Economics Letters, 2025
People often think ambiguous gambles – those where you are more uncertain about the probabilities – are “riskier”. The famous Ellsberg paradox, for example, showed people preferred a known 50/50 gamble to one where your chance of winning could be anywhere between 1% and 99%.
This paper makes a very simple point. For a gamble in which you either win something or lose your bet, your correctly calculated subjective variance of the outcome does not depend on uncertainty about your probability of winning. It only depends on your expected probability of winning. Uncertainty about the probability cancels out in the law of total variance. In simple mean–variance terms, ambiguity does not make the gamble riskier.
Key research finding: Ellsberg-type choices can’t be justified as rational mean–variance risk avoidance, because ambiguity does not raise the variance of a binary gamble’s payoff.
Practical advice: If you think “unknown probabilities = more risk”, be careful. That intuition isn’t about variance. It might be a perfectly reasonable preference to have but it’s not more risk in the traditional sense of “higher variance.”