When you pay cash for an article at the store, and the clerk counts out the coins for your change, he generally gives you the smallest number of coins that will make correct change. How does he insure it’s the smallest number? The method is so simple, we hardly if ever think about it: Count out quarters until the amount is under twenty-five cents, then count out dimes until it’s under ten cents, then nickels, and finally pennies. The same basic strategy works for paper money, too. Hundreds, fifties, twenties, tens, fives, singles. Obvious, right?
Actually, it’s not entirely obvious. Suppose one day, Congress authorized the Treasury to mint a new sort of coin, worth twelve cents. Now, how do you now give thirty-four cents in change, using as few coins as possible? Simple: Two twelvers, and one dime. Three coins.
But wait, hang on a second. Our simple change-making rule says you are supposed give a quarter first, then a nickel, and four pennies. That’s six coins! What went wrong here? The simple rule didn’t work. Is there something wrong with the rule?
Actually, the rule is fine; it just isn’t universal. If you ditched the twelver, then, the so-called “obvious” rule always gives you the fewest coins, when making change with the standard U.S. coin denominations. In other words, the rule is okay, provided you choose your coin denominations carefully. The point of this example was to demonstrate that what seems like an “obvious” solution doesn’t always work. Small changes which appear to improve the system, can affect whether it works or not. The Law of Unintended Consequences reigns supreme.
It’s appealing to imagine that the simple change-making rule should always work. For example, if you have to make change for thirty-four cents, why shouldn’t you take a quarter first? Doesn’t that make the problem much smaller? To give back the same 25 cents with smaller coins would take at least three coins (two twelvers and a penny, or two dimes and a nickel). But in this example, it happens that giving back 12 cents first (instead of 25 cents), gets you to a point where you can finish giving change with fewer coins than if you gave back the quarter first. There is a higher order interaction which subverts the simple intuition that, if you have to get to twenty-five cents eventually anyway, why not do it as quickly as possible?
So why is it that the rule works in one case, and fails in the other?
For making change, there’s a mathematical explanation — the U.S. coin denominations are chosen so that each coin’s value is at least as big as the sum of the values of all the smaller coins. If you do that, you can be sure the simple rule will work. If not, the rule can be broken. But there is a more important insight here, namely: The world just works like that sometimes. For some decisions, you can get the best possible outcome by choosing the biggest piece of pie first; in other cases, you get more in the long run if you take less up front. This is weird and counterintuitive, but true.
This is such a useful distinction, that it has its own name. If taking the best possible option first always leads to the best possible answer in the end, we say the decision possesses the Greedy Choice property. Intuitively, the Greedy Choice strategy can be reduced to the adage “think locally, act locally”. You look around at what’s immediately available, and pick the best. Sometimes Greedy Choice works, as in the case of making change with U.S. coins.
Unfortunately, most of the interesting decisions we have to make in life don’t have the Greedy Choice property. And what’s worse, we humans are generally not so good at solving problems that require a longer view. Even when we do manage to account for longer-term consequences — a strategy of “think globally, act locally”, as it is sometimes described — we often have trouble generalizing our solutions to society as a whole. After all, it’s a lot easier to say “think globally” than it is to do it. When individuals stop thinking globally to achieve personal advantage for themselves, the whole system goes out the window. Think how angry everybody gets when some asshole roars by in the breakdown lane, while the rest of you are stuck in bumper-to-bumper traffic. That jerk gets ahead, by making the traffic jam worse for everyone else. Pretty soon, even the most forgiving of souls sees the futility of obeying the rules, and before you know it, you’re run off the road by a priest in an SUV.
Unfortunately, we typically accept as rational, a common fallacy of collective action that “individuals acting in their own best interests in the short term, will eventually converge toward an optimal outcome for the group, over the long haul.” Sadly, this is usually not the case, as Garrett Hardin argued eloquently in his now well-known 1968 Science article entitled “The Tragedy of the Commons“.
Many of the problems we blame on the effects of political infighting and short-sighted leadership, can be more easily explained as failures of the Greedy Choice principle: We chose the path that seemed best at the time, but we came out weaker in the long run. For instance, why are so many American public schools substandard? Is it because our leaders are blinded by their own power, corrupted by pork-barrel budgeting and influenced by self-serving special-interests? That’s probably part of it. But a deeper and more interesting explanation is that we typically attempt to “fix” a broken school by spending more money on it. Public education clearly does not have the Greedy Choice property — you can’t necessarily get an optimal outcome by first addressing the “obvious” symptoms like low teacher salaries and inadequate facilities. Those are real issues, of course — but if we exhaust all our resources there, by the time we get to the underlying problems of parental apathy and flagging social networks, we won’t have the resources we need to work for positive change. Nevertheless, we doggedly resist taking a collective step back, to try to answer more difficult and fundamental questions, like “what should the goals of our educational system be?” and “how much do we value a free public education as a society?” It’s easier to attack the symptoms. In the long run, I’m convinced we do need to spend more money on our schools; but that’s only one piece of the pie, and we can’t consider it the whole confection.
The same can be said of other common structures adminstered by the Government, such as welfare and social security, trade and commerce, and the regulation of environmental resources: When there is a problem in one of these areas, we usually try to solve it by taking what seems to be the most advantageous step at this moment, rather than identifying longer-term advantages toward which we can work in a more reflective fashion. As individuals, we cannot simply put the blame on “the Government” or “big business”, and wash our own hands clean. Are government and corporations complicit in the ills of society? Certainly so! But are we poor individuals merely the unwitting victims of their depredations? Certainly not! Collectively, we say many nice words about saving the whales, preserving natural resources for the next generation, and fair treatment of workers; but our votes and our wallets stand firmly in support of our individual notions of the optimal outcome: Higher salaries for me. More benefits for me. Cheaper goods and services for me. Convenient transportation. Instant communications. When our leaders take a step backward, even in the hopes of greater rewards tomorrow, we punch our ballots for somebody who promises us peaches and cream today.
Now there is nothing at all wrong with wanting all these things for ourselves. But the simple fact is, devoting all of our powers and wealth to their acquisition means we are thus choosing to rate items such as education, social welfare, and natural resources as having lower priority. Not all our decisions are made in the voting booth, after all. And, what is lower-priority for the few soon becomes lower-priority for the many, because nobody wants to be the sucker stuck with the bar tab. A politician votes in favour of increased fuel-economy standards and raises gasoline taxes to pay for clean air programs, she wins accolades from environmental watchdogs. But when the cost of gas goes up, and the rate of auto sales declines due to higher cost, and the car manufacturers start laying off workers, who do you think gets voted out of office in the next election? How many times does that have to happen, before our leaders get wise to our unspoken agenda?
Seymour Papert argues that, in order to think clearly and rationally about a problem, you need a good mental model for it. He was talking specifically about children learning mathematics, but I think (and I’m fairly certain he would agree) that this is true for all of us, regardless of our ages, and in domains far beyond mathematics. It is high time we began, as a culture, to develop more sophisticated mental models for long-term societal decision making than “the market is up” vs. “the market is down”, and muzzy talking heads bickering about corporate profit and loss on television. Our life as a society does not possess the Greedy Choice property, and I believe until we individually accept this truth as something more than as simple truism, we are condemned to repeat History, whether we study it or no.