Annotated Edition

"Why sex-ratios in majors might be more than just bias" by Luana Maroja — with line-by-line critical notes on factual accuracy, logical validity, and rhetorical method.

Annotated by Chad M. Topaz

Note: The op-ed frames gender as a strict male/female binary. Gender is more complex than that. This annotation engages with the essay's own framing where necessary, but that should not be read as endorsement of the binary.

Op-ed: "Why sex-ratios in majors might be more than just bias" by Luana Maroja (April 15, 2026)

Responding to "Gender gap in economics department persists despite faculty interventions" by Hadley Levenson (March 18, 2026)

Updated May 2026: includes a postscript on the Heterodox STEM Substack repost, editor's note, and selected substantive comments.

Why this argument fails

1 Campus-wide arithmetic cannot diagnose a department-level problem. The essay argues that because Williams is roughly 50/50 male-female, some majors must skew male if others skew female — so concern about economics is misplaced. The math is trivially true. But it says nothing about why economics specifically skews 64/36, or whether that skew reflects a fixable climate problem rather than an inevitable law of nature.
2 The cited studies do not say what the essay claims they say. The essay invokes a meta-analysis of vocational interests (Su et al., 2009) as proof that preferences predict career choice "more accurately than discrimination." That study never measured discrimination. It also treats the "gender-equality paradox" (Stoet & Geary, 2018) as settled, but the finding required a corrigendum and the correlation is not robust across alternative measures (Richardson et al., 2020).
3 A field experiment directly challenges the fixed-preference story. The essay's core claim is that the economics gender gap reflects innate, largely immovable sex differences. But Porter & Serra (2020) found that a single brief role-model visit nearly doubled women's likelihood of choosing an economics major — from 9% to 17%. That result is hard to reconcile with preferences being strongly fixed by biology.
4 The essay attacks proposals nobody made. A March 18 Record article reported on the economics gender gap and discussed interventions like advising, role models, and inclusive programming. This essay reframes those as "covert quotas," "lowered admission thresholds," and "grade inflation" — then tears down its own inventions.
5 A false dichotomy drives the whole argument. The essay frames the question as "bias or choice" and picks choice. But in practice, institutional environment shapes choice: what students are exposed to, who teaches them, how welcome they feel, and what information they receive all influence which majors they pursue. The essay treats bias and choice as mutually exclusive, then declares choice the winner without weighing the evidence for interaction.
6 Evolutionary speculation stands in for causal evidence. The essay leaps from mammalian reproductive biology — females bear higher parental costs, males compete for mates — to the claim that this explains why men outnumber women in the economics major at a small liberal arts college. The inferential gap between "sexual selection shaped some average behavioral tendencies" and "that's why Williams econ is 64/36" is enormous, and the essay never bridges it.

The annotated text

Why sex-ratios in majors might be more than just bias

Luana Maroja · The Williams Record

On March 18, the Record published a piece on sex-ratio imbalance — an excess of men — in the economics major while ignoring similar or larger imbalances (including imbalances in the opposite direction) in other departments. But this is logic and math, pure and simple: In a college that is roughly 50 percent female, an excess of women in some majors (e.g., ~75 percent in biology and psychology in the class of 2026, based on a hand-count of departmental major rosters) must be balanced by an excess of men in others. Ultimately, this demand for equity (equal representation of the sexes in all majors) might be misguided.

Humans are not blank slates, and many studies show that males and females have, on average, different preferences and behaviors which can affect their choice of major and profession. While some of these differences are influenced by societal norms, others have been molded by a billion years of the evolutionary process of sexual selection. True fairness in representation lies not in achieving parity, but in respecting individual preferences.

The persistent underrepresentation of women in economics (36 percent in the department's 2023 internal report) is real. But the sources in the article try to explain this "imbalance" by lack of access, lack of incentives, or outright discrimination against women. A more evidence-based explanation should include the awareness that sex differences in educational and vocational preferences have been documented across decades of psychological research.

It is undeniable that society's incentives and prohibitions guide what is a permissible career path for each sex. However, as someone who studies evolutionary biology, I also note that millions of years of sexual selection have produced average differences in behavior and preferences between the sexes — differences that appear early, are cross-cultural, and persist even in the most egalitarian societies today. Past sexual selection produced not only different body sizes and strengths, but also different behaviors. In mammals, females bear the far higher reproductive costs — pregnancy, lactation, and extended parental investment — while male investment in most species is limited to a brief copulation and sperm delivery. Over millions of years, this asymmetry has favored greater male risk-taking, aggression, and drive for resources — all things that could enhance chances of acquiring a mate.

Females typically invest the most in offspring, making them the "limiting" or least available sex for reproduction, and thus the choosy sex. Sexual selection could thus have had some influence behind often-reported preference differences between sexes. Among humans, males are more "things-oriented," while females tend toward being "people-oriented." These patterns appear early: Even young children's drawings reflect this tendency, with girls drawing people more often than do boys, who like to draw vehicles and machines. Meta-analyses of vocational interests (the well-replicated "people vs. things" dimension) show large, cross-cultural sex differences that predict majors and career choices more accurately than discrimination. There is even a well-known paradox: Differences in professional higher education choices are more sex-biased in richer and more equal countries — likely because in these countries, girls are freer to choose careers they love, rather than being motivated to make money to survive.

Society accepts — without outrage — majors and professions that are heavily female-dominated. Today psychology and biology routinely exceed 60 to 80 percent female nationally, and fields such as nursing and several medical specialties are also overwhelmingly female. We also do not lose sleep over male-dominated professions like policing or trucking. So, why single out economics (and, similarly, political science) for criticism when in fact the overall distribution of majors must balance out to result in an overall 50 percent of women in the College?

There is danger in assuming every inequality reflects bigotry rather than choice. Quick-fix "solutions," implemented at other colleges, such as covert quotas, lowered admission thresholds for women, or grade inflation to retain women, can backfire spectacularly. Consider a simplified "quota" illustration: Suppose there are 100 male applicants and 10 female applicants. In both groups, test scores average 50, ranging uniformly from 1 to 100. If all 10 women are admitted but only the top 10 men are (enforcing equal sex-ratio for limited number of vacancies), the women cohort's average score is still 50 while the men cohort's is now 95. In this hypothetical, the result would lead to greater gender equity but also to a visible achievement gap that reinforces the very stereotypes the intervention aimed to dismantle.

Similar logic applies to artificial grade support. As the Record article noted, female economics students who do not receive an A in the intro economics courses are less likely to continue with the major than male students who receive a grade lower than an A. Major choice, however, is driven by intrinsic preferences, which also shape performance. Thus, efforts to increase representation without addressing underlying preferences might lead to more harm than good.

We should aim for welcoming environments that respect individual preferences and celebrate excellence — whether that leads a student into economics, psychology, or anywhere else — rather than engineering outcomes that ignore the data on why students actually choose their educational paths. If we are comfortable with women dominating biology and psychology, we must be equally comfortable with men dominating economics and political science.

Luana Maroja is a biology professor.

Whataboutism A news article about economics need not survey every department. Criticizing it for having a defined scope deflects from the specific evidence it presents.
Ecological fallacy The arithmetic is trivially true: at a 50/50 college, female-heavy majors must coexist with male-heavy ones. But that tells us nothing about why any particular major skews the way it does. Bias, climate, information gaps, or some mix could produce multiple distortions at once. System-level balance cannot show that a department-level problem is benign.
Straw man The Record article asked why economics specifically skews male and what might help. It never called for "equal representation of the sexes in all majors." Fabricating that demand and then calling it "misguided" is a textbook straw man. See the original: Williams Record, March 18
Straw man Almost no serious researcher holds a "blank slate" position. The mainstream view in psychology and neuroscience is that biology and environment interact. Attacking an extreme position few hold makes the author's own view look moderate by contrast.
Misleading timescale Sexual reproduction is ancient, but behavioral traits relevant to human career preferences have not been under selection for "a billion years." Mammals are ~200 million years old; primates ~60–80 million; the hominin lineage ~6–7 million. "A billion years" trades on scientific grandeur while implying a far stronger causal link than any evidence supports. Two paragraphs later the author herself writes "millions of years," contradicting her own figure.
Fair point, but misused Respecting individual preferences is an unobjectionable principle. But this sentence does motte-and-bailey work: it offers a retreat position ("just let people choose!") that conceals the essay's bolder claim — that the economics gender gap is mainly biological and interventions are harmful.
Scare-quote delegitimization Placing "imbalance" in scare quotes signals that the concept itself should not be taken seriously — dismissing the problem before engaging with it. The Record article cited peer-reviewed research, not ideology.
Unsupported claim Calling biological preferences "a more evidence-based explanation" while dismissing research on access, incentives, and discrimination is a rhetorical assertion of superiority, not an empirical one. The research literature on women in economics documents climate problems, grade sensitivity tied to belonging uncertainty, and the effectiveness of targeted interventions.
Lundberg & Stearns (2019) review decades of evidence on women's attrition from economics, documenting that the leaky pipeline involves climate, advising, and grading norms — not merely "preferences." Bayer & Rouse (2016) document the profession's specific climate problems.
Fair point, quickly abandoned This concession — that society shapes career paths — gets immediately overridden by the "However" that follows. The essay never returns to weigh societal factors against biological ones. It works as rhetorical inoculation: acknowledge the other side briefly, then spend the rest of the essay dismissing it.
Speculative causal leap The claim that sex differences "persist even in the most egalitarian societies today" leans on the contested Stoet & Geary (2018) "gender-equality paradox" — a paper that required a corrigendum correcting multiple errors and whose central correlation is not robust across reasonable alternative gender-equality measures (Richardson et al., 2020: rs = −.075, p = .518 with BIGI). Presenting this as settled fact misleads the reader.
Richardson et al. (2020) showed that replacing the GGGI with the Basic Index of Gender Inequality (BIGI) yielded a nonsignificant correlation between national gender equality and women's STEM underrepresentation. The result is sensitive to which equality measure and which countries are included — not the hallmark of a robust finding.
Accurate biology, irrelevant application The description of mammalian reproductive asymmetry is broadly correct. The inferential leap that follows is the problem: from "female mammals bear higher parental costs" to "men choose economics." That chain skips the vast complexity of human cultural transmission, institution-building, and socialization.
Non sequitur Grant that sexual selection shaped some average behavioral tendencies. The link from "male risk-taking and resource drive" to "men choose economics over biology" still does not follow. Biology involves competitive grant-seeking, fieldwork risk, and career uncertainty. Economics holds no monopoly on "risk" or "resource orientation" among academic fields. The mapping from evolved tendencies to specific modern majors is asserted, not demonstrated.
Oversimplification The people/things dimension is real, but it is a population-level average with large overlap between sexes. Su et al. (2009) measured interest inventories, not actual career or major choices, and the overall d = 0.93 on Things–People shrinks considerably for specific fields (e.g., d = 0.36 for science interests). Presenting the broadest dimension as though it maps directly onto who majors in economics elides this crucial detail. Su, Rounds, & Armstrong (2009), Psychological Bulletin, 135(6), 859–884.
Confound ignored Even very young children receive gendered toys, clothing, media, and adult modeling from birth. Drawing studies cannot cleanly distinguish "innate" from "very early socialization" — that would require far more controlled experimental designs than observing what kids sketch.
Fabricated claim The essay's most consequential misrepresentation. Su, Rounds, & Armstrong (2009) document sex differences in vocational interests. They do not pit preferences against discrimination in a predictive contest. The comparative claim — "more accurately than discrimination" — is the author's invention, not anything the cited study found.
Su et al. (2009) measured the magnitude and variability of sex differences across Holland/RIASEC interest categories. The study does not measure discrimination at all, let alone compare its predictive power to that of interests. The study concludes that sex differences in interests are large on the Things–People dimension and may contribute to occupational segregation — not that they outperform discrimination as an explanation.
Contested finding presented as settled The "gender-equality paradox" (Stoet & Geary, 2018) gets treated here as established fact with an obvious interpretation. In reality: (1) the paper required a corrigendum correcting data errors; (2) Richardson et al. (2020) showed the correlation is not significant under BIGI, a different gender-equality index; (3) the preferred causal story — that equality "frees" women to follow innate preferences — is one of several possible readings and remains unestablished.
Stoet & Geary's corrigendum (2019) corrected the description of their propensity measure, data for China, and figure labels. Richardson et al. (2020) replaced the GGGI with the BIGI and found rs = −.075, p = .518 for 77 countries — effectively no relationship. They concluded that "these patterns tell us little about global, causal relationships between nation-level measures of gender equality and women in STEM."
Unsupported premise "Society accepts — without outrage" is an empirical claim about public attitudes, offered without evidence. True or not, it does rhetorical work: it makes concern about economics look uniquely irrational, when the real question is whether a particular field has specific, documented problems worth addressing.
False equivalence Comparing economics to trucking and policing ignores vast differences in prestige, compensation, policy influence, and documented climate dynamics. Different fields can have different causal stories behind their gender gaps. Male-dominated blue-collar work tells us nothing about whether the Williams economics department has a climate that discourages women.
Logical error repeated This is the ecological fallacy from paragraph one, restated as a rhetorical question. "The distribution must balance out" is not an argument that any particular imbalance is caused by preference rather than environment. The arithmetic constraint says nothing about the causal story at any specific department.
Straw man / loaded framing "Assuming every inequality reflects bigotry" is a position the Record article never took. That article reported evidence on grade sensitivity and climate, and discussed advising and role-model interventions. Reframing measured concern as an assumption of universal bigotry is a straw man wrapped in loaded language.
Poisoning the well "Covert quotas, lowered admission thresholds, grade inflation" — the Record article proposed none of these. It discussed information sessions, advising, female role models, and inclusive programming. This sentence links equity efforts to the most disreputable possible versions of intervention, priming the reader to equate concern about the gender gap with corruption or lowered standards. See the original: Williams Record, March 18
Rigged hypothetical A thought experiment built to make intervention look absurd. It assumes an extreme 10:1 applicant ratio, admits all women regardless of score while taking only top men, and treats the intervention as quota-based admission rather than recruitment, mentoring, or climate improvement. None of this resembles anything the Record article discussed. A more realistic scenario — modest outreach increasing the female applicant pool — would likely produce an entirely different result.
Bait-and-switch The Record article discussed supportive emails, advising, role models, and inclusion efforts — not "artificial grade support" or grade inflation. Recasting those interventions as grade manipulation is a misrepresentation of the actual discussion.
Real finding, multiple interpretations The grade-sensitivity finding is genuine. But its interpretation is contested: it could reflect lower confidence, stereotype threat, belonging uncertainty, advising patterns, perceived returns to effort, or classroom climate — not only "intrinsic preferences." Lundberg & Stearns (2019) review multiple mechanisms.
Begging the question "Major choice is driven by intrinsic preferences, which also shape performance" is the contested claim, stated as though it were settled. Whether observed preferences are substantially innate or shaped by institutional environment is exactly what the debate is about. The argument is circular: it assumes the conclusion it needs to prove.
Porter & Serra (2020) showed that a single 15-minute role-model visit nearly doubled women's likelihood of choosing economics as a major (from 9% to 17% baseline). That result is hard to reconcile with a strongly fixed-preference account, though the authors note that disentangling channels (information vs. inspiration) is left for future work. The finding is consistent with preferences being substantially shaped by context, belonging cues, and role models.
Non sequitur Even if preferences play a role, it does not follow that environmental interventions produce "more harm than good." The essay never weighs harms from inaction — talented women discouraged from economics by a fixable climate, a loss of human capital and individual flourishing. Worrying about intervention harms while ignoring status-quo harms is not balanced analysis.
Motte-and-bailey conclusion "Welcoming environments that respect individual preferences" is the unobjectionable motte — almost no one disagrees. But the essay's actual argument (the bailey) has been that biological sex differences largely explain the economics gap, that interventions resemble quotas and grade inflation, and that equity efforts may do "more harm than good." The conclusion retreats to safe ground after spending the entire essay discrediting those efforts.
Symmetry fallacy This assumes the causes are symmetric across fields. But if economics has documented hostile-climate problems that biology does not (or vice versa), comfort with one outcome does not logically require comfort with the other. Different departments can have different causal stories. The parallel is assumed, not demonstrated.
The AEA's own 2019 Professional Climate Survey (Table 2) found that only 20% of female economists agreed or strongly agreed they were satisfied with the overall climate in the field, compared to 40% of men. Table 3 shows that 48% of female respondents reported personally experiencing discrimination or unfair treatment based on sex, compared to 3% of men. The essay offers no comparable field-specific climate evidence for biology or psychology. The symmetry it assumes is asserted, not demonstrated.

What a responsible version of this argument would have had to say

A serious essay on this topic would acknowledge that average sex differences in vocational interests exist — while also noting these are population-level averages with large overlap, that their magnitude varies by subfield, and that getting from "average interest difference" to "64/36 representation in one department" requires accounting for many mediating factors.

It would engage with experimental evidence that information, role models, and climate interventions can substantially shift women's economics enrollment. Porter and Serra's (2020) field experiment found that a single brief role-model visit nearly doubled women's likelihood of majoring in economics. That result is hard to square with a strongly fixed-preference account.

It would address the documented climate problems specific to economics — the AEA's own 2019 survey found that 48% of female economists reported sex-based discrimination and only 20% were satisfied with the field's climate (Tables 2–3) — rather than asserting the gap must reflect preference because biology and psychology are female-dominated.

It would describe the actual interventions discussed in the Record article — advising, role models, inclusive programming — instead of substituting "covert quotas" and "grade inflation."

And it would reckon with a basic fact: if you claim "interventions to increase women in economics may do more harm than good," you need to show you have seriously weighed the harms of doing nothing. This essay never does.

Postscript · The Substack repost (May 2026)

What's new

Two weeks after this annotation appeared, Maroja reposted the original op-ed on the Heterodox STEM Substack, with hyperlinks added but the argument otherwise unchanged. The actual response to this annotation lives in two places below the repost: an editor's note and a comment thread. The body of the Substack post — being a near-verbatim re-publication of the original op-ed — is already addressed above. What follows engages only the new material.

The headline finding is short. The editor's note offers no substantive engagement with any of the 28 objections raised in this annotation. It does make one falsifiable claim about the annotation itself — that it "ignores the mathematical logic" — and that claim is demonstrably false. The rest shifts from the argument to personal attack and guilt by association. The comment thread reproduces the original op-ed's central arithmetic error and adds a few new ones.

Same color coding as above: red for factually false or scientifically misleading, orange for logic failure, blue for rhetorical manipulation, gray for fair-point-but-misused.

The editor's note

Excerpted from the editor's note appended below the Substack repost.

This essay was first published in the Williams Record on April 15, 2026. It was almost immediately attacked by Chad Topaz, a DEI zealot well-known for his previous cancellation campaigns. As documented on these pages, Topaz is:

a Williams College professor previously part of the Math Department, but now in the Humanities Department. Prof. Topaz was behind the cancellation of Prof. Abigail Thompson, due to her criticism of the use of diversity statements in job hires. The ensuing cancellation resulted in many letters both in favor and against Prof. Thompson's argument. Following the controversy, Professor Topaz published a paper on the ethnic and gender "diversity" of signatories of both his own letter (against Prof. Thompson) and the letters in defense of Prof. Thompson, initiated by other mathematicians. It is interesting to note that Prof. Topaz's organization used to receive donations to help others write diversity statements for academic positions.

Topaz has written a lengthy "rebuttal" of Prof. Maroja's article, in which he — ironically for a math professor — ignores the mathematical logic Prof. Maroja points out.

Another character, Phoebe Cohen, promptly joined forces, sharing her enlightened view on the topic. According to Cohen, biologists at Williams and all over the country have excelled in female-friendly pedagogy while economists, physicists, and computer scientists continue to teach their subjects in a way inaccessible or alienating to women. Cohen then hastens to add that "people DO loose [sic] sleep about the fact that construction is majority men and nursing is majority women."

Ad hominem The classical fallacy of attacking the person rather than the argument. The labels "zealot" and "cancellation campaigns" do work in place of evidence — they tell the reader how to feel about the person before any claim about the work has been made. The editor's note nowhere addresses any of the 28 specific empirical, logical, or rhetorical objections raised in this annotation. Calling someone a name is not a rebuttal.
Guilt by association — and one false factual claim This biographical paragraph operates as guilt by association — a sub-form of ad hominem. Rather than address the substance of any of the 28 objections raised in this annotation, the editor's note recites past activities of the annotator and invites the reader to dislike them on that basis. Most of the events described did happen, though in loaded terms: the annotator did organize an open letter responding to a 2019 essay about diversity statements, did publish a peer-reviewed analysis of signatory demographics, and did co-found QSIDE, an organization that works on academic-equity research. The specific claim that QSIDE "used to receive donations to help others write diversity statements," however, is false. That program was discussed internally but never implemented; the organization did not receive donations for any such service. What does the rest of the rhetorical work is not neutral biography but the framing — "cancellation campaign," scare-quoted "diversity," "interesting to note." Whether the reader approves or disapproves of the events that did happen has no bearing on whether the empirical claims in this annotation are correct. Notes 1–28 either hold up to scrutiny or they do not. The biographical paragraph does not engage that question.
Scare-quote delegitimization The same move flagged in note 7 of the original annotation: placing a word in scare quotes signals that it should not be taken seriously, without offering a reason. The annotation in question is a 28-point line-by-line critique citing peer-reviewed literature in psychology, economics, and biology. Whether it is a good rebuttal or a bad one is a question with an answer; signaling distaste is not that answer.
Demonstrably false Notes 2 and 19 of this annotation engage the math directly. The arithmetic identity — at a 50/50 college, female-heavy majors must be balanced by male-heavy ones — is conceded as "trivially true." The point this annotation makes, and the editor's note ignores, is that a system-level identity carries no information about the cause of any specific imbalance. This is not a failure to engage the math. It is the distinction between an arithmetic identity and a causal inference. Pointing it out is engaging with the math, not ignoring it. The "ironically for a math professor" jab is exactly backward: identifying when a true arithmetic statement does not bear on the causal question at hand is precisely what mathematical training equips a person to do.
Ad hominem plus misparaphrase "Another character" and "her enlightened view" sneer at a colleague while also misrepresenting her. Cohen's actual Bluesky posts said three things: (1) biology majors going to roughly 60% female is a development of the last few decades; (2) this maybe owes to changes in pedagogy, mentoring, and the rise of women in senior biology positions; (3) people do, in fact, lose sleep over gendered occupational segregation, contrary to Maroja's "we don't lose sleep" claim. The editor's note recasts this as an unhedged charge that economics, physics, and computer science "continue to teach their subjects in a way inaccessible or alienating to women" — a comparison Cohen did not make. Whether her actual hypothesis about biology pedagogy is correct is an empirical question the editor's note neither engages nor accurately describes.

The comment thread

Selected comments under the Substack post that engage the substantive question; other comments have been omitted.

Anna Krylov

This is a simple math — an excess in one corner creates a depletion in another. … It is almost never acknowledged that under-representation of women in some areas of STEM needs to be taken together with the over-representation of women in other fields.

Coel Hellier (replying to Krylov)

In their eyes there is nothing wrong with a large over-representation of women in academia overall — just so long as there is no part of it with under-representation.

Patrick D. Caton

Every woman in my daughter's engineering class, their fathers were all engineers. Not the largest of sample sizes, but a telling correlation.

J Chicago, with reply from Alexander Simonelis

I believe male/female trends in spatial ability are observed (on the average, of course, which might have an evolutionary basis, but also, if present, might have a direct impact)? … Or other fields where spatial ability is relevant — maybe also some kinds of engineering, physics, chemistry? [Simonelis, in reply: "Not to mention math and structural engineering."]

Ecological fallacy, restated The same arithmetic move from the original op-ed (notes 2 and 19), now in shorter form. Yes: at a closed population with roughly equal sex ratios, surplus in one subgroup must be balanced by deficit elsewhere. This is true and uninformative. A conservation identity at the system level says nothing about the cause of any specific surplus or deficit at the department level. Department-level explanations require department-level evidence — climate surveys, role-model experiments, advising studies, course-grade analyses — not arithmetic.
Asymmetry-of-concern claim, overstated The premise — that critics treat female over-representation in academia as untroubling — is presented as obvious. The actual landscape is more mixed than that. Organized advocacy for men in nursing dates at least to 1971. There is sustained public and academic discussion of male underrepresentation in K–12 teaching, social work, library science, elementary education, and undergraduate enrollment overall. Whether Hellier finds that discussion adequate is a separate question; the implication that it does not exist is unsupported.
Anecdote does not distinguish the stories Caton offers this as evidence for an innate-preference story, but the anecdote does not actually distinguish innate preference from exposure, modeling, encouragement, networks, and informational access. Having an engineer parent is a textbook example of the kind of role-model and occupational-exposure mechanism that could shape major choice — the same family of mechanisms Porter & Serra (2020) experimentally confirmed for economics. The observation he reports is at least as compatible with the environmental story as with the genetic one. Citing it in support of only the latter is selective.
Spatial ability — real, malleable, not dispositive Three problems with this framing. (1) Magnitude. Across Hyde's (2005) review of 46 meta-analyses, 78% of psychological gender differences fall in the close-to-zero or small range (d ≤ 0.35). Spatial differences are real but vary widely by subtype: mental rotation around d = 0.56–0.73, spatial visualization around d = 0.13–0.19. Substantial overlap between sexes throughout. (2) Malleability. Uttal et al.'s (2013) meta-analysis of 217 training studies found average effect sizes of Hedges's g = 0.47, stable across delays, with transfer to untrained spatial tasks. Spatial skill is a trainable input, not a fixed cap. (3) Relevance. Even granting innate spatial differences, the question at hand is the Williams economics gender gap. Economics centrally involves econometrics, calculus, microtheory, and writing — not mental rotation. The mapping from "men score higher on rotation tasks" to "men major in econ" is asserted, not demonstrated.
Hyde (2005), reviewing 46 meta-analyses across cognitive, communication, social/personality, well-being, and motor domains: 30% of effect sizes close-to-zero (d ≤ 0.10), 48% small (0.11 < d < 0.35), 15% moderate, 6% large, 2% very large. The cognitive variables most relevant to academic-major choice — math problem-solving (d = +0.08), vocabulary (d = +0.06), reading comprehension (d = −0.09), math computation (d = −0.14) — sit firmly in the close-to-zero range. Uttal et al. (2013) also found that training effects on spatial skills did not differ substantially by sex, indicating that whatever average gap exists is responsive to the same kind of practice that closes it.

What this exchange reveals

A pattern is now visible. The original op-ed advanced empirical claims that did not survive a careful look at the cited literature. When the gaps were pointed out — paragraph by paragraph, with citations — the response was to repost the op-ed with hyperlinks added and to append an editor's note dominated by personal characterization rather than empirical engagement. The comment section then reproduced the original arithmetic error and added a few new threads: a spatial-ability framing that ignores effect-size variation and training data, an asymmetry-of-concern claim that overlooks decades of public discourse, and an anecdote about engineer fathers that fits the role-model mechanism at least as well as the innate-preference one.

None of this is a substantive rebuttal. A real reply to the original annotation would have to grapple with what Su, Rounds, & Armstrong (2009) actually measured, with Porter & Serra's (2020) experimental result, with the Stoet & Geary (2019) corrigendum and the Richardson et al. (2020) reanalysis, with the AEA (2019) climate survey numbers, and with the ecological-fallacy structure of the math argument. Until that engagement appears, the original 28 objections stand.

References