The Secretary Problem with a Selection Committee: Do Conformist Committees Hire Better Secretaries?

Steve Alpern () and Vic Baston ()
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Steve Alpern: Warwick Business School, University of Warwick, Coventry CV4 7Al, United Kingdom
Vic Baston: Department of Mathematics, University of Southampton, Southampton SO17 1BJ, United Kingdom

Management Science, 2017, vol. 63, issue 4, 1184-1197

Abstract: This paper analyzes a variation of the secretary problem in which two selectors with different fields of interest each want to appoint one of the n candidates with as much expertise as possible in their field. Selectors simultaneously vote to accept or reject: Unanimous decisions are respected, and candidates with a split decision are hired with probability p . Each candidate arrives with expertise x and y in the two fields, uniformly and independently distributed on [0, 1] and observable to both selectors. If a candidate with expertise pair ( x , y ) is hired by unanimous decision, the payoffs to the selectors are simply x and y . However, to model the level of conformity in the firm, we deduct a positive “consensus cost” c from the utility of a selector who has rejected a candidate who is nevertheless hired. We show (Theorem 1) that each stage game has a unique equilibrium in which there are two thresholds, z < v , and say selector I accepts candidate ( x , y ) if x > v or x > z and y > v . We show that for sufficiently large p and c , decisions are unanimous, and that as the number n of candidates goes to infinity, the equilibrium value of the game goes to the golden mean. We show that as the consensus cost c increases from 0, this hurts the selectors (Theorem 4) but helps the firm (Theorem 6), whose utility from hiring candidate ( x , y ) is a weighted average of x and y . Thus a little conformity is good for the firm.

Keywords: games; group decisions; voting; committees; industrial organization; firm objectives; organization and behavior; decision making; secretary problem (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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