rules of fair division

abstract: the subject of this note is the problem of equitable or fair division. we consider the simple case, where two individuals have to split a constant sum of money, say us-dollars 100, which they will get by reaching an agreement. the divisionshould satisfy both, in the sense that everyone considers his amount as a fair share. in welfare economics and game theory different rules or schemes were proposed to solve this problem. the most important of this fair division schemes are discussedin this paper. first we consider three rules, the kemeny solution, the nash solution, and the welfare solution, and compare this rules with the axioms of nash's bargaining problem. in the second part we give a new interpretation and a rigorous proofof a remarkable theorem of lerner. this rule is not consistent with the bargaining model of nash, because it involves uncertainty, whereas the first three refer to decisions under certainty.