Reverse lotteries with friends

reverse lottery pays out a little bit each time you pay but sometimes lead to horrific disaster. For instance, going without a seatbelt. You enjoy a momentary convenience every time you drive, but occasionally you die. Relatedly, wearing your seatbelt can be seen as a lottery: you pay a tiny inconvenience each time for an occasional huge win.

Like all lotteries, whether it is good to play depends on the payoffs, and one might reasonably decide to play some lotteries and reverse lotteries and not others. However, as Scott points out, it can be tempting to play reverse lotteries too much. I think this happens in particular from learning what is good by experience. If you play a reverse lottery once, probably you get a reward, and want to do it again. So you do, and get another reward, and it starts to seem like a pretty good idea. You get a lot of visceral feedback about the good aspect, and none about the bad. At least for a while. This seems like a real problem, and a neat way of thinking about it.

So presumably normal lotteries should be the opposite. You play them a few times, and it is a bit bad each time. So you quickly give up and never see the glorious reward. This doesn’t seem true of the literal lotteries in which people gamble for fun. At least plenty of people are not put off for a very long time, in spite of never winning. But maybe those are a weird instance of the abstract lottery class—for instance, because the prospect of winning a lot of money is made very salient. You might imagine that the negative lotteries would be very off putting in the analogous case: if every time you don’t wear your seatbelt, you hear about another person dying from that very choice, you wouldn’t be so tempted by the no-seatbelt reverse lottery.

I’m still confused about how individuals feel about lotteries, because I’m failing at thinking of clear examples where I know how people behave and they don’t have a really salient message about how the thing might go well. Possibly this is just because nobody does things that go badly almost all the time. Which is as good a segue as any into the thing I actually wanted to think about.

How do groups feel about lotteries and reverse lotteries?

Groups often learn whether a thing is good by one person trying it, and telling their friends, who then try it if the message was favorable, and so on. On this model, we might expect groups to do the worst kind of failing to think about the low chance outcomes.

For instance, suppose that a bakery sells reverse lottery cakes. They taste nice, but occasionally they make you sick for a day. Alice tries them, and likes them, and tells her friends. They like them. Soon lots of people are loving the reverse lottery cakes, and saying nice things about them. Eventually Zoe gets a badly upset stomach.

This might go ok for group epistemology—maybe Zoe tells her friends, and they radically lower their opinions of the cakes upon hearing how much Zoe hates them (probably too much, since Zoe is one of their few friends), and not only cease eating them themselves, but also warn their other friends, and maybe eventually everyone becomes accurately aware of the costs (I haven’t checked under what circumstances if any you end up at a good equilibrium).

There are many ways this might not happen though. For instance, if Zoe is less of an enthusiastic proponent of not eating reverse-lottery cakes than her friends are of eating them. Or if people just count up how many people around them like a thing—e.g. “of all my friends, only one doesn’t like reverse-lottery cakes, so probably I will like them”. Or if people disproportionately trust a large number of agreeing friends more than an outlier. These seem more plausible to me than the opposite alternatives, where Zoe becomes a disproportionately fierce critic of the reverse lottery bakery, or where other people hear that there is someone out there—a friend of a friend of a friend—who really didn’t like the reverse lottery cakes and update too much on this.

There are some important ways these opposite things happen though. For instance, large negatives are more newsworthy than small positives, so for things where the downsides are worthy of a story, I’d expect there to be some correction, though I’m not sure whether it should over or undershoot in general. For instance, people are famously over-concerned about sharks. If they just got their information from swimming and hearing about swimming trips from their friends, I might expect them to be under-concerned. However shark attacks make for fairly compelling reading.

So the kinds of situations that I expect crowds to over-invest in reverse lotteries are those where the costs aren’t really huge or fascinating. Or where it is hard to trace the effect to the (partial) cause. An example off the top of my head is going to theme parks. Most people I know like going to theme parks, as far as I can tell. Two people I know strongly dislike it, because they were injured at theme parks in the past. Without looking at the statistics, it is tempting (for me at least, intuitively) to say, ‘Well, basically everyone thinks it’s good. Maybe those two people were doing something weird. It’s probably fine’.


I was thinking about this because I was writing about a principle of being a good person that I feel emotionally compelled by. I wondered about the causal history of my liking it. I figured I should know about that, so that I could have a more consequentialist view on whether it was actually good. And I realized that maybe I got excited about it after a handful of times where it seemed very useful for making good decisions or being in a good mental state. But I can see how it might go wrong one time in a thousand, and when it does, how it might perhaps sometimes causes some sort of humanitarian crisis or something. If I go around praising this principle based on my own feelings after buying a handful of reverse lottery tickets, then other people might buy more of them, even if it was never a good idea in expectation, and even if I could have predicted that. So I figured I should rethink my principle (I haven’t yet), and not go around praising things that I admire just because I feel like it.


2 responses to “Reverse lotteries with friends

  1. michealvassar

    Really curious about the principal and would love to encourage more discussions like that!

  2. Two of the examples you mention, shark attacks and eating bad food, are sort of special examples: we’re extremely sensitive to risk involving foodstuffs and predators, for perhaps obvious reasons. Driving is different: almost everyone speeds even though most of us have seen mangled cars at the side of the road. I don’t want to get all armchair evolutionary psychologist here but perhaps there are some risks we’re just much more sensitive to emotionally?


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