Professor Twitter and the Problem of the Low False Rape Narrative

Yesterday1 I saw an interesting argument taking place in my twitter feed and couldn’t let it go without comment2.  For the purposes of this post, we are going to refer to the twitter author in question as Professor Twitter.  So how did this all start?  Professor Twitter posted the following:

MRA @reddit thread encourages men to record sex to avoid false rape allegations

1/2 Sigh: 1. Recording sex w/o consent is a sex crime; 2. recording sex doesn’t prove it’s not rape

At this point I agree with Professor Twitter’s sentiment – after all, this is a plainly ridiculous suggestion.  Then, The Professor follows up:

2/2  3. Statistical likelihood of being falsely accused of rape is infinitesimal

This, of course, is where the arguments started.  Scott tweeted suggesting that perhaps a claim such as that should come with some sort of citation (which is how I first saw what was going on), and soon others followed, asking for The Professor’s source.  Now, the prevalence of false rape accusations is not Professor Twitter’s areas of expertise, rather The Professor brought it up more as a tangential point.  However what I found interesting, and worthy of a post, is where the argument went next:

Upper-end estimate of unfounded (not false) rape claims is 8%; vast majority of rapes never reported at all http://www.huffingtonpost.com/2014/12/08/false-rape-accusations_n_6290380.html …

The Huffington Post article mentions three US data points on false reporting all of which I have previously discussed: The Lisak study, the Lonsway article, and FBI data.  While the FBI data is indeed unfounded instead of false, the same cannot be said of Lisak and Lonsway’s studies.  Both Lonsway’s 8% as well as Lisak’s 10% upper ends dealt specifically with false reporting.  For whatever reason though, Professor Twitter is trying to imply that the top ranges all deal with unfounded rates 3.

Professor Twitter then began to receive criticism that the sources in question, while coming up with seemingly low rates, didn’t appear to support a classification of “infinitesimal.”  The Professor responded with:

More than half of rapes never reported, so even higher % means extremely small statistical likelihood

Oh look, the false rape claim truthers have arrived & they think I care about their math-challenged ideology

There is just one problem with Professor Twitter’s argument – it happens to make no mathematical sense.  Unreported rapes have absolutely no effect on the statistical likelihood of being falsely accused.  It doesn’t matter if there are 10 million unreported rapes a year or 0, the probability of being falsely accused is exactly the same.  Why is this the case? The probability of being falsely accused is dependent on the number of false accusations that occur and the size of the potentially effected population.  Whether false accusations are 8/100 (8%) or 8/1,000,000 (0.0008%), the number of accusations (8 in this example), and thus the probability of being falsely accused, is unchanged4.

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  1. I’ll be honest, the only reason I can get a timely post out is because the bulk of this was already written.  I’ve already posted about false rape allegations quite a bit and I planned to save this one for down the road, but then Twitter came along and wrecked that plan so here you go
  2. https://xkcd.com/386/
  3. That doesn’t seem very professor like
  4. There is a certain delicious irony to ridiculing your critic’s supposed “math-challenged ideology” while simultaneously demonstrating a complete lack of understanding of basic probabilities