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

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.