Minority hiring and the geometric distribution

This post is about an elementary fact of probability applied to University policy. The policy challenge is what many universities face, namely how to bring the racial and ethnic composition of the faculty in line with the pool of qualified candidates. One policy idea that gets voiced repeatedly is “When you conduct a faculty search, just make sure you invite the top few URM applicants [1] for an interview.” This sounds reasonable at first blush, but under current California law such a policy is illegal. Here is a way to understand why:

Suppose for the sake of argument that the targeted identity group are redheads. Policy proposal (A) is “Make sure you interview the top few redheads”. Because academic merit has nothing to do with hair color, the average redhead is just as good as the average blond, right? Yes, but not so for the top-ranked redhead. If redheads make up 5% of the applicant pool [2] then on a merit-ranked list of all applicants the top-ranked redhead will typically be at position #20.

Now consider this policy (B): “First rank all the applicants by merit. Then pull out the redheads and improve their rank by a factor of 20; for example a redhead ranked #60 on the list gets promoted to #3. Then invite people for interviews from the top of the list.”

Most people will look at policy (B) and say “that’s ridiculous, you can’t justify that”. But (A) and (B) are (on average) the same policy. The proof – as probability books love to say – is left to the reader.

[1] For non-US readers: URM = under-represented minority.
[2] I’m pulling that number out of thin air.

3 thoughts on “Minority hiring and the geometric distribution

  1. Wow, thank you so much for your VERY meaningful contribution to this complicated topic. Turns out, it’s all just simple math! Wow!! 10/10 would read again

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    1. I sense a hint of sarcasm in this comment, but at the risk of belaboring the obvious: It *is* a complicated topic, and no, it’s not just simple math. The post merely points out that two policies that sound different are actually the same. They are not pulled out of thin air: Policy A is discussed frequently by people at my university whereas Policy B would be rejected out of hand by those same people. I don’t pretend that the issues surrounding minorities in academia boil down to a math problem, nor that I have a ready solution.

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      1. First of all, I sincerely apologize for my sarcasm. It’s not a productive way to have this conversation and I regret coming in hot like that. I appreciate your grace in moving beyond my tone to hear my message and have a dialogue. This is a challenging conversation and we all need to have patience with each other, so thank you for setting the tone in that respect.

        That said, allow me to clarify my original message…

        I think you’ve taken a very clear political position here. I think it’s a position that supports the racism that’s baked into the ivory tower. And I think you’re hiding behind math to abdicate your responsibility, as one who holds power in that institution, to do better. In your hyper-reductionist hypothetical scenario, you’ve excluded every variable that matters most and only included those variables that make the ongoing racial awfulness of academia seem reasonable. You are in a position of power and influence. You can do so much better than this. You could be working actively to increase access to people who’ve been historically locked out of higher education. Beyond this blog post, you might be doing that, I don’t know. But this blog post works in the opposite direction by gaslighting those who know for a fact that this issue goes so much deeper than the math you’ve laid out.

        Why do you think there is a single, knowable, measurable axis along which candidates can be objectively ranked? Why do you ignore the fact that URM candidates with identical measurables consistently get ranked lower? Why do you assume that candidates are even evaluated in a way that can be described as objective? Why do you assume that a hiring committee has the ability to discriminate the quality of candidates with any level precision?

        I request that you either delete this blog post or, even better, make a follow up in which your hypothetical scenario includes the possibility of any/all of the following: a multidimensional space of candidate ranking (e.g. an estimate of candidates’ ability to cope with and overcome adversity; an estimate of candidates’ ability to make students feel welcome; an estimate of how likely a candidate’s work is to meaningfully address an unmet need in society); bias on the part of the hiring committee; noise on the part of the hiring committee; an incentive for the hiring body to hire people with a range of diverse backgrounds; a threshold above which all candidates are considered “qualified” above a given ranking; … etc etc etc

        Your blog post also harkens to a very common implicit idea not only academia but in any hyper-competitive space within the umbrella of western capitalism: “Our institution won’t be able to compete if we let the URMs in.” You will be hard pressed to convince me that you don’t believe that sentiment nor will you be able to easily convince me that that sentiment isn’t fundamental to your motivation to make this blog post to begin with. I do have an open mind and an open heart. But you’ve got a long row to hoe if you want to change my mind in this regard.

        The ivory tower does not need to be protected from being overrun by “underqualified” URM outsiders. Quite the opposite: insofar as the culture of academia mimics the hyper-competitive capitalist culture of western society at large, it must seek healing (and progress) by making space for those who have traditionally been locked out. Or else it will fall victim to the same sickness afflicting the rest of our institutions.

        Thanks for taking the time to consider these issues.

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