This week Occupy Math looks at the myth of zero-sum games. A game is zero-sum if all gains by some players are exactly balanced by losses by others. Examples of zero-sum games are poker (with friends — no house cut), rock-paper-scissors, or any simple game in which one player wins and the other loses. People very often declare that a social or political situation “is a zero-sum game”. What’s the problem here?
Many games (and most social and political situations) are not zero-sum — and people promote conflict and waste by claiming they are.
Occupy Math has already done an entire post on prisoner’s dilemma which is not a zero-sum game at all. It models cooperation and conflict, with the potential for all winners or all losers. The game is interesting because the highest payoff for one player and the highest total payoff are incompatible — and trying for the highest individual payoff often leads to the lowest total payoff. That, however, is very much a mathematical abstraction. Let’s look at real world situations and games that model it.
In 1904, Oliver Wendell Holmes, Jr. said that “taxes are the price we pay for a civilized society”. A common point of view in modern politics is that taxes are a waste and a boondoggle with the deeply stupid slogan It’s your money. When smart people say stupid things, its because they are trying to trick you. The slogan “It’s your money” pretends that taxes are a zero-sum game, that either you have the money or the government does. While that seems pretty obvious, it is a very narrow view that ignores many important factors. Let’s look at some of them.
- Waste, fraud, and abuse. One big way that taxes are not a zero-sum game is that the money is sometimes completely wasted. The famous bridge to nowhere, defense contracts that yield no defense, or public health spending on stuff that only works because of the placebo effect. The examples are almost endless.
- Transport. Taxes are used to maintain the transportation network. From the roads to air traffic control, tax money keeps people moving, goods flowing, and the modern economy moving along. The wealth and freedom generated by transportation infrastructure is incredibly more valuable than the tax money spent on it.
- Public education. An educated populace makes better decisions on average, creates more wealth, pays more taxes, and is better able to take care of itself. An extreme example of the benefits of publicly funded education is the relationship, in the developing world, between educating women and containing population growth. The short version is that educated women have fewer children. Education is phenomenally non-zero-sum.
- Research and conservation of knowledge. From public libraries which are everywhere to the original research funded by the NSF, NIH, NSERC, DARPA, CIHR, NEA, DOE, ERC, USDA, and a hundred other government organizations in dozens of countries, tax dollars allow us to retain, use, and extend our cultural wealth. Curing disease, extending lifespan, discovering microchips, conserving nature, and feeding the world better than ever before all follow from tax dollars. An incredible return on investment.
In summary, the implication that taxes are a zero-sum game is both common and untrue in every possible way.
Consider the public goods game. This game models public taxation. Each player is given some money. They then secretly contribute some, all, or none of that money to a common pool by passing a concealed envelope. The experimenter then doubles the money in the envelope and divides the result evenly among the participants. This game models the behavior involved in public taxation under the assumption that it is not difficult to cheat on your taxes. Notice that the total payout is highest when everyone contributes all their money — but the person with the highest comparative payout is the one that contributes the least. While there are many variations of this game, a very common result is that people are happy to let others pay for the benefits they receive. If everyone else pays for the roads, you can still drive on them. This creates a slippery slope, however, where the roads are not maintained, necessitating warm, fuzzy organizations like the IRS.
A famous example in this area is Warren Buffet’s observation that he pays a lower tax rate than his secretary. Mr. Buffet feels that this is unjust — and he has a point. Rich people have a lot of options to keep their tax rates low Donald Trump famously avoided some or all of his taxes for years — which would not be fair if they were getting the same benefits as the rest of us, but they are not. Rich people benefit far more from public taxation than the rest of us.
For example, a rich businessman uses the transport network far more than the average citizen.
The scientific and medical research that benefits us all is more available to and often generates profits for the wealthy in a disproportionate fashion. Wealth brings greater access to the media, meaning that the rich have greater access to free speech than the average citizen. In a just world their tax rate would be higher, not lower. There is game theory here too: the ability to control the rules of the game is the ultimate source of ability to win. Ironically,
Rigging the game so the rich win big hurts even the rich.
Henry Ford paid his workers well and said that his motive was that he did not want anyone working for him that could not afford his car. The wealthy need consumers and a working economy to maintain their wealth. There is a correct range of taxation — if you can minimize waste, fraud, and abuse — that maximizes the public good, though we are still arguing about how to compute it. It matters a lot what you spend the money on and there are many options. All this complexity aside, pretending taxation is a zero-sum game and that the government is your opponent is a road to ruin. You have to watch the government like a hawk and insist at the ballot box that it acts as a responsible steward of the public purse, but with an alert citizenry the government can, and has, done an incredible amount of good and generated phenomenal wealth.
The current political movement that characterizes all government spending as a waste ignores the public good in favor of various private goods. It is part of a diseased belief that, in order for one person to win, another must lose. Concentration of wealth is an example of a positive feedback loop with the potential for destructive effects. Well run systems are almost never zero-sum games and its important to be able to identify what the potential outcomes are and how they might be better or worse than zero-sum. A sharp eye for the win-win situation is what is needed.
Lets end with an interesting example that gives some caveats. An example of a worse than zero-sum game is the ultimatum game. An amount of money is at stake. One player proposes a division of the funds, the second accepts or rejects this division. If the second player accepts, the division of the money is as the first player proposes, otherwise no one gets anything. This game has a zero-sum outcome — the money as stated is just divided — and an outcome that completely wastes the money. This game models a situation in which a deal is being contemplated but, for some reason, there is only one chance to agree.
Most of what we know about the ultimatum game comes from experiments run on American college students taking economics or psychology classes. They typically demand near-parity. The excellent work of Joseph Henrich shows that these results may not be representative. To oversimplify some of his results, there are parts of Asia where no division of the money with funds going to the second player is acceptable because it is perceived as a gift that creates an obligation. On the other side of the spectrum of possibilities, there are places in Africa in which there is no expectation of parity and any proposed amount is welcome. The caveat is this — what we know about zero-sum games, economic games, and the politics of taxation are very much centered in our own culture.
The take home message is that few games are zero-sum and cooperation is definitely positive-sum.
There are many other interesting economic games and dozens of variations on the games Occupy Math has mentioned in this post. All of them are tools for the mathematical and experimental analysis of human behavior, an evidence-based technique that is used all too seldom. Keep firmly in mind that claiming a zero-sum situation is often a tool of deception and oppression and check the situation for yourself. Someone who is speaking nonsense may be a fool, but it is more likely that they have motives that are not transparent. Occupy Math hopes you have enjoyed this post, but don’t make him guess: comment or tweet!
I hope to see you here again,
University of Guelph,
Department of Mathematics and Statistics