Overconfident people are more exposed to “black swan” events: a case study of avalanche risk

Abstract

Overconfidence is a well-established bias in which someone’s subjective confidence in their own judgment is systematically greater than their objective accuracy. There is abundant anecdotal evidence that overconfident people increase their exposure to risk. In this paper, we test whether overconfident backcountry skiers underestimate the probability of incurring a snow avalanche accident. An avalanche accident is a typical “black swan” event as defined by Taleb (The black swan: the impact of the highly improbable, Random House, New York, 2007) because it has a very low probability of occurring but with potentially dramatic consequences. To consider black swan events when studying overconfidence is particularly important, in light of previous findings on the role of overconfidence when feedbacks on tasks previously performed are inconclusive and infrequent. We run our test by measuring individual overconfidence using standard tools from the literature and then use a random effect logit model to measure its effect on the probability to take the ski route. We show that (1) overconfidence is widespread in our sample; (2) practitioners who are more prone to overestimate their knowledge are also more likely to take risks associated with a ski trip under the threat of avalanche danger, a result robust to a set of specification tests we perform. This suggests that overconfident people are more exposed to black swan events, by taking a risky decision that can bring about fatal consequences.

Appendix A

Here, we consider the case in which the explanatory variable affected by measurement errors—the overconfidence score in our case—is included in the regression together with other explanatory variables. The regression coefficient $\beta_{a}$ in Eq. (4) is the marginal effect of a unit variation of the true overconfidence level $a_{i}$ on $\alpha_{i}$, the largest level of risk the ith respondent is available to take (and, by that way, the probability of undertaking the route) holding the other explanatory variables constant. By holding the other explanatory variables constant, the variance of the overconfidence score relevant to Eq. (10) falls to $\sigma_{a}^{2} \left( {1 - R_{a}^{2} } \right)$, where $R_{a}^{2}$ is the proportion of the variance of the true overconfidence score explained by the regression on the other explanatory variables included in Eq. (4).

Clearly, $R_{a}^{2}$ cannot be directly measured since the regression of the true overconfidence on the other explanatory variable is not feasible. The feasible regression is the one of $z_{i.}$—the observable overconfidence score—on the other explanatory variables. Let $R_{z}^{2}$ be the fraction of the variance of $z_{i.}$ explained by this regression. Then, the following identity holds:

$$ \left( {A1} \right) R_{z}^{2} = \frac{{\sigma_{a}^{2} R_{a}^{2} }}{{\sigma_{a}^{2} + \sigma_{v.}^{2} }} , $$

from which we recover:

$$ \left( {A2} \right) R_{a}^{2} = \frac{{R_{z}^{2} \left( {\sigma_{a}^{2} + \sigma_{v.}^{2} } \right)}}{{\sigma_{a}^{2} }} $$

This way we recover the multiplicative attenuation bias as:

$$ \left( {A3} \right) \left[ {\frac{{\sigma_{a}^{2} \left( {1 - R_{a}^{2} } \right)}}{{\sigma_{a}^{2} \left( {1 - R_{a}^{2} } \right) + \sigma_{v.}^{2} }}} \right]^{0.5} $$

In the case of the regression of the observable overconfidence score $z_{i.}$ on the other explanatory variables, results are those in Table 5. The $R^{2}$ of this regression is as large as 0.086, definitely a very low value. But this is driven by the large variance of the measurement error on the overconfidence score. By taking it into account as in $\left( {A2} \right)$, the $R^{2}$ of the regression of the true overconfidence on the other explanatory variables turns out as large as:

Table 5 OLS regression of the overconfidence score on the individual characteristics included as control variables in the random effect logit regression

$$ R_{a}^{2} = \frac{{0.086 \left( {25.03 + 70.06} \right)}}{25.03} = 0.33 $$

Finally, the attenuation bias resulting from $\left( {A3} \right)$ turns out as large as:

$$ \left[ {\frac{{25.03\left( {1 - 0.33} \right)}}{{25.03\left( {1 - 0.33} \right) + 70.06}}} \right]^{0.5} = 0.4395 , $$

just marginally lower than the one previously found (0.51 in (16)). As a result, the bias-corrected estimate for the effect of one standard variation of the true overconfidence is 0.1516, just slightly higher than 0.1308, the estimate in Sect. 3.