[Cushman]

Hmm, I’m still not following exactly what you’re pointing out. What’s the model you mentioned about variance in dice rolls? I assumed we were talking about the coin flip model where all individual payoffs go to zero with probability 1, so no one has any expected income to pay an insurance premium out of.

The article is pretty pointedly about wealth redistribution, i.e. pooling of windfalls rather than of risk, but I don’t think that was lost on anyone... are you talking about a different model where there’s some sort of insurable situation?

[notahacker]

I meant coin flips rather than dice rolls!

But no, the payoffs don't go to zero: it's heads you double your wealth, tails you lose 40%. That's insurable risk. (if the payoffs went to zero there would be no benefit to pooling... the only winning move is not to play)

The article pretty pointedly is about social insurance, but it doesn't make a particularly good case for it since it's a completely abstract model which bears no relationship to the actual reasons wealth and income disparities exist and feeding unemployed people might be a good idea. Rich people don't need to gamble 40% of their wealth on each economic interaction (they're perfectly capable of diversifying their own portfolios) and very rarely get bailed out with a share of lots of less rich people's earnings when their investments suck.

The non-straw man version of "mainstream economics" absolutely understands how risks work and literally invented the type of game theoretic model the author is using to show what he thinks "mainstream economics" is missing

[Cushman]

Ah, I believe I understand now. No, I’m afraid this risk is not insurable.

Any insurer would have to guarantee some share of the 1.05x EV per toss, call that share itself X. The insurer would keep the remainder of the EV as premium, call that Y.

X and Y are both positive so it seems at first like you should be able to underwrite this. However, the math will not work out unless you change the dynamics of the model in some way.

The fundamental problem is that this is a model for a sequence of N events, and X (and therefore Y) are exponential functions of N. After some finite N, it’s only the insurer’s most recent guarantee that matters to the total payoffs. No previous events are consequential; the brute force of exponential math says the exponent alone dominates.

So we can just think in terms of x^N. At some point the insurer must pay out x^N in losses from the previous x^(N-1) in gains.

In other words, regardless of the premium charged, or the number of individuals whose risk is pooled, this individual’s status as an insurer doesn’t give them any special exemption from exponential reality that prevents individuals in general from remaining solvent in the limit of this model.

(I haven’t totally worked through the outcome table for the author’s proposed solution— I’d encourage you to do that if you think the solution might be flawed. But this does indeed seem to be a situation where any individual who attempts to capture the EV will fail, and only unconditional sharing can succeed.)