Intrinsic Uncertainty - An Explanation of the St. Petersburg Paradox

Consider any situation involving uncertainty, where the random variable of interest (e.g., payoff) is X. Let there exist a random variable, say Y, which represents the uncertainty intrinsic to the situation, and let there exist a function g such that X=g(Y). Our contention is that, once the intrinsic uncertainty has been identified, the relevant summary value is g(E(Y)), even though this may not be equal to the expectation E(g(Y)) of the variable of interest. We discuss two examples in which we can identify the random variable representing the intrinsic uncertainty. One of these examples is the St. Petersburg Paradox, where we argue that the intrinsic uncertainty is represented by the length of the game, and therefore, the variable of interest is the (finite) payoff received at the expected length of the game, as opposed to the infinite expected payoff of the game. As a result, we are able to resolve the St. Petersburg Paradox even under risk neutrality, i.e., without recourse to the strong risk aversion represented by a bounded utility function in the expected utility framework