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.

Actually, I suppose it is technically incorrect to say that unreported rapes don’t have any effect on the statistical likelihood.  The prevalence of unreported rapes is measured through survey data.  Anytime people bring up these types of statistics they assume that all the reports are factual⁵, which seems rather doubtful.  There is certainly room for reasonable minds to disagree about whether the percentage that are false is higher or lower for unreported rape vs reported rape, but if someone wants to argue that survey results are 100% accurate, I will happily take the other side of that bet.  If even one of those unreported rapes turns out to not be factual, the likelihood would be increased.

There is a greater issue here though.  I’ve simply never understood the logic behind the argument that if false reporting of rapes is “low” by someone’s definition, that somehow means people shouldn’t care about it.  If the topic you are really concerned about is rape, that seems like a silly argument to make.  I can demonstrate this point with some simple math.

I should forewarn you at this point that I am going to make some ridiculously one-sided assumptions and will only be dealing with the stereotypical scenario involving rape perpetrated by a male against a female.  Let’s start by looking at an undergraduate class of 4,000 students.  For the purposes of this example we will make the simplifying assumption that everyone is heterosexual, and the class is evenly made up of 2,000 men and 2,000 women. How many rapes will occur over the 4 years of college?  Let’s take the most aggressive study possible – the infamous one in four statistic.  That gets us to how many women will be assaulted – 500, but not necessarily how many instances of assault.  The study finds that 22.8% were multiple-rape victims, but we want to be aggressive here, so let’s assume that every one of those 500 women was assaulted twice, which gives us 1,000 total rapes⁶.

Now, how many total instances of sex happened during the 4 years? This time we are going to be fairly conservative.  We’ll start with the assumption that only 10% of the class, or 400 students, has sex regularly.  For our purposes we’ll also assume that anyone who doesn’t have sex regularly, doesn’t have any sex at all.  What are we calling regular sex?  Again we are trying to be conservative and well say regular sex is only, on average, 1 time per week.  400 per week times 52 weeks a year gets us to 20,800 per year, which is 83,200 over 4 years.  Of course this is people having sex, not instances of sex, so we have to divide by 2 to get 41,600.  1,000 rapes divided 41,600 total instances of sex means that only 2.4% of total sex was rape.  Keep in mind we used completely one-sided assumptions to get here.  We tried to make the instances of rape as large as possible, and the total instances of sex as small as possible and we still only ended up with 2.4%.  Here is what it looks like if you flex some of those assumptions:

This is why I don’t really understand the “the rate of false reporting of rapes is really low” arguments.  Even if false reporting of rate is low, rape as percentage of total sex is even lower and very few people would argue that we don’t really need to care about rape.  About the only argument you can make here with any validity would be that rape affects more people than false accusations of rape.  But that isn’t a particularly great argument either.  Essentially it boils down to the idea that if the percent of people harmed is low enough, then we don’t have to care.  On a percentage basis, there aren’t many Jews in the US, nor are there many homosexuals.  The percentage of trans-gendered individuals is even smaller.  What rights would society be rightfully allowed to deprive those populations of simply because they are in the minority?