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Preference Trees.

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This paper develops a probabilistic choice model, called Preference Tree or Pretree, which describes choice as a covert hierarchical elimination process. Each alternative is represented as a measurable collection of aspects and the entire ensemble of aspects is assumed to have a tree structure. At each stage one selects an aspect i.e., a branch of the tree with probability that is proportional to its measure and eliminates all the alternatives that do not belong to the selected branch. The process continues until only a single alternative remains. Pretree is considerably more parsimonious than the more general model of Elimination-by-Aspects EBA because it has at most 2n rather than 2 to the nth power parameters, where n is the number of choice alternatives. At the same time, Pretree is much less restrictive than models e.g., Luce, 1959 which assume that the strength of preference of x over y is independent of other alternatives. It is shown that the proposed model, which is based on random selection of aspects, is also compatible with a different decision strategy in which the aspects are considered in a fixed sequential order. Finally, Pretree is applied to the analysis of choice that is constrained by a partition imposed on the offered set e.g., an agenda. It is shown that choice probabilities are unaffected by constraints if and only if the constraints are compatible with the structure of the tree. The effect of an agenda on individual choice is investigated experimentally, and its implications to committee decision making and consumer behavior are discussed.

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Technical rept. no. 1, 1 Dec 78-1 Oct 79.



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