back
1 comments
Because for all his grandiose claims to novelty, he's basically created a completely abstract game theoretical model of the concept of insurance, which suffice to say is not something "mainstream economists" are unaware of.
Can you say more about that? I can see the loose analogy to socializing risk, but I’d usually think of the concept of insurance along the lines of “many small winners pay for a few big losers”; this looks to me more like “a few big winners pay for many small losers”.
The example seems to be in between (it's an illustration based around variance in series of dice rolls). But the principle of insurance is pooling risk rather than the distribution of risk: (and a Lloyd's syndicate bailing out a natural disaster looks a lot like a few big winners paying for many small losers)

The principle of a few big winners pay for many small losers is pretty well understood in other areas too: it underpins Sand Hill Road as well as the social insurance of welfare states....

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?

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

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.)

There's nothing magical about the pooling of risk and reward being administered by an entity which is an insurance agent that makes the payoff matrix look different in this model. Yes, this includes the fact that sometimes the syndicate returns a little more to its members than was put in and sometimes a little less depending on who flipped which coin toss.

All of which is moot to my original point which was that the OP's original argument that the mainstream economics profession is focused purely on expected value with no concept of risk is laughably wrong.

They're in fact a few steps ahead of him, because they also assess pooling of earnings in terms of moral hazard and adverse selection, instead of naively assuming that expected return and downside risks are evenly distributed across the population and invariant with respect to wealth pooling. Adverse selection is the actual reason private insurers are unlikely to take on the burden of insuring things like unemployment (people that find it easy to find employment and have lots of savings will rationally avoid participating unless its compulsory, which means more people wanting to claim on it than pay in), but of course introducing variation in likelihood of payoffs to the model leads to potentially very different outcomes...

Ok, I had never seen it simplified like that though, and definitely wasn't aware that from a random coin you can be net positive if you cooperate, that's a surprise to my knowledge and I find that idea very valuable.

Edit: also I don't see it very similar to insurance, since insurance is withholding wealth in order to distribute it occasionally when needed because it's zero-sum. But if distributing it all the time everywhere is a net positive gain, that's entirely different than the insurance game.

> also I don't see it very similar to insurance, since insurance is withholding wealth in order to distribute it occasionally when needed because it's zero-sum. But if distributing it all the time everywhere is a net positive gain, that's entirely different than the insurance game.

Insurance is zero-sum (negative-sum, actually) when it comes to money. It is not zero-sum overall, because reducing risk is valuable. A 50/50 shot at either 10 million dollars or nothing is significantly less valuable (to anyone who isn't already very rich) than a guaranteed 5 million.

The expected return on both those examples is the same, 5 million.
Yes, but even homo Economicus isn't trying to maximize expected income, they're trying to maximize expected utility. Unless you're completely indifferent to risk, the sure thing is better.
Indifferent to risk, or seeking of risk, or having any other computable utility function on any other measurable that we’d have to accept as equally valid if we want to convince any non-economist that we aren’t just using utility as a weasely word for money :)

That’s not even snark, humans preferring both of higher risk and lower payoff is a canonical psycho-economic result. And even the question of whether the concept of a rational utility maximizer is well-founded is the exact subject of this very fine article!

> or seeking of risk

Sure. I very much doubt anyone seeks risk because it's risk. They do it for the thrill, or for social reasons, or because calculating risk is hard, etc.

> having any other computable utility function on any other measurable that we’d have to accept as equally valid if we want to convince any non-economist that we aren’t just using utility as a weasely word for money

Almost anything else will do just as well. If you can buy it (or the means to acquire it) on the market, then there's always some point at which twice as much money buys less than twice as much. Maybe 10 million is not enough to hit that point, or 5 million is too much, but the curve flattens out somewhere. And if you can't, then the money makes no direct difference, but can still buy you food and shelter and free time with which to pursue your other projects.

I suppose in principle you could actively want to not have money (and not want to give it away either), in which case getting rid of 10 million is probably not twice as hard as getting rid of 5, but that hardly seems realistic.

Not after taxes!

Most first world governments "fine" you quite a lot of money if you work on risky things. For example, if you earn $100,000 for ten years, vs $1,000,000 on one of those random years, after taxes you would have $720,000 vs $520,000 if you lived in San Francisco.

I don't think this is right at all? I think it's backwards... If the $1M is a capital gain from an investment you made multiple years ago - which is what windfalls from "work on risky things" actually look like - it will be taxed less than ten years of $100k of income.

I think you're right if you're thinking about lottery winnings or other kinds of non-capital-gain windfalls like a gift from a benefactor, but those aren't the result of valuable "work on risky things".

Which is completely meaningless if you only have the potential to exercise the option once.
Yep, which is why it's a really good demonstration of why expected return isn't the only useful concept!