Sensitivity Analysis in Decision Making: a Consistent Approach

Several recent works show that sensitivity analysis (SA) of decision-support models shares distinctive features with respect to the SA of generic simulation models. Purpose of this work is, then, to define the mathematical framework for the formulation of SA questions consistent with the theory underlying the decision-making model at hand. We define and compare the SA problem faced by a von Neumann-Morgenstern (vNM) decision maker to the problem that arises for a Bayesian decision maker. The SA problem for a VNM decision maker can be properly solved by making use of local SA methods. However, models containing non-binary events turn the problem into a constrained one, whose the solution requires the utilization of constrained derivatives. We then formulate the SA questions for a Bayesian decision maker. We show that to perform SA in the light of the state of belief one ought to utilize an approach based on the distance beteween distributions. We employ a recently introduced SA method that, while drawing form the Bayesian literature, shares the distinctive feature of avoiding to presuppose a change in the prior/posterior distributions. Investigation and comparison of the information and insights decision makers derive from the approaches conclude the work.