reversals.
• Systematically varying the monetary amounts and
  locations of probability centroids would enable
  separate estimation of probability weighting and
  subjective utility functions.
• Loss frames have yet to be studied.
• The effects of ambiguous versus conflicting
  utility assessments have yet to be investigated.

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Thanks!