CHOICE IN TREE-BASED DECISION PROBLEMS

Abstract. Decision makers often have to make choices from alterna-tives which have a given structure. For example Rubinstein and Salant (RS) (2006) study the case where the decision maker has to make the choice from set of alternatives which appear in the form of a list. RS have characterized such choice functions from lists with some axioms. In this paper we look at the case where decision maker has to make sequential decisions. For instance, decisions made on agendas in legis-lature often follow a tree structure (Ordeshook and Schwartz). Here we characterize the choice from binary trees with some plausible axioms. We show that the chosen element is the maximal element according to a complete order over the set of alternatives. For ternary and higher order trees the choice function follows a naive rule. Then it selects the element, that can be reached in a tree, by selecting an offspring of a particular position (e.g. middle-most for a ternary tree) at each and every node of the tree. Lastly we comment on the choice functions from mixed trees