How Numerical Cognition Explains Ambiguity Aversion

Abstract

Consumers generally prefer precise probabilities or outcomes over imprecise ranges with the same expected value, a bias known as ‘ambiguity aversion.’ We argue that two elementary principles of numerical cognition explain great heterogeneity in this bias, affecting consumer choices in many domains where options are characterized by varying levels of uncertainty (e.g., lotteries, discounts, investment products, vaccines, etc). The first principle, the ‘compression effect,’ stipulates that consumers’ mental number lines are increasingly compressed at greater number magnitudes. This alone suffices to predict ambiguity aversion as it causes a midpoint (e.g., $40) to be perceived as closer to the upper bound of a range (e.g., $60) compared to its lower bound (e.g., $20). Furthermore, as the compression effect distorts the mental number line especially at lower numbers, it follows that ambiguity aversion should decrease around greater numbers. The second principle, the ‘left-digit effect’ causes a range’s relative attractiveness to decrease (increase) disproportionately with every left-digit transition in its lower (upper) bound, thus increasing (decreasing) ambiguity aversion. Due to the overall compression effect, the impact of the left-digit effect increases at greater numbers. We present 34 experiments (N = 10634), to support the theory’s predictions and wide applicability.