Does a sense of fairness make us better bargainers?

Most ultimatum games, in which one player makes a take-it-or-leave-it offer to another, result 60-40 splits.  This occurs because the player making the offer knows that their offers will be rejected if seen as too "unfair." Some hypothesize that this notion of fairness makes us better bargainers so there might be some evolutionary basis for passing on a sense of fairness.

See how monkeys behave when they get an unfair payoff.