There’s a very trendy social media phenomenon of asking women whether they would rather meet a man or a bear in the wilderness.
Now, the original TikTok video questioner wasn’t actually transporting women into the wilderness and having them encounter a bear or a man. (Is this next? Wilderness Bear Challenge or something? Please leave the poor bears in peace, ‘k?). It’s clearly a hypothetical question used to test gut instincts.
If the question is probing gut instinct, and you don’t actually have to worry about the consequences, you can say whatever your instincts tell you, or say whatever you think sends the message you want to send. That’s what man vs bear is really about — instinct and posturing. (Unfortunately, rather than embracing this aspect of the scenario, many people then try to rationalize their posturing and instinct by referring to the original question.)
Gut instincts are great at rapidly merging a variety of different considerations (including “this isn’t real”) and coming up with a quick usually-okay answer. But they’re bad at thinking things through carefully. And they’re absolutely terrible at statistics. (There are some rough heuristics that can help a bit.) If you are going to do anything remotely important that critically involves statistics, and you have time, don’t go with your gut. Use math; get help if you don’t know how. Then ask your gut. If you let your gut give the answer and then try to rationalize it with math, you’re almost surely going to make a lot of mistakes. (People who rationalize their bear or man choice, or who rationalize their displeasure with someone else’s bear or man choice, almost always exhibit really basic errors in reasoning and estimation.)
Since the question was hypothetical, it actually wasn’t critical to know the relative danger posed by men or bears. It was perfectly legit to answer the question with an answer based on posturing (but not to pretend that the posture was based on a careful consideration of risks!).
But what if we actually wanted to make a decision based on risk, not on fears, not on validating emotions, not on “I can’t be bothered to get numbers so let’s just call both dangerous and work from there”, not a rationalization of gut instinct? Could we do it?
Making Decisions is Complicated
There’s an entire field of academic inquiry called decision theory which, like the name suggests, tries to figure out how to make good decisions. We’re not going to go very deep into it. If you want to learn more about decision theory, read Wikipedia, ask your friendly neighborhood LLM, or if you want to learn about it on Medium, follow Cassie Kozyrkov.
The key insight we need — given that our instincts are bad at probability — is that we need to quantify things. We need some math.
If we have two options, A and B, then if we can compute “how good is this” scores, U(A) and U(B) so we can compare (U for “utility”, as in expected utility calculations). It’s convenient if we have just one number to represent the balance between the two alternatives, so we could calculate U = U(A)-U(B) and say we pick A if U > 0 and B if U < 0, and flip a coin otherwise.
However, we mustn’t forget that we are almost never entirely certain of how things will turn out. If we’re going to make wise decisions, we’ll often need to estimate the extent of our uncertainty. One can have sophisticated treatments of probability distributions of expected utility given current knowledge, but we’ll settle for simple error bounds: U = U₀ ± εU.
Now we’re ready to make some decisions! If we could calculate U = U(bear)-U(man), we’d be ready to go. If U₀ >> εU (where >> means “much greater than”) then we’re sure we should pick bear. U₀ << -εU means we’re sure we pick man. U₀ in between means it’s more of a tossup (and -εU < U₀ < εU means it’s really a tossup).
Important point: if we cannot make a decision with confidence because our error is large, it does not mean that the two options are of equal utility! It may very well be that one option is far better than the other. Our problem in that case is that we can’t tell, which, if it’s important, ought to lead us to find ways to get better estimates if we can. In any case, the high-error condition should be reported as “we don’t know what’s better” not “yeah about the same”.
So, what is our utility function?
If you meet a bear in the woods, you don’t know exactly what’s going to happen. Probably the bear will run away, or look at you and go about its business. Less likely, it might be curious or friendly — or beg for food if it has a lot of experience with humans. But if the bear is really hungry, or in a really bad mood, it might injure or kill you. It might eat you. It might eat you while you’re alive.
How do we handle our calculation of goodness when different outcomes are possible? One easy way to do this is come up with both a utility and a probability for each outcome, and add them all up: U(bear) = p(bear kills you)*U(bear kills you) + p(bear goes away)*U(bear goes away) + p(friendly bear)*U(friendly bear) + …. People don’t seem to actually do this, but we could argue that we probably should, as long as we actually get the right p and U values.
We can do this with men, too: p(man kills you)*U(man kills you) + p(man rapes you)*U(man rapes you) + p(man goes on his way)*U(man goes on his way) + p(man tells you where to see a really cool bear)*U(man tells you where to see a really cool bear) + ….
Now we have a whole bunch of terms and we have to try to find numbers for them. If we can’t, we’re just defaulting to using our gut feeling — after wasting a bunch of time writing down symbols.
Typically, it’s not that hard to estimate the utility of things. People do occasionally make big mistakes about how much they’ll like something, but typically the errors on utility are modest for something like this. (“Gosh, I’m pretty sure I really don’t want to be eaten by a bear…but…who knows, maybe it’s great?”)
Usually the hard part is estimating probabilities, especially the probabilities of rare events. If the rare event is something which is no big deal, then we may as well not even bother including it in our calculation. For instance, if you don’t care all that much about dying, you might, in that case, base your decision primarily on how cool your bear or man experience is liable to be. But what do we do about rare events which are very, very important if they do happen?
I happen to really like bears; not everyone does. However, like most people, I really dislike the idea of dying in the near future. Most men won’t kill you in the woods and neither will most bears: both probabilities are quite low. This is where our intuition needs the most help. Super big downside * really tiny probability = your intuition uses bad heuristics that only accidentally align with what is sensible.
Estimating the frequencies of death by bears and men
We can get to other outcomes later, but let’s start with death. It’s clear what “death” is, and it’s clearly of large negative utility.
When one wants to estimate the probability of a rare event, it’s extremely important to pay attention to the scenario. If you postulate a rare scenario (e.g. “suppose you have just been bitten by a black mamba”) then you can only confuse yourself if you look at statistics that are dominated by ordinary cases (e.g. “0.03% of deaths worldwide are caused by black mambas”). This sort of reasoning (“so you have nothing to worry about”) is an example of a base rate fallacy which results in failure to properly estimate conditional risk. For the record: if you get teleported into the woods with a black mamba and get bitten because the black mamba is annoyed that it’s not in its native habitat, you are almost certain to die. The reason that only 0.03% of deaths are caused by black mambas is that black mambas don’t bite all that many people.
So, you’re in the woods. You’re a woman. (If you are actually a man, or agender, or anything else, and don’t want to identify as a woman— too bad! This is a hypothetical question. You are now a woman.) And you have to meet either a man or a bear. Great! We’ll just look at all the encounters between women and men in the woods, all the encounters between women and bears in the woods, and…oh. Nobody’s kept statistics on that.
You certainly can’t generalize to the population as a whole, because women don’t spend most of their time alone in the woods. Any numbers you get are going to be dominated by drastically different conditions. For instance, in Houston in 2023 there were about 350 homicides, all committed by people; there were zero deaths by bear. This tells us nothing about the relative rates, because there are zero bears in Houston, and the murders were not in the woods.
In the absence of ideal statistics, we’re going to have to find alternate ways to make estimates, and the error bounds will probably be large.
One way to estimate is to find individual accounts where the encounters are documented or at least can be guessed. This increases our error (in a largely unknowable way) because different individuals may be more or less vulnerable to violent men or violent bears. But if the account includes a way to estimate the number of encounters, at least we’re not doing something as inaccurate as (3 deaths to bears)/(120 bear encounters + 119,999,880 non bear encounters) = 1/40,000,000. (Instead of 1/40.)
Now, we shouldn’t cherry-pick based on whether the person died or not. Rather, we have to find people who have lots of accounts of bear encounters first, and then see what happened to them. That would be similar to the premise of the question: in the woods, and then you encounter a bear.
A relatively modest number of people actually spend a lot of time around bears, largely because people know that bears can be dangerous. One notable example is Grizzly Man, who lasted 14 summers until being eaten. Although there were a lot of repeat encounters with bears in the same location, just because a bear (or man) doesn’t kill you one day doesn’t mean they won’t on another. So we could say he had maybe somewhere between 100 and 1000 encounters before being eaten. Charlie Vandergaw spent around 30 years with bears without being killed, but with several close calls. That could be up to maybe 2000 independent encounters. Vitaly Nikolayenko made it 26 years before getting killed.
Another way to estimate, also from individual accounts, would be if we had accounts of encounters that went in a dangerous direction, but didn’t result in death, as long as we knew something about the ratio of danger to deaths. Bear biologist Lynn Rogers works with black bears, which are less aggressive than grizzlies, and while trying to explain how safe black bears are admits she’s been bitten (more than once) and clawed (she shows pictures) over her 50 year career. (She also commits a blatant error in calculating conditional risk: yes, you can get a Ph.D. and still make incredibly dumb mistakes in reasoning, especially when motivated.) So, she’s had maybe thousands of encounters and isn’t dead, but should she be? We know that brown bear attacks result in death about 1/7th of the time (and also that ). Black bears, being less aggressive and also less powerful, probably have a lower ratio. But Lynn Rogers, while not dead, is probably running close to the expected number of encounters before death.
So, overall, it’s seeming like death as an outcome of meeting a bear is plausible in about 1/100 to 1/10,000 of encounters, if they happen in a fairly natural way (e.g. you aren’t teleported directly in front of a bear who is confused and panicked by your sudden appearance), and you don’t do anything stupid, and you might be mauled in maybe 1/20 to 1/2,000 encounters. Something sort of like that. (Mauling can be bad.) This is assuming you’re also on your best bear behavior, but you don’t know in advance whether it’s a happy content bear or a pissed off angry bear or a starving bear or whatever.
What about the danger posed by men? The overall murder rate is no use because people typically murder those they know, it’s not a random encounter, etc. etc.. (Likewise for sexual assault.) Furthermore, there are good reasons to believe that it varies a lot by country.
So again, we have to use proxies, and we have to pick which men; we’ll take as most representative the men you’d be likely enough to find in bear country in North America, since that’s the relevant comparison for most of the people being asked. (Furthermore, if we’re not going to shake things up by transporting the bears to an unfamiliar environment, we shouldn’t do it for the men, either.)
We again don’t have the statistics that we really need. And we certainly can’t say that there are never any serial killer/rapists at all in “the woods”; there have been (and there have been not quite in the woods). The risk isn’t zero. But lots of people sing the virtues of solo female hiking, and defense against men isn’t a big topic (but at least one of those encouraging articles can’t resist making a base rate fallacy! — did I mention that people’s instincts were bad at statistics?). This suggests that the number isn’t going to be huge.
To try to approach a more quantitative estimate, we can use as a proxy the statistics for national park deaths in the U.S.. Across five billion visits to national parks, there have been only 43 murders. Even if only 0.1% of those are solo women traveling somewhere that might be considered “alone”, and every murder was a random man murdering that hiker, given that you do tend to run into solo male hikers (I cannot remember a time when I’ve gone hiking and not), the rate couldn’t possibly be higher than 1/100,000 or so. Of course, national park visitors aren’t entirely typical, there is a higher risk of discovery, etc. etc..
Another way to estimate is to look at murder rates in low-population-density areas where one would expect a reasonable number of solo encounters. Chelan County in Washington State is one of the most remote and wild counties in the state, with a population of about 80,000. The county-wide data shows a murder or two a year, and glancing through news reports does not reveal any recent incident of a woman being murdered by a stranger. Having been in somewhat remote areas, it at least has been my experience that rather a lot of people end up pretty much alone not that rarely, and that you will sometimes run into someone. There are probably hundreds of thousands of solo encounters per year, or at least tens of thousands, and people aren’t dying. Like with the national park data, this suggests a murder-by-random-encounter rate of under 1/100,000.
(A third way is to estimate, from the bear density and the human density, the likely relative encounter rate for women of bears vs men, and compare that to the death rate — and this too yields a vaguely similar result also with very wide error bounds.)
So our conclusion should be: under similar and somewhat realistic conditions, men are probably about 100 times less lethal to encounter than bears in North America. Our confidence bounds are pretty terrible; it might be 10x, it might be 1000x. 100,000x seems right out, as does 0.1x (1x and 10,000x seem doubtful).
Not all deaths are equal; not all ills are death
Death isn’t the only thing we have to worry about. Being raped and murdered is strictly worse than being murdered, but being eaten alive — which bears tend to do, if they’re going to eat you, because they’re tough and you’re meat, so why bother making sure you’re dead?— is also quite horrible.
But the biggest factor that might alter the outcome is the difference between being mauled and raped. Firstly, in contrast to the 6-to-1 ratio of nonlethal attacks to killings reported for brown bears, murder-by-stranger rates for women are roughly 100x lower than rape-by-stranger rates, though it’s less clear whether this holds in wilderness conditions. Furthermore, if we use the elevation in suicide rate amongst rape survivors as a proxy for how bad, in practice, women view rape vs death (granting that we can’t have dead people report to us how bad death was), we can estimate that the overall negative utility calculation is probably dominated by sexual assault, perhaps by roughly a factor of 10–20, because of the markedly higher rate. In contrast, the maulings seem unlikely to change the overall calculations by an order of magnitude.
The bottom line: bear or man?
Neither bears nor men are likely to kill you (whether you’re a woman or a man). The risk of any substantially negative outcome, under plausible conditions in North America, is well under 1%, as long as you behave appropriately for the situation.
If meeting a bear would be a transformative experience for you, go for the bear, because p(I met a bear and I’m okay) is high and U(I met a bear and I’m okay) is big and positive.
Otherwise, if staying alive is by far your most important consideration, you can be quite confident that you should pick man; even our really imprecise estimates, all indications are that men are drastically safer (at least 10x safer, but probably much more): p(bear kills you) is much higher than p(man kills you), and U(bear kills you) is not astoundingly different than U(man kills you). So, p(bear kills you)*U(bear kills you) is a lot worse.
However, if you are a woman and consider being raped to be around 1/10th as bad or worse as dying, then the estimates we’ve made do not allow a decision to be made with confidence. p(man rapes you) might be higher than p(bear kills you). Or it might not. It is quite likely that one or the other choice would have a considerably higher expected utility, but because our estimates are so bad we can’t tell which one. If you consider being raped to be 100x worse than dying, then we can once again be fairly confident that you should choose a bear (but the 100x number should be doubted because very few people act consistent with that value): p(bear kills you)*U(dead) is probably small compared to p(man rapes you)*100*U(dead).
In conclusion, if someone offers (whether you’re a man or a woman) to transport you to the woods to meet either a bear or a man (or a woman, for that matter), insist on either a detailed statistical analysis of deaths and population densities of bears and humans in the woods and a half hour or so to crunch numbers; or just insist on a Rottnest island quokka. They’re absurdly cute, completely safe, and because they have so little fear you’ll be able to take it out of the woods to some place where it can have a happy life after you enjoy meeting it.