Grievance studies hoax
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The grievance studies hoax, also sometimes dubbed Sokal Squared, was a stunt conducted by James Lindsay, Helen Pluckrose, and Peter Boghossian in which they spent months studying and writing in order to create 20 articles filled with false information in fields they believed to be 'grievance studies'. Such fields included gender studies and queer studies, among others; the authors hoped to expose the low standards in these disciplines and willingness to publish bullshit if it comported with the reviewers' beliefs.
The authors then submitted these articles to various peer-reviewed journals in a relevant field to see if the articles would get published or rejected. The hoax unraveled and had to come to an abrupt end in October 2018 when a Wall Street Journal reporter started noticing some fishy aspects about "Helen Wilson", one of the fabricated academics listed as an author on one of the papers. In total, 7 of the submissions were accepted and 4 of those were published before retraction, 5 more were still under review when the hoax ended, and 9 were rejected outright. One of the more widely publicized claims by the hoaxers was that one of their papers accepted for publication, specifically in the feminist social work journal Affilia, was a rewritten version of a section of Mein Kampf from an intersectional feminist perspective. Affilia put out a statement in response, noting, "The article does not espouse racism, anti-Semitism, or any other fascist ideology; the parallels to Mein Kampf were limited exclusively to word choice in the descriptive text." But because the hoaxers submitted the paper under false identities, the journal's statement also said, "In light of this situation, Affilia is investigating changes to current protocol to improve accountability processes." David Banks compared the article's text to that of the Mein Kampf chapter it was supposedly based on and "couldn’t find a single phrase that matched." He also pointed out that the message of the hoax article was quite different from that of Mein Kampf: "This isn’t an article demanding concentration camps for men, it’s just a pedantic argument about neoliberalism."
Only two of the papers were published in mainstream academic journals, Hypatia and Sex Roles, the paper making it into Hypatia was fairly benign, as the core idea was about humor being used to fight oppression and it quoted relevant literature. Other journals publishing some of the sillier papers, such as Affilia and the Journal of Poetry Therapy, are tailored for practitioners rather than academics. 
Since the hoax, the members of the group began raising eyebrows by making extensive connections with right wing publications to promote their work including Jordan Peterson, Quillette, and Glenn Beck. This process arguably climaxed with the founding of a new website called *New Discourses* under the ownership of a notoriously racist Christian nationalist organization called Sovereign Nations  as the exclusive outlet for their work and members opening collaborative projects with Discovery Institute grifters in favour of Donald Trump's anti-Critical Race Theory policies.
Lindsay and Boghossian attempted a similar hoax in 2017. The goal was to get a nonsensical paper titled The Conceptual Penis as a Social Construct published in NORMA (a respected gender studies journal), but failed. After being rejected from other journals, they were asked to pay $625 to get their paper published in a low-quality, publishing-mill journal titled Cogent Social Sciences. Lindsay himself stated the hoax "mostly failed". However, he succeeded in impressing anonymous donors enough to pay him to assemble a team to work "90 hours a week" in order to create the eponymous Sokal Squared hoax.
The authors didn't include a control group in their experiment, as noted by Sarah Richardson, Harvard Professor of Women's Studies, "By their own standards, we can't scientifically conclude anything from it." (i.e. they did not spend months crafting false papers for economics, psychology, or other fields to compare publication rates) Science writer Jim Schnabel concluded "the educated public makes a decision based not on the scientific merits of the hoax but on the relative orthodoxy of the hoaxer and hoaxee. In effect, the result of the trick is decided in advance by the power relations of the field." The relative orthodoxy in this case was "not an orthodoxy of scientific legitimacy but rather the emerging consensus of tech bros, Davos billionaires, and alt-right misogynists."
A number of professors at Portland State University signed an open letter which accused the trio of exploiting "credulous journalists interested mainly in spectacle" to conduct academic fraud and dishonesty. "[B]asic spite and a perverse interest in public humiliation seem to have overridden any actual scholarly goals."
Trust and peer review
It is difficult to see what the hoax proved by getting papers based on fraudulent data published in their target fields. University of Washington Biology professor Carl T. Bergstrom had this to say on the misguided and dishonest nature of the hoax:
The worst thing, though, is that the project is uninformative. For self-styled critics of academia, the hoaxers appear woefully naïve about how the system actually works. The entire force of their stunt lies in the fact that they managed to get several satirical papers published. But it makes no sense to judge the health of a field by looking at what an insincere author can get through peer review. Publishing a bad-faith paper based on fraudulent data proves nothing more about the state of a research field than passing a bad check proves about the health of the financial system.
Peer review is simply not designed to detect fraud. It doesn’t need to be. Fraud is uncovered in due course, and severe professional consequences deter almost all such behavior. Nor is the peer-review process designed to weed out every crazy idea.
The fact that a team of bad-faith academics willing to fake data could get an article published in a 'grievance study' journal is not particularly scandalous, especially when one of the very reasons dishonest researchers might fake their data in the first place is to help them get their work published. Reflecting on the many documented instances of actual academic fraud, it is difficult to think of a field that couldn't be conceivably duped by a team of academics who are willing to lie and invent data for the sake of duping referees.
In short, the peer review process works because referees can trust the author's reporting on data and methodology to be genuine; once you allow the author to lie then all bets are off. Arguably all 'Sokal Squared' proved was that the peer review system can't detect fraud, something we already knew.
The 'Sokal Squared' hoax was primarily a big "gotcha" moment for people who aren't academically trained, have no idea how the process of peer review works, and are haunted by the mythical communist professors that live rent free in their heads. For everyone else, it was just a bunch of right wing hacks proving nothing.
- Article in Areo magazine by the authors who conducted the hoax describing their results
- The controversy around hoax studies in critical theory, explained, Zack Beauchamp, Vox
- What an Audacious Hoax Reveals About Academia, Yascha Mounk, The Atlantic, October 5, 2018
- A Portland State University Professor Made Up a Study of Dog-on-Dog Sexual Assault—and Got the Hoax Published, Aaron Mesh, Willamette Week, October 9, 2018
- See the Wikipedia article on Grievance Studies affair.
- Hoaxers Slip Breastaurants and Dog-Park Sex Into Journals, Jennifer Schuessler, New York Times
- Duped academic journal publishes rewrite of ‘Mein Kampf’ as feminist manifesto, Amanda Borschel-Dan, Times of Israel
- Affilia statement
- Squared is Still Nothing, David Banks, Cyborgology
- Hypatia Tricked, Justin Weinberg, Daily Nous
- Why the Grievand Studies Hoax Was Not Unethical But It's Not Very Interesting Either, James Taylor, Bleeding Heart Libertarians
- Why The Conceptual Penis Hoax Was A Bust, Phil Torres, Salon]
- Here's What Critics Say About That Big New Hoax On Gender Studies
- Conceptual Penises and other trolling
- See the Wikipedia article on List of scientific misconduct incidents.