(as embedded in the Mallows model) is highly unstable, another reason we find it to be unrealistic: even an infinitesimal change away from ${\theta}= 1$, where the asymptotic optimal strategy rejects about $37\%$ of the candidates, results in an optimal strategy that asymptotically rejects either $0\%$ or $100\%$ of the candidates. This suggests a goal for future work of finding models where the asymptotic optimal strategy varies continuously with parameterizations of the distribution.

We now mention some earlier work in this area. Martin Gardner’s 1960 Scientific American column popularized what he called “the game of googol,” although the problem has roots which predate this. His article has been reprinted in [@gardner]. One of the first papers to systematically study the game of best choice in detail is [@gilbert--mosteller]. Many other variations and some history have been given in [@ferguson] and [@freeman]. Recently, researchers (e.g. [@kleinberg08]) have begun applying the best-choice framework to online auctions where the “candidate rankings” are bids (that may arrive and expire at different times) and the player must choose which bid to accept, ending the auction.

Only a few papers have previously considered nonuniform distributions for the secretary problem. Pfeifer [@pfeifer] considers the case where interview 