I'd consider fractional Kelly (whether half, quarter, two-thirds, etc.) still a member of the Kelly family. After all, it arises when one performs a full Kelly allocation on some fraction of one's wealth, keeping the rest out of the market. It's not that Kelly is an "inaccurate proxy" -- it is provably the allocation that maximises growth -- but that people for various reasons don't want to maximise growth. They prefer slower growth in exchange for other properties, such as more cash being available for emergency needs.
> 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?
Insurance isn’t about maximising overall outcome (we know it doesn’t do that!) It’s about managing critical (often existential) risks. You buy insurance when you need to protect against an unrecoverable loss (house burned down, car was stolen, permanently injured and unable to work, etc.) that you can’t just “ride out” and self-finance.
...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.
> 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?