Skill reputation, prospect theory, and regret theory

When a risky decision involves both skill and chance, success or failure is a signal of the decision maker's skill. Adopting standard models from the career concerns literature, we show that a rational desire to avoid looking unskilled may help explain several anomalies associated with prospect theory, including probability weighting, loss aversion, and framing. Prospect theory's four-fold pattern of probability weighting predicts that decision makers favor long-shots, avoid near sure-things, buy insurance against unlikely losses, and take risky chances to win back large losses. We find that this pattern emerges because winning a gamble with a low probability of success is a strong signal of skill, while losing a gamble with a high probability of success is a strong signal of incompetence. Regarding loss aversion, a fear of looking inept provides an alternative explanation for the puzzle of why people are so risk averse for small gambles. Such behavior can arise because losing any gamble, even a friendly bet with little or no money at stake, reflects poorly on the decision maker's skill. Finally, we find that framing affects choices because different formulations of a question provide different information about how a decision maker's actions will be interpreted. While the theoretical predictions of skill signaling closely parallel those of prospect theory, they differ in some cases, allowing for tests between the theories. The theoretical predictions are also closely related to, but distinguishable from, those of regret theory.