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A Best-Choice Problem with Multiple Selectors

Hagit Glickman
Journal of Applied Probability
Vol. 37, No. 3 (Sep., 2000), pp. 718-735
Stable URL: http://www.jstor.org/stable/3215608
Page Count: 18
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A Best-Choice Problem with Multiple Selectors
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Abstract

Consider a situation where a known number, n, of objects appear sequentially in a random order. At each stage, the present object is presented to d ≥ 2 different selectors, who must jointly decide whether to select or reject it, irrevocably. Exactly one object must be chosen. The observation at stage j is a d-dimensional vector R(j) = (R1(j), ..., Rd(j)), where Ri(j) is the relative rank of the jth object, by the criterion of the ith selector. The decision whether to stop or not at time j is based on the d-dimensional random vectors R(1),..., R(j). The criteria according to which each selector ranks the objects can either be dependent or independent. Although the goal of each selector is to maximize the probability of choosing the best object from his/her point of view, all d selectors must cooperate and chose the same object. The objective studied here is the maximization of the minimum over the d individual probabilities of choosing the best object. We exhibit the structure of the optimal rule. For independent criteria we give a full description of the rule and show that the optimal value tends to d-d/(d-1), as n → ∞. Furthermore, we show that as n → ∞, the liminf of the values under negatively associated criteria is bounded below by d-d/(d-1).

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