Happy “1st of tha Month“! My previous post presented Adam Smith’s analysis of the psychology of lotteries. In summary, we buy lottery tickets out of the “vain hope” we might win a jackpot, i.e. we are motivated by the size of the prize, not the mathematical probability of winning. But what about negative lotteries like insurance? Why doesn’t the remote possibility of a large loss motivate more people to buy insurance?

For Adam Smith, the paradox is why insurance markets exist at all! Left to our own devices, most people will avoid buying any insurance because of optimism bias: we systematically underestimate the probability of loss. How many of the insurance policies pictured below, for example, would most people have if we weren’t required by law or “nudged” by our employers to have them?

Or in Adam Smith’s day, how many houses were insured against the risk of fire, or how many British ships were insured against the risk of loss at sea? It turns out, hardly any! According to Smith,

“Taking the whole kingdom at an average, nineteen houses in twenty, or rather perhaps ninety-nine in a hundred, are not insured from fire. Sea risk is more alarming to the greater part of people, and the proportion of ships insured to those not insured is much greater. Many fail, however, at all seasons, and even in time of war, without any insurance.” (WN, I.x.28; my emphasis)

Instead, the Scottish philosopher-economist introduces what is to my mind an even deeper paradox: if people systematically undervalue the risk of loss, why does insurance exist at all? How do insurance companies make money? According to Smith, they don’t! He reports:

“That the chance of loss is frequently undervalued, and scarce ever valued more than it is worth, we may learn from a very moderate profit of insurers. In order to make insurance, either from fire or sea-risk, a trade at all, the common premium must be sufficient to compensate the common losses, to pay the expense of management, and to afford such a profit as might have been drawn from an equal capital employed in any common trade. The person who pays no more than this evidently pays no more than the real value of the risk, or the lowest price at which he can reasonably expect to insure it. But though many people have made a little money by insurance, very few have made a great fortune; and from this consideration alone, it seems evident enough that the ordinary balance of profit and loss is not more advantageous in this than in other common trades by which so many people make fortunes.” (WN, I.x.28; my emphases)

Unlike modern economists, however, Smith’s goal is not chastise us for our irrational decisions. He concedes, for example, that eschewing insurance can sometimes be the right move:

“This [the decision to not buy any maritime insurance] may sometimes perhaps be done without any imprudence. When a great company, or even a great merchant, has twenty or thirty ships at sea, they may, as it were, insure one another. The premium saved upon them all may more than compensate such losses as they are likely to meet with in the common course of chances.” (WN, I.x.28)

But why is “the chance of loss … frequently undervalued” by most people? As with lotteries, Smith once again appeals to an emotional explanation:

“The neglect of insurance upon shipping, however, in the same manner as upon houses, is, in most cases, the effect of no such nice calculation, but of mere thoughtless rashness and presumptuous contempt of the risk.” (WN, I.x.28; my emphasis)

Notice how Adam Smith, irony of ironies, rejects the rational actor model of modern economics! People are not bloodless or rational automatons. When we buy lottery tickets with negative expected value, or when we refuse to insure our largest investments, we are letting our emotions take over.

But what if these decisions are the rational move, after all?! Perhaps the emotional thrill from the mere possibility of winning a large jackpot is worth the cost. And perhaps it makes sense to run the risk of a large catastrophe (like a house fire) given how remote and small this risk is. Aren’t all of our decisions in life like playing a lottery? Sometimes, the potential payoffs are large. Most of the time they are small. But what if the potential payoffs are actually negative? (To be continued…)