A working paper by UMich grad student Jason Kerwin considers how “fatalistic” thinking can lead even rational individuals to increase risky behavior when they learn that risks are higher than they thought. It sounds crazy, but the investigation is motivated by some interesting empirical patterns, including the fact that in a recent survey in Malawi, overestimation of HIV risks from unprotected sex was associated with higher rates of engagement in unprotected sex. How can this be? Kern crystalizes the logic as follows. Suppose that you tell a potential risk taker that the true risk of contracting HIV is higher than they thought. Well,
a change in the per-act risk affects not only the marginal cost of the acts the agent is deciding over, but also a stock of previously-chosen acts over which one no longer has any control. If an agent’s perceived per-sex-act risk of contracting HIV rises, this has a direct effect of increasing the marginal cost (in expected utility) of having more risky sex. But it also increases the probability that the agent already has HIV, which decreases the marginal cost of more risky sex. When the second effect dominates, increases in perceived risks will lead to more risk-taking rather than less.
Kerwin develops the logic formally by modeling perceived risk of HIV infection in terms of a cumulative distribution function that incorporates not only the next act in question, but all past acts. Such CDFs typically have inflection points and become concave in their upper reaches. So, an upward shock to someone’s belief about where they stand currently can result in a diminishment in the relative magnitude of added risk relative to any benefits whose value is unaffected by the belief shock. When this occurs, the effect of increasing perceived risk is to increase the attractiveness of the risky behavior.
Paper here: link