When Peter, who will take a third and a third only, encounters Mary, who consistently demands two thirds, they divide the resource amicably, and come out clearly ahead of their poor and brutish neighbors. However, asking two thirds is sometimes too much if you encounter another with the same strategy, there can be no peaceful solution. Similarly, asking one third is too little if the other is like you. Luckily, this strategy can also move Hobbesville out of its compulsive squalor. While a chance mutation producing a single Rousseauan would have no advantage, a small group of fair-minded individuals could establish a foothold if they had a preference for dealing with each other.
Fair division is the single evolutionarily stable strategy.
An inclination towards fair division, then, is the predicted outcome of the evolutionary process. This means we should expand the subjective utility function to include a sense of fairness. Rather than assuming, as Hobbes did, that selfishness is the bedrock of human motivational psychology, an evolutionary consideration leads us to expect fairness to be valued for itself. Fair sharing, however, is a windfall mentality, and does not solve a host of other problems relating to cooperation. The rational act is predicated upon the extreme case of interacting exclusively with individuals who have the same strategy as yourself what game theorists call perfect correlation.