Characterizing EVOI-Sufficient k-Response Query Sets in Decision Problems

In finite decision problems where an agent can query its human user to obtain information about its environment before acting, a query’s usefulness is in terms of its Expected Value of Information (EVOI). The usefulness of a query set is similarly measured in terms of the EVOI of the queries it contains. When the only constraint on what queries can be asked is that they have exactly k possible responses (with k \ge 2), we show that the set of k-response decision queries (which ask the user to select his/her preferred decision given a choice of k decisions) is EVOI-Sufficient, meaning that no single k-response query can have higher EVOI than the best single k-response decision query for any decision problem. When multiple queries can be asked before acting, we provide a negative result that shows the set of depth-n query trees constructed from k-response decision queries is not EVOI-Sufficient. However, we also provide a positive result that the set of depth-n query trees constructed from k-response decision-set queries, which ask the user to select from among k sets of decisions as to which set contains the best decision, is EVOI-Sufficient. We conclude with a discussion and analysis of algorithms that draws on a connection to other recent work on decision-theoretic knowledge elicitation.