Optimal Selection Using Algorithmic Rankings with Side Information

In this paper, we model an agent navigating a noisy ranking of candidates, each with different values. In addition to the ranking, the agent has access to a binary signal for each candidate about whether they are "free" or "busy", where being busy is a signal both of increased candidate quality and decreased candidate availability. For example, in a job market, candidates might be busy if they are already employed. In this paper, we study the incentives and welfare of the three major actors - the firms selecting candidates, the company developing the ranking tool, and the candidates being ranked and society as a whole. First, we study the incentives of the firms, deriving the optimal strategy for selecting candidates, and studying when there are "benefits to congestion" where firms can benefit from free-riding on the hiring decisions of previous firms. Next, we study the welfare implications of this setting, showing that increasing the accuracy of the ranking tool can have paradoxical effects, such as reducing societal welfare (in terms of the total value of employed candidates) and increasing notions of unfairness among candidates. We conclude by discussing the implications our results have for how algorithmically-generated ranking systems should be constructed.