Sequential Decision Making under Uncertain Future Preferences

We present a model of sequential decision making under uncertain future preferences, assuming that the evolution of the trade-off weight vector is constrained by set inclusion. We consider different mechanisms for selecting the next trade-off weight vector: a mechanism working against the decision maker (DM) (M), a mechanism trying to aid the DM (B), and (briefly) a probabilistic mechanism (P). Piecewise linear, convex upper and lower bounds on the optimal value function are determined for mechanisms M and B. Conditions are given that guarantee that the optimal value function is piecewise linear and convex for all three mechanisms. Procedures for computing these bounds and determining associated strategies are presented. A hypothetical situation involving an individual seeking promotion is used to illustrate the model and the numerical techniques.