The hiring problem and Lake Wobegon strategies. Extended draft version, http://www.eecs.harvard.edu/~kirsch/pubs/ hiring/hiring-submit.pdf

We introduce the hiring problem, in which a growing com-pany continuously interviews and decides whether to hire applicants. This problem is similar in spirit but quite dif-ferent from the well-studied secretary problem. Like the secretary problem, it captures fundamental aspects of deci-sion making under uncertainty and has many possible ap-plications. We analyze natural strategies of hiring above the current average, considering both the mean and the median averages; we call these Lake Wobegon strategies. Like the hiring problem itself, our strategies are intuitive, simple to describe, and amenable to mathematically and economically significant modifications. We demonstrate several intriguing behaviors of the two strategies. Specifically, we show dra-matic differences between hiring above the mean and above the median. We also show that both strategies are intrin-sically connected to the lognormal distribution, leading to only very weak concentration results, and the marked im-portance of the first few hires on the overall outcome.