Robustness of Discrete Decisions to the Worst Case Distribution

This paper proposes a robustness measure for discrete decisions subject to uncertainty in the state probabilities. The robustness measure is the worst case difference in expected payoffs between the chosen action (the decision) and all other actions, as the state probabilities are allowed to vary simultaneously over prescribed tolerance ranges. In contrast to the more difficult to assess single distribution, the current approach requires only the assessment of an interval for each state probability; i.e. it works with a more easily assessed spectrum of distributions. It is shown that the robustness can be determined with an algorithm that is much simpler than the usual linear programming techniques. Its computational simplicity makes this algorithm amenable to manual calculation.