> It's complete nonsense to make up a number like oh my car has a 33% chance of developing a big fault this year out of thin air
Are you claiming regular people cannot learn to make calibrated probability judgments and/or look up car failure rates? Maybe that is the problem with the Kelky-based framework: it requires forecasting a probability distribution and many people are not great at that, although they could learn it.
Since it wasn't clear from your comment, what alternative framework are you proposing for the insurance decision?
...but it does do that under the assumption of compounding, and that's part of why it exists. I recommend learning about the Kelly criterion and E log X strategies to see why.
The key insight is we shouldn't look at the arithmetic expectation of profits of isolated bets beccause that causes us to overinvest in uncertain profits and underinvest in insurance.
I think I really can sometimes tell if I’m riskier or safer than the average person. I can observe other people’s behavior and compare it to mine. But even then, my impressions will be subject to a lot of biases (eg. everyone thinks they are an above-average driver).
If I assume the insurance company has done the math so they make a decent margin, and if I’m confident I’m a better or worse risk, it’s possible I can use that reasoning to guess whether insurance is a good value for me.
You're not against the insurance company. Your decision is relatively separate from theirs.
Given I’m unable to produce the probabilities necessary to compute the Kelly criterion, I can’t use that to make the decision. Instead, I have to use dumb heuristics like “I need liability insurance to get rid of my risk of ruin” or “I can easily afford to replace my car, but my passion is parking underneath dead trees during storms, so I should pay for comprehensive coverage.”
In either case I have no idea how to compute the probabilities, but I’m still pretty sure I made the right decision.
The value of insurance to the buyer depends on the buyer's wealth. The insurance the electronics store offers on the tablet I buy is well-priced for their target audience but not for someone with my emergency expense buffer.
Could work! I don't know how, though.
When I feasibility tested by asking my wife to guesstimate a couple of these she ended up very close to official statistics. The first-level trick she used is Fermi estimation.
You can totally do it and it's worth practicing. There are even competitions in it open for anyone! I like the Quarterly Cup at Metaculus. The next iteration starts early January.