"Recently an ambitious cross-cultural study in 15 small-scale societies on four continents showed that there were, after all, sizable differences in the way some people play the Ultimatum Game. Within the Machiguenga tribe in the Amazon, the mean offer was considerably lower than in typical Western-type civilizations—26 instead of 45 percent. Conversely, many members of the Au tribe in Papua New Guinea offered more than half the pie. Cultural traditions in gift giving, and the strong obligations that result from accepting a gift, play a major role among some tribes, such as the Au. Indeed, the Au tended to reject excessively generous offers as well as miserly ones. Yet despite these cultural variations, the outcome was always far from what rational analysis would dictate for selfish players. In striking contrast to what selfish income maximizers ought to do, most people all over the world place a high value on fair outcomes. <>

Getting Emotional: Economists have explored a lot of variations of the Ultimatum Game to find what causes the emotional behavior it elicits. If, for instance, the proposer is chosen not by a flip of a coin but by better performance on a quiz, then offers are routinely a bit lower and get accepted more easily—the inequality is felt to be justified. If the proposer’s offer is chosen by a computer, responders are willing to accept considerably less money. And if several responders compete to become the one to accept a single proposer’s offer, the proposer can get away with offering a small amount.

These variations all point to one conclusion: in pairwise encounters, we do
not adopt a purely self-centered viewpoint but take account of our co-player’s
outlook. We are not interested solely in our own payoff but compare ourselves with the other party and demand fair play.

Why do we place such a high value on fairness that we reject 20 percent of a
large sum solely because the co-player gets away with four times as much?
Opinions are divided. Some game theorists believe that subjects fail to grasp
that they will interact only once. Accordingly, the players see the offer, or its rejection, simply as the first stage of an incipient bargaining process. Haggling about one’s share of a resource must surely have been a recurrent theme for our ancestors. But can it be so hard to realize that the Ultimatum Game is a one-shot interaction? Evidence from several other games indicates that experimental subjects are cognitively well aware of the difference between oneshot and repeated encounters.

Others have explained our insistence on a fair division by citing the need, for
our ancestors, to be sheltered by a strong group. Groups of hunter-gatherers depended for survival on the skills and strengths of their members. It does not help to outcompete your rival to the point where you can no longer depend on him or her in your contests with other groups. But this argument can at best explain why proposers offer large amounts, not why responders reject low offers.

Two of us (Nowak and Sigmund) and Karen M. Page of the Institute for Advanced Study in Princeton, N.J., have recently studied an evolutionary model that suggests an answer: our emotional apparatus has been shaped by millions of years of living in small groups, where it is hard to keep secrets. Our emotions are thus not finely tuned to interactions occurring under strict anonymity. We expect that our friends, colleagues and neighbors will notice our decisions. If others know that I am content with a small share, they are likely to make me low offers; if I am known to become angry when facing a low offer and to reject the deal, others have an incentive to make me high offers. Consequently, evolution should have favored emotional responses to low offers. Because one-shot interactions were rare during human evolution, these emotions do not discriminate between one-shot and repeated interactions. This is probably an important reason why many of us respond emotionally to low offers in the Ultimatum Game. We may feel that we must reject a dismal offer in order to keep our self-esteem. From an evolutionary
viewpoint, this self-esteem is an internal device for acquiring a reputation,
which is beneficial in future encounters."

Source: The Economics of Fair Play, Karl Sigmund et al. 

Brock,
You may have turned down $4, but would you have turned done $4,000 over a sense of fairness? Probably not. 

If I were you, I wouldn't bet $6,000 on that.

When I say I require fairness, I mean it. Size matters not.