The unbearable lightness of expected utility

In chapter 8 of my book, Risk Intelligence, I discuss the concept of expected utility.  To calculate the expected utility of a course of action, the first step is to estimate – separately – the probability of success, and the potential gains and losses that success and failure would entail.  Next, one does a little math, multiplying the probability of success by the potential gains, and multiplying the probability of failure by the potential losses.  Finally, we adding these two figures together to end up with the expected utility of that course of action.  After doing this for each possible action, the rational choice is to pick the action with the highest expected utility.

Expected utility is an abstract concept. It doesn’t refer to any actual win or loss: it’s the average amount you would win or lose per bet if you placed the same bet an infinite number of times. But this ethereal figure takes on an almost physical nature for the expert gambler, looming even larger in his consciousness than the actual profit or loss that hypnotises the rest of us. Expert gamblers see something different when they look at a poker table or a roulette wheel. Most people see a range of prizes; they see a single abstract figure.

This was brought home to me one night when a highly successful gambler invited me to accompany him to a casino. This particular gambler made all his money betting on horses. He shunned casinos, and only ventured in on this occasion because he wanted to give me and his other companions the thrill of seeing someone playing for high stakes. We followed him over to the craps table.

Craps is a dice game in which players place wagers on the outcome of the roll of two dice. My gambler friend proceeded to show off by placing bets of 1000 US dollars on the pass line, one after the other. A pass line bet is won immediately if the first roll is a 7 or 11. If the first roll is a 2, 3 or 12, the bet loses (this is known as “crapping out”). If the roll is any other value, it establishes a point; if that point is rolled again before a seven, the bet wins. If, with a point established, a seven is rolled before the point is re-rolled, the bet loses (“seven out”). A pass line win pays even money; in other words, my friend stood to win or lose a thousand dollars on each bet.

However, as he told me later over cocktails in the casino bar, it wasn’t this figure that was at the forefront of his mind. Instead, he just treated each bet as a bit of fun that cost him fourteen bucks. Although not a casino gambler, he was familiar enough with craps to know that the expected value of a pass line bet is -0.014. And this meant that, on average, each bet of a thousand dollars would leave him fourteen dollars less well off. The actual profit or loss at the end of an hour on the craps table could be anything from plus fifty thousand dollars to minus fifty thousand, and my friend would be aware of this figure too. But the figure that mattered most for him was the expected value of minus fourteen bucks per bet. That’s not a good-value bet, of course. Which is why, in any other circumstance, my gambler friend would never play craps.

Right + Early II: The Ehrlich/Simon Bet

In the article I mentioned in my last post, the New York Times said Jeremy Grantham was right but early. Jeremy Grantham passed the favor along by saying that Paul Ehrlich was right but early. He referred to a famous 1980 bet between economist Julian Simon and Paul Ehrlich, an entomologist who specializes in being spectacularly wrong about everything.

At the time, Ehrlich was claiming we were running out of commodities and prices would soon soar, destroying global civilization and killing billions of people. Simon challenged him to pick any five commodities and any date more than year away. Ehrlich picked Chrome, Copper, Nickel, Tin and Tungsten and 1990 as the date. A  basket was created with $200 worth each (at 1980 prices) of the five metals. The difference between the inflation-adjusted to 1980 dollars price of the basket in 1990 and $1,000 would be paid by Simon if the basket cost more than $1,000, or to Simon if the basket cost less than $1,000.

All five commodity prices went down, the basket was worth an inflation-adjusted $618 in 1990, so Ehrlich paid $382. Ever since Ehrlich and his fellow travelers have been explaining why he was really right (it’s just those inconvenient facts that got in the way). Now Grantham trumpets that Ehrlich has finally be proven right. I checked the numbers and as of last Friday the inflation-adjusted prices were Chrome ($196.60), Copper ($241.83), Nickel ($200.52), Tin ($126.42) and Tungsten ($205.36) for a total of $970.73.  However Grantham claims Ehrlich still won because three of the five commodities sell for more than $200. Actually what I find most impressive is how little commodity prices have moved over the years in real terms.

Grantham misses the risk intelligence point completely. Ehrlich claimed to be absolutely sure the prices would skyrocket. He was so sure, he pushed for policies that would impoverish or kill more than half the world, and he supported China’s horrendous population control policies (it turned out democracy and economic growth were far more effective in solving population growth). Moreover, he claimed to understand why prices would increase, meaning he should have been able to pick the five commodities most likely to go up in price, and the time interval most likely to prove him right. Being almost right 20 years after the deadline is WRONG!

Simon did not claim the prices would surely and always be below $1,000, just that it was a good bet given a specific deadline. Nevertheless, it is interesting that commodity prices have not declined in real terms. Since the beginning of the industrial revolution the ratio of commodity value to finished good value has fallen, as design and fabrication become more important (an apple is worth its commodity value, a pot is worth more than a lump of clay, a computer chip is worth far more than the sand and other materials it is constructed from).

I think what Simon perhaps underestimated was the tripling of real global GDP from the greatest economic boom in human history that brought billions out of poverty. Commodity consumption remained roughly constant, so commodities have roughly one-third the relative economic importance in 2011 versus 1980. If GDP had grown more slowly, real commodity prices would have declined. But explosive growth offset the long-term trend toward making labor and intangible assets more valuable than physical stuff; therefore real commodity prices stayed about the same.

The big difference between Simon and Ehrlich’s ways of thinking is not that Simon was right and Ehrlich wrong. It’s observing, and learning from observation, versus denying or explaining away all contrary evidence. That’s why Ehrlich is always so certain, even when his story is 180-degrees different from his story last year.

Now, guess which of Simon or Ehrlich’s ideas are shared by more policy experts.

Right + Early = Wrong and in denial

The New York Times had a fawning interview with Jeremy Grantham, describing him as “right but early.” If you tell me it will rain tomorrow, and it doesn’t but it rains next week, you were wrong. If you claim you were just early, you are in denial about being wrong.

It is possible to make a useful prediction when you are uncertain of the timing. I might say, for example, that commodity prices are in a bubble and will decline to half their current values sometime in the next five years. That could be right or wrong. But if I say merely that commodity prices will decline someday, I will either be proven right or the issue will still be open. I cannot be proven wrong, so the prediction has no meaning.

People with poor risk intelligence seize on current trends and extrapolate them to absurd levels. They get a lot of publicity for this. Other people argue against them, pointing to signs that the trend is already slowing, that it generates countervailing forces and that in any case it has to hit some limits.

What happens next? Either the trend does accelerate to cause some disaster, proving the prophet of doom correct. Or the trend slowly and quietly slows and reverses, in which case people never think to credit the skeptic with a victory. If they think about it later, they remember the trend and the guy who postdicted it, and misremember the order of events so they think he was right. The skeptic is remembered as a guy who denies all possibility of disaster and confused with people who either don’t care about disaster or profit from them.

Reputation tends to go to lucky fools and doomsayers who never remember being wrong (and therefore never learn).