For the past 25 years experimental economists--of which I am one--have been infatuated with a pie-splitting problem known as the Ultimatum Game. Experimental economists are the hands-on tinkerers of my profession; where other economists attempt to build models from first principles, or extract empirical data from a messy universe, we build our own little universe out of volunteers and computers, and see how our theories work when real people get our hands on them. The Ultimatum Game is so popular because it is simple to explain and simple to run, yet its results involve one of the most complex problems of society: what are we saying when we say something is "fair"?





If you're anything like most Americans, you probably hear or speak that word many times a day. "It's not fair!" screams the petulant child. "That's a fair price," claims the smooth salesman. "I'm trying to be fair," sighs your boss. The magical mystery of fairness is that everyone knows what people are saying when they claim that something is (or isn't) fair--and yet agreement on fairness itself often eludes us. The ultimatum game is the economist's attempt to understand how fairness works.





In the standard version of the game, two people are paired, and one of them is randomly selected to receive $10. That person is called the "proposer", while the other volunteer is known as the "responder". That's because once he receives the $10, the proposer has the responsibility of offering some number of his dollars to the responder. The responder, as the name suggests, gets to decide whether to take that offer.





Here's the twist: if the responder rejects the offer, neither of them gets anything.





In an experiment run by robots, where neither party has any sense of fairness to be offended, the natural result should be that the proposer offers a single dollar. After all, $1 is better than nothing, and if computers had noses, they wouldn't cut them off to spite their face. People, on the other hand, do it all the time. If they don't think the offer is enough, they won't take it--they will cost themselves money just to punish the proposer. They don't care what is optimal; they care about what is fair.





If you listen to the discussions that go on during and after these experiments, that's what you hear, over and over. The logic tends to be a bit circular:





"Why did the proposer offer $5 to the responder?"

"Because that's fair."

"What is a fair outcome in the ultimatum game?"

"The proposer offers $5 to the responder."





That's not a very satisfactory defintion: fairness is both the cause for the action, and the effect of it. We need more precision, because as the Ultimatum Game illustrates, unless markets are fair, they do not work very well. To coin a phrase, we are always dependent on the fairness of strangers.





Because the word is so central to how markets work, I've been engaged in a somewhat dizzying struggle to understand it better, or at least clarify how economists apply it to economic behavior. That's the topic of my latest paper. Early in my project I turned to one of my favorite linguists, Anna Wierzbicka of Australia National University, for her insight into the meaning of the word. Luckily for me, when I emailed her she pointed out that she had recently published a whole chapter on this very topic in her book English: Meaning and Culture .





Did you know that fair is one-to-one untranslatable into any other language--that it is distinctly Anglo in origin? And a relatively new word at that? (Late 18th century, actually--the industrial revolution apparently also vastly enhanced our capacity to complain.) But the twisted history of "fair" is even more interesting than that. For the original antonym of fair is not, as most modern Americans would probably expect, unfair. If you want to understand the roots of fairness, look not to ethicists, but to baseball, which still uses the original dichotomy. If a ball is hit outside the bounds of fair play, it's not unfair--it's foul. That's an important clue. As Columbia law professor George Fletcher had noted in his 1996 book Basic Concepts of Legal Thought, the Anglo-American notion of fairness is firmly rooted in the rules of a game.





These observations have deep implications for our understanding of this social concept, particularly as it relates to economics. Let me be clear: I am not claiming that Anglophones are the only fair people on the planet. It's just that fair doesn't have an exact equivalent in any other language. Other languages either directly import the English word, as in the German exclamation, "Das ist nicht fair!", or fail altogether to have a comparable word, as is the case for French.





German speakers might note that they frequently also use the word gerecht in addition to fair; French speakers might say that they have not one but two words for it: juste and équitable. True enough. However, depending upon context, gerecht is also translatable into English as just or equitable. That's a three-to-one translation, not one-to-one, and probably one reason why the Germans directly import the English word. And while équitable is often translated as "fair", it can also be rendered as equitable, and similarly, juste can be translated into English as just. These languages may have the sense of fairness, but we have a word for it that they do not.





All very interesting, but . . . why does this matter? For one thing, it suggests that the concept of fairness is not necessarily ubiquitous to human cultures. More importantly, however, the translation problem actually helps us to pin down the concept of fairness as it relates to justice and equity. Wierzbicka makes a compelling case for the differences in meaning among fair, just, and equitable, which can be illustrated by the rules of another game.





When the NBA suspends players for leaving the bench to join a fight on the court, the question that sports commentators debate is "Are the suspensions fair?", not "Are the suspensions just?", nor "Are the suspensions equitable?" There's no moral first principle that tells us whether players on the bench should be allowed to join fights. Nor is the central issue whether all the players got punished equally. As Steve Pinker might note, the case for claiming that the words are different is simply that it doesn't feel right to substitute the words interchangeably in context after context, even if some contexts are ambiguous. The question then becomes, what are the common features of the contexts in which we feel uneasy using a word other than fair?





Wierzbicka's research indicated that there are two key contextual elements that make fair precisely the right word for the situation. First, the circumstances entail a tradeoff in welfare between individuals: some action benefits one person at the expense of another. The second element is that other people in the community think that there are limits to how much people are allowed to cost others in order to benefit themselves.





Suspending players who join fights makes all basketball players better off by decreasing the number of fights that get out of hand. Nonetheless, suspensions are hotly debated, because the community demands balance--suspensions need to be long enough to deter fights without crippling the careers of the players involved. The desired balance is highly context-specific, and so sports commentators and fans endlessly discuss exactly what circumstances are relevant in determining what constitutes acceptable suspensions. A player coming off the bench to engage a fight on the court calls for much different response than a player already on court, or a player who heads into the stands to deck a fan.





How does this free us from that circular reasoning we saw in the ultimatum game? Instead of looking inwards for some inherent sense of the word, we look outward, towards the community standards that externally ground the interaction. When two subjects are randomly assigned to the roles of proposer and responder, it is not some pure platonic ideal of fairness that causes a proposer to offer $5. Rather, the proposer knows that other people would think offering less than $5 is below the socially acceptable limit in this situation, and so the proposer obeys those tacit rules.





This explains another widely observed phenomenon: proposers who have earned the right be the proposer, say by doing well on a quiz, offer much less to responders than those who are randomly chosen. What is truly amazing is how accurately proposers ascertain the limits of what they can offer. The rate at which their responders reject their offers doesn't change when proposers who have earned their position offer them a smaller portion of the pie[1]. We (most of us) implicitly agree that earning an advantaged position calls for the application of different rules than does randomly endowing someone with a windfall. Moreover, we all have a pretty good sense of what those rules are; most offers are accepted.





No matter how much we may feel that fairness is a pure principle, it's really a regular social rule, a custom. (Another surprispingly revealing word: you have probably seen the words "customary rates" applied to gratuities and sales commissions). Fairness really boils down to an issue of agreement: can we agree on what rules this particular context calls for? In a future post, I'll expand on what this means for markets and public policy. Until then, let me leave you with another observation of how a small change in the circumstances changes behavior.





A while back, experimenters tried to focus the proposers on the responder's alternatives by asking them to consider what the responder might be expecting. The experimenters expected this to lower the average offer, by reminding proposers of the fact that anything they gave the responders was better than nothing. What they found, to their surprise, was that proposers significantly increased their offers. Just mulling the "customary rate" seems to lead proposers to focus on the possibility that responders may not agree with a lower offer--and hence to make higher offers. [2]





That's why we're hands-on tinkerers. You never know what you're going to get until you actually run the experiment.





Update : The New Yorker's James Surowiecki : The New Yorker's James Surowiecki asks a good question about how much cross-cultural variation there really is in our sense of fairness. The answer is, a surprising amount





[1] [Hoffman, Elizabeth, Kevin McCabe, Keith Shachat, and Vernon L. Smith. 1994. "Preferences, Property Rights, and Anonymity in Bargaining Games." Games and Economic Behavior, 7(3): 346-380]





[2] [Hoffman, Elizabeth, Kevin McCabe, and Vernon L. Smith. 2000. "The Impact of Exchange Context on the Activation of Equity in Ultimatum Games." Experimental Economics, 3(1): 5-9]