ranks are independent but have cumulative distribution functions containing parameters determined by the position of the interview. The paper [@reeves--flack] considers an explicit continuous probability distribution that allows for dependencies between nearby arrival ranks via a single parameter. Inspired by approximation theory, the paper [@kleinberg--etal] studies some general properties of non-uniform rank distributions for the secretary problem.

We now outline the rest of the paper. In Section \[s:setup\] we review the form of the optimal strategy for games of best choice, and show in Section \[s:tilt\] that any sufficiently local statistic will generate a game with an optimal strategy having the same form as the classical model. In Sections \[s:ew\] and \[s:aew\], we obtain precise and asymptotic results for the Ewens model. The Mallows model is treated in Section \[s:m\].

The weighted game of best choice {#s:setup}
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Fix a discrete probability distribution on the symmetric group ${\mathfrak{S}}_N$ where $f(\pi)$ is the probability of the permutation $\pi~\in~{\mathfrak{S}}_N$. This defines a game of best choice as follows.

\[d:pflat\] Given a sequence of $i$ distinct integers, we define its [**flattening**]{} to be the unique permutation of $\{1, 2, \ldots, i\}$ having the same relative order as the elements of the sequence. Given 