COWLES FOUNDATION FOR RESEARCH IN
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COWLES FOUNDATION DISCUSSION PAPER NO. 1829 Optimism and Pessimism with Expected Utility David Dillenberger, Andrew Postlewaite, and Kareen Rozen October 2011 Savage (1954) provided a set of axioms on preferences over acts that
were equivalent to the existence of an expected utility representation. We show that in
addition to this representation, there is a continuum of other "expected
utility" representations in which for any act, the probability distribution over
states depends on the corresponding outcomes. We suggest that optimism and pessimism can
be captured by the stake-dependent probabilities in these alternative representations;
e.g., for a pessimist, the probability of every outcome except the worst is distorted down
from the Savage probability. Extending the DM's preferences to be defined on both
subjective acts and objective lotteries, we show how one may distinguish optimists from
pessimists and separate attitude towards uncertainty from curvature of the utility
function over monetary prizes. Keywords: Subjective expected utility, Optimism, Pessimism, Stake-dependent probability |
