Some thoughts on how we may massively misjudge the weightiness of decisions that involve doing a risky thing many times:
There’s a huge difference between riding on the back of a motorcycle once, and buying a motorcycle to ride every weekend, or between buying a cookie and buying a box of 25 cookies, or between taking a boxing lesson once and sparring regularly.
Unfortunately, our minds don’t necessarily give this difference between doing something one time and doing something T times appropriate weight. In many cases, the risk of the decision actually scales up proportionally to our prediction for T, the number of times we’ll do the thing. The problem is that how “significant” the decision feels to us may NOT scale up proportionally to T. So the “weightiness” of risky decisions can easily be miscalculated. We may be too worried about doing a thing once, and not nearly worried enough about doing it T times.
Consider the basic mathematics of repeated risks. When we do something that has pretty low risk “R” each time we do it (say, a 1 in 1000 chance of being seriously hurt), and the risk each time is independent of the previous times, then if we do it once we have a risk of R, whereas if we do it twice, we have two chances for the bad thing happening, so the risk is about 2*R. Likewise, the total risk we take on when we do it T times (for T not super large) is about T * R. This is the basic risk formula you should keep in your mind.
[A semi-technical side note for the math-interested: when we do the thing twice the risk of the bad thing happening the first time OR the second time if each event is independent is actually R + R – R^2. The R^2 comes about from considering the possibility that the bad thing happens both of the times. For intuition on this point, consider two circles that are slightly overlapping. To find the total area of the circles (i.e., the total probability of the events represented by the circles) you can’t just add up the two areas (i.e., add the probabilities), because you’ll double count the overlapping part (i.e., the part representing the event occurring in both instances), so you’ll have to subtract something away (the R^2 in this case, which has this form due to the assumption that the events are independent). However, if R is small, then R^2 is super small, so we can ignore it by assuming it’s 0; hence the total risk ends up being about 2R = R + R – 0. Therefore, the math mentioned above breaks down if you’re doing a thing with really high risk, or if you do the thing a large number of times relative to the risk level – this makes sense because if you have a 50% chance of dying each time then clearly if you do it four times you don’t have a 450% = 200% chance of dying. Likewise, if you have a 1% chance of dying each time and you do it 200 times, you also don’t end up with 1 %200 = 200% chance of dying. But for small, independent risks that you do a moderate number of times, R * T is a good rule of thumb.*]
So if you’re about to commit yourself to do a thing 30 times, you’re taking on about 30 times the risk compared to if you decide to do it once! Does your brain properly appreciate that huge multiplier? Do you feel on a gut level that doing something 30 times more often is 30 times riskier? Probably not. As the risk R gets bigger, a decision, of course, becomes more significant, but the actual risk is about T * R, so R is not enough to consider. If we mainly just consider R, then we probably end up too risk-averse on one-off decisions, and not nearly risk-averse enough on repeated decisions!
Let’s consider motorcycles. According to the National Highway Traffic Safety Administration, in 2006, you had, on average, about a 1 in 26,000 chance of dying for every 100 miles spent riding a motorcycle. For reference, this is 11x the chance of dying than a 30-year-old male has on a random day or 24x the chance of death that a 30-year-old female has on a random day.
So if you are considering buying a motorcycle, and predict you will ride it 100 miles each week for the next five years, that’s about 52 weeks * 5 years = 260 times that you ride 100 miles, so your risk of dying is amplified by 260:
R * T = (1 / 26000) * 260 = 1 / 100
That means you’ve just taken on a (predicted) 1% chance of death by buying this motorcycle! Of course, injuries are much more common than death (about 20x higher it seems), so the chance of injury you’ve taken on is much higher than that. So this is a very weighty decision. It becomes weightier still if you think you’ll ride it for ten years instead of 5. But even in the five-year case, consider: how much money would you pay NOT to have to roll a 100 sided die where death occurs if you roll a 100, and injury occurs if you roll, say, an 80 or higher? That’s the kind of die roll you’re taking on by choosing to ride a motorcycle 100 miles a week for five years.
[Note: sometimes, the risk PER time that we do something goes down the more we do it because we become more skilled. For instance, when we swim in the ocean as a weak swimmer, we are more likely to drown than if we do it as a strong swimmer. But then again, as a strong swimmer, we may take greater risks by swimming on stormy days, and as a weak swimmer, we may be cautious and stay very close to shore, so the risk per time on average could increase as we do it more. It’s hard to make a general rule about how the risk per time varies as you do something more often.]
Part of the reason we can underestimate risk is that we convince ourselves that we can stop at any time. For instance, we can buy a motorcycle and then later just decide to stop using it. Sure we can, but the question is, will we? We need to make the decision based on what we predict will happen, not what could theoretically happen.
The point is here that doing a “risky” thing once is far less risky than doing a risky thing many times (about T times more risky!), but your brain won’t necessarily perceive the right relationship. For small independent risks, the total risk of a bad thing happening scales with the number of times T you do the thing. So remember the risk formula: R * T, and teach it to your brain.
So I urge you: be appropriately wary of repeated risks! There are many things that are fine to do once that are a bad idea to do T times, for moderately large T.
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