On determining the importance of attributes with a stopping problem

In this paper we try to answer the question of how one can determine the relative importance of the different attributes of a product. In order to answer this question a stopping problem model is constructed. An agent faces a sequence of i.i.d. multi-attribute products. From each product, he can observe only one attribute. At each period the agent has to decide whether he wants to stop and take the best product he has observed so far, or whether he prefers to continue the observation process and observe an attribute of the next product in the sequence. We find the optimal observation policy and the conditions under which it observes only one attribute, rendering it the most 'informative'. When the sequence of products is finite, second-order stochastic dominance characterizes the case in which an optimal strategy observes only one attribute in the sense that if it holds between any two random variables induced by the expected utility given an attribute, it is never optimal to observe the 'dominating' attribute. When the sequence of products is infinite, observing one attribute only is always optimal. The seeming discrepancy between finite and infinite horizon models vanishes for a sufficiently large horizon, making the infinite horizon optimal attribute the one chosen for a long period in finite horizon problems as well.