I examine from a conventionalist perspective the Nash bargaining problem that philosophers use as a tool for analyzing fair division. From this perspective, the solutions to bargaining problems are conventions that can emerge from inductive learning and focal point effects. I contrast the conventionalist approach to analyzing the bargaining problem with the better-known rational choice approach, which I criticize for having overly demanding epistemic presuppositions and for producing disappointing results. I apply a simple model of inductive learning to specific bargaining problems to show that agents can learn from repeated experience to follow a variety of bargaining conventions in a given problem. I conclude that such agents can come to regard two such conventions as focal for the bargaining problem, one that assigns claimants equal shares of a good and another egalitarian solution of equal payoff gains, and that the egalitarian solution tends to prevail when these two solutions differ. I conclude further that the above analysis lends support for admitting interpersonal utility comparisons into the analysis of fair division problems, and also suggests a focal point explanation of the wide acceptance of the Aristotelian proportionality principle of distributive justice.