There is a must-read op-ed in the Record from the JA Advisory Board about the interaction between entries and cluster housing. They want the JA/entry system to have no meaningful connection to anchor housing. There is a lot of good stuff here, but, for now, I want to focus on some math.

The integrity of the JA selection process depends upon the ability to look at all applicants and choose those qualified individuals who will be part of an effective and diverse class of JAs, not those who are relatively more qualified than others in their geographic area. A particular affiliation should neither automatically guarantee nor preclude an individual’s position as a JA.

This provides another chance for CUL to do its job and gather some data. For example, how evenly dispersed were this years JA’s in terms of first year entries?

Ignoring actual data, this is still a fairly interesting statistical problem. Assume that we can rank all 150 JA candidates accurately. Assume that men and women are ranked interleavedly — meaning the best candidate is women, second is a man, third a women and so on. Assume that they are randomly distributed among 5 clusters. Assume that the JA selection process, now that it can select anyone (while keeping gender balance) gets the top 50 candidates. On average, how suboptimal would the JA’s selected under a cluster regime be, relative to this ideal?

In other words, the worst ranked male and female are 50 and 49 in this, the optimal world. What rank to the worst male and female have with cluster restrictions.

Where are my MATH/STAT/COMPSCI friends when I need them?

Actually, my intuition is that the JA advisory board is wrong and that, on average, the results would not be much less optimal than under the current pick anyone process. I might guess that, on average, the worst selected might be around 75. (Of course, it is a value judgment as to the cost of having a JA ranked at 75 instead of one ranked 50.) But there will almost certainly be years in which it is 100. But this is an empirical question!

Don’t make me start posting R code again . . .

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