left-to-right maxima are the only information required to play these games optimally. Also, it seems remarkable that even for $\theta = 1$ where this result is reported to be well-known, we have not encountered reasoning along the lines we have given here. Hence, our proof gives a new perspective on an important result from the literature on the secretary problem; see Remark \[r:hist\].

In our setting, we interpret $c(\pi)$ as a goal for intrinsic learning by the interviewer, over the course of the $N$ interviews. The first model is based on the Ewens distribution where $c(\pi)$ is the number of left-to-right maxima in $\pi$. When ${\theta}> 1$, this has the effect of amplifying the probability of experiencing candidates whose rank exceeds that of all earlier candidates. The second model is based on what has become known as the Mallows distribution where $c(\pi)$ is the number of inversions in $\pi$. When ${\theta}< 1$, this has the effect of dampening the probability of experiencing “disappointing pairs,” where an earlier candidate ranks higher than a later candidate. In terms of permutation patterns, the Mallows model weights each permutation $\pi$ by the number of $21$-instances in $\pi$, which facilitates comparison with results in [@fowlkes] 