BoundedRationality_TheAdaptiveToolbox.pdf

310 WulfAlters
utility function, prospect theory explains 50% of the reduction by the concavity
of the utility function, and the other 50% by rank-dependent devaluation of the
lottery.
Monetary equivalents of 105 binary lotteries [p, x; (IT—p),y] were investigated
with/? = 1%, 10%, 20%, 50%, 80%, 90%, 99%, andx = 10000, y = 5000,
1000, 500, 0, -500, -1000, -5000, -10,000, andy =-10,000, x = 5000, 1000,
500,0, -500, -1000, -5000. To explain the median of the observed evaluations,
the predictions of prospect theory (with the median parameters a = 0.88 and
Y = 0.61 reported by Tversky and Kahneman [1992]) were worse than those of
prominence theory, while both theories were about equally accurate when the
probability evaluation function of prospect theory was replaced by that of prominence
theory (see Albers 1998a).
Two Crucial Experiments
The following experiments test predictions that are uniquely devied from prominence
theory. They address the main point of the theory, namely that subjects
neglect the steps below the finest perceived full step. It is my intent to show that
subjects — although they generally perceive these steps — neglect them when
they are confronted with a task that creates a finest perceived full step cruder
than these steps.
Experiment 1 (new kind of preference reversal paradox): Consider the
lotteries A = [1/2,5000; 1/2,-1000] and£ = [l/2,1000;l/2,0].
1. Decide which of the two lotteries you would prefer.
2. Then determine the certainty equivalents of both lotteries.
Result: The majority of subjects prefer B to A, but evaluated higher than B.
How can this be explained? Under the comparison condition, both lotteries are
evaluated in a combined task. The finest perceived full step is two steps below
the maximum of the absolute values of all payoffs, i.e., two steps below 5000 or
1000. The values of the 50%-50% lotteries are obtained via the midpoints on the
utility scales. For lottery .4, the steps are-1000, 0, 1000, 2000, 5000. Since the
steps in the range of negative payoffs are counted twice, one obtains the mid
point after 2.5 of 5 steps, i.e., the certainty equivalent of ^4 is 500. For Lottery B,
we have the steps 0,1000. The certainty equivalent ofB is at the midpoint of this
step, i.e., 500 (by linear interpolation). Thus, the two lotteries have the same values,
and subjects may prefer B to A since it does not involve negative payoffs.
When both lotteries are evaluated separately, they are evaluated in separate
tasks, and the finest perceived full steps are determined separately. For Lottery
A, the finest perceived full step does not change, since it contains the maximum
absolute value of both lotteries. Its certainty equivalent is still 500. For Lottery
B, the maximum absolute payoff is 1000. This gives the finest perceived full step