### On Hill’s work on ‘Greater Male Variability Hypothesis’ (GMVH)

#### by Sebastian Benthall

I’m writing in response to Ted Hill’s recent piece describe the acceptance and subsequent removal of a paper about the ‘Greater Male Variability Hypothesis’, the controversial idea that there is more variability in male intelligence than female intelligence, i.e. “that there are more idiots and more geniuses among men than among women.”

I have no reason to doubt Hill’s account of events–his collaboration, his acceptance to a journal, and the mysterious political barriers to publication–and assume them for the purposes of this post. If these are refuted by future controversy somehow, I’ll stand corrected.

The few of you who have followed this blog for some time will know that I’ve devoted some energy to understanding the controversy around gender and STEM. One post, criticizing how Donna Haraway, widely used in Science and Technology Studies, can be read as implying that women should not become ‘hard scientists’ in the mathematical mode, has gotten a lot of hits (and some pushback). Hill’s piece makes me revisit the issue.

The paper itself is quite dry and the following quote is its main thesis:

SELECTIVITY-VARIABILITY PRINCIPLE. In a species with two sexes A and B, both of which are needed for reproduction, suppose that sex A is relatively selective, i.e., will mate only with a top tier (less than half ) of B candidates. Then from one generation to the next, among subpopulations of B with comparable average attributes, those with greater variability will tend to prevail over those with lesser variability. Conversely, if A is relatively non-selective, accepting all but a bottom fraction (less than half ) of the opposite sex, then subpopulations of B with lesser variability will tend to prevail over those with comparable means and greater variability.

This mathematical thesis is supported in the paper by computational simulations and mathematical proofs. From this, one can get the GMVH if one assumes that: (a) (human) males are less selective in their choice of (human) females when choosing to mate, and (b) traits that drive variability in intelligence are intergenerationally heritable, whether biologically or culturally. While not uncontroversial, neither of these are crazy ideas. In fact, if they weren’t both widely accepted, then we wouldn’t be having this conversation.

**Is this the kind of result that should be published?** This is the controversy. I am less interested in the truth or falsehood of broad implications of the mathematical work than I am in *the arguments for why the mathematical work should not be published (in a mathematics journal).*

As far as I can tell from Hill’s account and also from conversations and cultural osmosis on the matter, there are a number of reasons why research of this kind should not be published.

The first reason might be that there are errors in the mathematical or simulation work. In other words, the Selectivity-Variability Principle may be false, and falsely supported. If that is the case, then the reviewers should have rejected the paper on those grounds. However, the principle is intuitively plausible and the reviewers accepted it. Few of Hill’s critics (though some) attacked the piece on mathematical grounds. Rather, the objections were of a social and political nature. I want to focus on these latter objections, though if there is a mathematical refutation of the Selectivity-Variability Principle I’m not aware of, I’ll stand corrected.

The crux of the problem seems to be this: the two assumptions (a) and (b) are both so plausible that publishing a defense of (c) the Selectivity-Variability Principle would imply (d) the Greater Male Variability Hypothesis (GMVH). And if GMVH is true, then (e) there is a reason why more of the celebrated high-end of the STEM professions are male. It is because at the high-end, we’re looking at the thin tails of the human distribution, and the male tail is longer. (It is also longer at the low end, but nobody cares about the low end.)

The argument goes that if *this claim (e)* were widely known by aspiring females in STEM fields, then they will be discouraged from pursuing these promising careers, because “women have a lesser chance to succeed in mathematics at the very top end”, which would be a biased, sexist view. (e) could be used to defend the idea that (f) normatively, there’s nothing wrong with men having most success at the top end of mathematics, though there is a big is/ought distinction there.

My concern with this argument is that it assumes, at its heart, the idea that women aspiring to be STEM professionals are emotionally vulnerable to being dissuaded by this kind of mathematical argument, even when it is neither an empirical case (it is a mathematical model, not empirically confirmed within the paper) nor does it reflect on the capacity of any particular woman, and especially not after she has been selected for by the myriad social sorting mechanisms available. The argument that GMVH is professionally discouraging assumes many other hypotheses about human professional motivation, for example, the idea that it is only worth taking on a profession if one can expect to have a higher-than-average chance of achieving extremely high relative standing in that field. Given that extremely high relative standing in any field is going to be rare, it’s hard to say this is a good motivation for any profession, for men or for women, in the long run. In general, those that extrapolate from population level gender tendencies to individual cases are committing the ecological fallacy. It is ironic that under the assumption of the critics, potential female entrants into STEM might be screened out precisely because of their inability to understand a mathematical abstraction, along with its limitations and questionable applicability, through a cloud of political tension. Whereas if one were really interested in reaching mathematics in an equitable way, that would require teaching the capacity to see through political tension to the precise form of a mathematical abstraction. That is precisely what top performance in the STEM field should be about, and that it should be unflinchingly encouraged as part of the educational process for both men and women.

My point, really, is this: the argument that publishing and discussing GMVH is detrimental to the career aspirations of women, because of how individual women will internalize the result, depends on a host of sexist assumptions that are as if not more pernicious than GMVH. It is based on the idea that women as a whole need special protection from mathematical ideas in order to pursue careers in mathematics, which is self-defeating crazy talk if I’ve ever heard it. The whole point of academic publication is to enable a debate of defeasible positions on their intellectual merits. In the case of mathematics research, the standards of merit are especially clear. If there’s a problem with Hill’s model, that’s a great opportunity for another, better model, on a topic that is clearly politically and socially relevant. (If the reviewers ignored a lot prior work that settled the scientific relevance of the question, then that’s a different story. One gathers that is not what happened.)

As a caveat, there are other vectors through which GMVH could lead to bias against women pursuing STEM careers. For example, it could bias their less smart families or colleagues into believing less in their potential on the basis of their sex. But GMVH is about the variance, not the mean, of mathematical ability. So the only population that it’s relevant to is that in the very top tier of performers. That nuance is itself probably beyond the reach of most people who do not have at least some training in STEM, and indeed if somebody is reasoning from GMVH to an assumption about women’s competency in math then they are almost certainly conflating it with a dumber hypothesis about population means which is otherwise irrelevant.

This is perhaps the most baffling thing about this debate: that it boils down to a very rarefied form of elite conflict. “Should a respected mathematics journal publish a paper that implies that there is greater variance in mathematical ability between sexes based on their selectivity and therefore…” is a sentence that already selects for a very small segment of the population, a population that should know better than to censor a mathematical proof rather than to take the opportunity to engage it as an opportunity to educate people in STEM and why it is an interesting field. *Nobody* is objecting to the publication of support for GMVH on the grounds that it implies that more men are grossly incompetent and stupid than women, and it’s worth considering why that is. If our first reaction to GMVH is “but can no one woman never be *the best off*?”, we are showing that our concerns lie with who gets to be on top, not the welfare of those on bottom.