Value without absolute convergence

We address how the value of risky options should be assessed in the case where the sum of the probability-weighted payoffs is not absolutely convergent and thus dependent on the order in which the terms are summed (e.g., as in the Pasadena Paradox). We develop and partially defend a proposal according to which options should be evaluated on the basis of agreement among admissible (e.g., convex and quasi-symmetric) covering sequences of the constituents of value (i.e., probabilities and payoffs).