I have a scandalously radical idea about how to resolve the transgender restroom crisis. Let’s use two rusty, neglected, but potentially still-useful tools: (a) reason / rationality, and (b) mathematics. Regarding both, despite a diligent internet search, I have been able to find no – as in “identically zero” – documented, or even **un**documented / anecdotal, instances of a trans person committing any sexual assault, or even non-sexual assault, in any restroom. (By contrast, Binging or Googling for sexual assaults *against* transgender people, i.e., where the transgendered person is the **victim** rather than the perpetrator, easily and instantly returns multiple digits' worth of "hits".) So, despite that, for the purposes of this column, I will assume that, *contra* the facts as I have been able to determine them, the propensity for trans people committing sexual assault is the same as the same propensity for sexual predation in the general population. In addition to being a practical necessity – after all, I *do* have to start somewhere – this has the additional advantage of establishing a statistical “does-not-exceed ceiling” on the prevalence of sexual predation on the part of trans people. I.e., under these assumptions, it will be possible to derive a number quantifying the **maximum** probability of being a victim of sexual predation committed by a transgender person – always bearing in mind that, as far as I have been able to determine, actual, empirical evidence for such sexual assault seems to be zero. With all the above in mind …

o Given that the bills currently being considered by State legislatures pertain to public bathrooms, a relevant question is *How many public bathrooms are there in the United States?*

According to Quora.com, there are – I’m using numbers as round as possible – about 200 million public restrooms in the United States. Let’s assume they are evenly divided between men’s and women’s restrooms: 100 million for men; 100 million for women. Granted some restrooms are epicene / unisex, but I will assume the numbers for these will not materially affect the following, because the unisex numbers are assumed to be small, and besides, if a restroom is unisex, then the “where to go” problem for trans people is moot.

o Another relevant issue would be *How many trans people are there in the United States?*

According to InfoPlease, there are approximately, in round-as-possible numbers, about 700,000 transgender people in the United States.

o Given that I am assuming – **again, contra the evidence I have been able to ascertain** -- that the prevalence of sexual predation in the trans community is essentially the same as for the general population, the number of sexual predators (of all types) in the US is also relevant. According to StatisticBrain, there are about – again, round numbers – 750,000 sexual predators in the US. (I am assuming that being a convicted sex offender is synonymous with “sexual predator,” an assumption that seems reasonable to me –

*modulo*the distinction between “convicted” and “latent but inactive and undiscovered”.)

Since the US has a total population of about 330 million, this means that the proportion of sexual predators relative to the general US population is approximately 750,000 / 330,000,000, or .00227, i.e., about one-tenth of two percent.

Now, if the same proportion of sexual predators prevails in the transgender community, that means that the number of transgender sexual predators – of all types – is .00227 x 700,000, or, in round numbers, about 1600 trans sexual predators in the US as a whole.

Now … given all the above … and assuming the propensity for sexual predation in the trans community is approximately the same as that same propensity in the general US population … given all that

*What is the probability that I will encounter an experience of sexual predation perpetrated by a transgender person in any given men’s restroom?*

Well, obviously this requires that the trans person and I happen to use the same restroom at essentially the same time. If the two of us are “ships that pass in the night” … no harm, no foul.

All other things being equal – which they aren’t, of course, but keep reading – the probability that I will enter **any** of the given public restrooms in the US – from Unalakleet, AK, to Key West, FL – is obviously 1 chance in 100,000,000, i.e., a probability of 10^{-8}.

In order to suffer sexual assault, it would be necessary for one – I am assuming *only* one -- of the purely hypothetical 1600 sexually predatory trans people enter the same restroom. The probability of this is 1600 / 100,000,000, i.e., 1.6 x 10^{3} / 10^{8} = 1.6 x 10^{-5}.

So the probability of us both – myself **and** the sexually predatory trans person – entering the same restroom at the same time, assuming both uses of the restroom were independent events, i.e., not causally related, would then be:

The probability that I will enter the men’s room x the probability that one of the 1600 trans people will enter = 10^{-8} x (1.6 x 10^{-5}) = 1.6 x 10^{-13}, in round numbers, **about 1 chance in ten trillion.**

Furthermore, if we take into account gender differences -- a trans male would presumably no longer use the women's restroom -- then the probability is even smaller.

In that case, we have 800 sexually predatory trans males -- the "male half" the original 1600 -- entering the same men's restroom as I. The probability that one of the 800 will enter **any** given men's room is 800 / 100,000,000, i.e., 8 x 10^{2} / 10^{8}, i.e., 8 x 10^{-6}. So the probability that our hypothetical trans predator would enter **the same men's restroom as I** would be similar to the previous case: 10^{-8} x (8 x 10^{-6}) = 8 x 10^{-14}, in round numbers, *about 8 chances in 100 trillion*.

(I would wager that it would be fascinating to calculate the corresponding probability of suffering a sexual assault if we replace our hypothetical trans sex predator by a hypothetical sexually repressed, conservative member of Congress or the clergy. The difference, of course, is that the latter is decidedly *not* merely hypothetical.)

Of course, as I said earlier, all things are not equal. It is exceedingly unlikely that I will use any public men's restroom in Unalakleet, AK, or in Key West, FL, in any realistically conceivable future. I may well **never** use such a facility in **either** place. It is much more likely that I will use public facilities in my immediate vicinity, probably the Greater Seattle area, or where I have family and in-laws -- in my case, Wichita, KS, or somewhere on the Big Island of HI, respectively. So, as a matter of practical fact, I will not have all 100 million men's restrooms at my disposal, so the "hunting ground" for a hypothetical trans sexual predator would be dramatically smaller. But so would the hypothetical trans sexual predator **population: **the smaller "hunting ground" is, I would argue, compensated for by a correspondingly **smaller "hunter" population**. So, in light of those mutually compensating circumstances, the conclusion seems to me warranted that the foregoing probabilities would likely change, but not dramatically so when we concentrate on the real world.

**So what's the overall bottom line vis a vis State trans bathroom legislation, both enacted and proposed?**

Very simply, even under the most wildly *pessi*mistic assumption -- not borne out by any actual data I am aware of and have been able to discover -- that the incidence of sexual predation within the transgender community is comparable to the same incidence within the general US population ... even under such pessimistic assumptions ... the probability of anyone of either sex experiencing sexual assault in a public restroom perpetrated by a transgendered individual is literally a few chances in ten or a hundred trillion -- i.e., approaching identically zero. Moreover, the foregoing implicitly assumes that a hypothetical trans sexual predator would be irresistibly driven to assault me the moment he encountered me in a men's room. But even the most viciously depraved serial predators like the Green River killer and Ted Bundy do not assault literally every woman they encounter. So even my order-of-magnitude estimates above are unrealistically pessimistic. Rather, as I said in the beginning, the foregoing estimates are in the nature of "not-to-exceed ceilings", i.e., the probability of being assaulted by a trans sexual predator in a public restroom is **no more than** about 1 in 10 trillion or 1 in 100 trillion, depending on the size of the population of predators. And even those order-of-magnitude estimates implicitly assume that **every** trans sexual predator would respond to **every** restroom encounter, Terminator-cyborg-like, by automatically attacking **every** potential victim.

For some perspective on what these numbers mean, consider ... Let's say that, **once each minute**, a given transsexual sexual predator enters a bathroom with a potential victim. Let's also assume that our hypothetical trans sexual predator is indeed a transsexual Terminator-cyborg whose programming instills in him an irresistible imperative to attack **every single potential victim every single time he encounters such**. Those order-of-magnitude estimates imply that -- **worst case** -- the trans predator would carry out an **actual** attack once in 20 million years, in the 1-in-10-trillion case, and once in 200 million years in the 1-in-100-trillion case (round-as-possible numbers in both cases). Finally, consider that 200 million years is a little less than the length of time since the end-Permian Great Extinction event that killed off 90% of the species on the planet.

(Granted, the foregoing numbers only yield the probability that **one** trans predator will attack **one** victim, whereas there are -- by assumption -- 1600 trans predators in the hypothetical "hunter" population. But relative to the population of the US, the number of public restrooms, and the vanishingly small probability of one-on-one encounters -- the magnitude of the relevant numbers, both large and small -- the exponent of 3 on the 10 in the 1600 -- 1.6 x 10^{3} -- makes only a negligible difference.)

In view of this, it is utterly unconscionable that State legislatures are even contemplating, much less passing, legislation that would force transgendered individuals to agonize about what they will do in lieu of a loo.

**James R. Cowles**

Image credits:

All images public domain

To nit pick a bit. Yes, the total population of the U.S. is approximately 330 million. Of that number, however, of that number, approximately 47 million are children less that 12 years of age (i.e. presumably pre-pubescent) [http://www.childstats.gov/americaschildren/tables/pop1.asp] and approximately another 40 million are 65 and over (when criminal behaviors of all kind drop dramatically ) [https://en.wikipedia.org/wiki/Demography_of_the_United_States].

That still leaves some 243 million people, which still if recalculated using that number leaves the numbers quite clear as to how negligible any threat is – without padding it with persons completely incapable of or quite unlikely to commit sex crimes.

Excellent point … thanks … I should have refined the number for the US population to make it rather more “real world”.

JRC

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