We show that continuous models of stimulus-driven attention can account for skewness-related puzzles in decision-making under risk. First,we delineate that these models provide awell-defined theory of choice under risk. We therefore prove that in continuous - in contrast to discrete - models of stimulus-driven attention each lottery has a unique certainty equivalent that is monotonic in probabilities (i.e., it monotonically increases if probability mass is shifted to more favorable outcomes). Second, we show that whether an agent seeks or avoids a specific risk depends on the skewness of the underlying probability distribution. Since unlikely, but outstanding payoffs attract attention, an agent exhibits a preference for right-skewed and an aversion toward left-skewed risks. While cumulative prospect theory can also account for such skewness preferences, it yields implausible predictions on their magnitude. We show that these extreme implications can be ruled out for continuous models of stimulus-driven attention.
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