As mentioned below, expected value here refers to the flow of funds. Yes, it is different from the utility of the (guaranteed) value, which is also different from (and greater than) the expected utility of the risky action.

The monetary difference between what I'm referring to and what you're referring to, incidentally, is what economists call the premium. (The naming of "insurance premiums" is not a coincidence.)

Arrow wrote the seminal paper on understanding insurance, for anyone who's interested in how this is calculated.

For the first part you're assigning a value to a thing beyond it's market cost and saying everyone is in fact a winner, and that's a little strange. Risk pooling via a private insurance company is negative sum because someone makes a profit beyond their costs. That should not then be taken to mean it's a bad deal (it isn't).

Of course. If that weren't true, people would not buy insurance.

> Risk pooling via a private insurance company is negative sum

If you only consider monetary costs and benefits, yes. But this ignores the (non-monetary) value to the insured of not being exposed to the risk (because that risk exposure has been transferred to the insurer).

> That should not then be taken to mean it's a bad deal (it isn't).

I agree that it's not a bad deal; I'm just saying that the reason it's not a bad deal is that people consider more than just monetary costs and benefits.

> It is not there to save you money. The expected value of all insurance is negative, and that's intentional.

You might well be right. But I wasn't trying to tell him what he meant; I was pointing out that viewing "expected value" solely in terms of monetary value does not explain why people buy insurance in the first place. To explain that, you have to take into account non-monetary costs and benefits.

The same is true for any economic transaction that involves anything other than pure financial instruments. For example, I go to the grocery store and buy various items for money. If I only consider monetary value, the "expected value" of this transaction is negative. Does this seem like a useful way to explain the economics of grocery stores?

Contrast this, for example, with trading stocks. Here there is no non-monetary value involved; people don't eat stocks, or get any other non-monetary benefits from them. So when analyzing the stock market, it is appropriate to use "expected value" to mean monetary value.

When I go to the grocery store, the expected value is exactly zero. In every possible outcome, I expect to exchange some amount of money for a basket of goods with an equal value.

That's the general meaning I'm using, but in this case the range of possible outcomes is pretty narrow--basically I buy food and eat it. The small probability of some of it being bad, and me either having to throw it away or getting sick from it, isn't significant for what we're discussing here.

> When I go to the grocery store, the expected value is exactly zero. In every possible outcome, I expect to exchange some amount of money for a basket of goods with an equal value.

Then either your grocery store is overpriced or you are being really pessimistic about the value you get from your food. Also you have a pessimistic view of economics.

My expected value from grocery shopping is positive: I expect to get more value out of the groceries than the money I spend on them: I can't eat money. The expected value to the grocery store owner is also positive: they weren't going to eat all those groceries anyway, so the money is more useful to them than the groceries were. In other words, the transaction as a whole is positive sum. This is how wealth is created: people make positive sum exchanges that redistribute things to increase overall value.

Of course, this whole viewpoint I'm expounding requires a concept of value that is uncoupled from monetary value. You don't appear to have that concept: you appear to believe that the "value" of anything is equal to the money you can exchange for it. That is not a fruitful way to view value if you want to understand how wealth is created. Notice that the "value" of both the groceries and the money had to be different for me and the grocery store owner for the exchange to take place; that is how all positive sum exchanges work and how wealth creation happens. If everything had the same value to everybody, which is what is implied by equating "value" with monetary value, the economy would be completely stagnant and no wealth would ever get created.

"If everything had the same value to everybody, which is what is implied by equating "value" with monetary value, the economy would be completely stagnant and no wealth would ever get created."

That's untrue. Even if everyone had the same utility function with respect to every single possible good and service, (i) wealth would still be created (e.g. by a woodworker transforming a piece of wood into a piece of furniture) and (ii) trade would still take place (because, even in the absence of differing utility functions, there are still productivity gains to be had from specialisation).

Anyway, we've veered way off topic. The comment to which you replied "The expected value of all insurance is negative, and that's intentional" was entirely correct, as long as you don't want to use a definition of 'expected value' that nobody uses.

The same good or service having different value to the two parties to a transaction doesn't require them to have different utility functions. It just requires the utility functions to depend on variables that differ between the parties. For example, the utility of a given item of food depends on how much of it you already have (the grocery store has a lot more of it than me, so it's worth less to them).

> we've veered way off topic

I'm not so sure. Health care seems like an area where it should be obvious to everybody that non-monetary costs and benefits are a huge factor that must be taken into account.