This paper discusses proportional solutions to bargaining situations, focusing on interpersonal utility comparisons. The author, Ehud Kalai, presents a model where individuals must compare utilities to reach a cooperative outcome. The paper addresses the question of which cooperative outcome will be chosen in a bargaining situation, using a Nash-type approach. It shows that under plausible axioms, individuals must be doing interpersonal utility comparisons. The paper introduces two principles: monotonicity and negotiation by stages. Monotonicity states that if additional options are available, no one should lose utility. Negotiation by stages restricts solutions to those invariant under decomposition of the bargaining process into stages. The paper also discusses the Nash condition of independence of irrelevant alternatives and individual monotonicity, showing that these are compatible in the author's model and lead to interpersonal utility comparisons. The paper presents a solution that is proportional, meaning that individuals gain "equally" in the given situation. This is related to John Rawls' approach in "A Theory of Justice." The paper also addresses the difficulty of the indeterminacy of the scale of the utility functions, suggesting that agreement proportions can be left as open parameters. The paper concludes that proportional solutions are necessary for fair bargaining outcomes, and that these solutions can be derived from a "simple" game and applied to more complex games. The paper also discusses the connection between the proposed solution and Rawls' max-min approach to justice. The results show that proportional solutions are descriptive and not applicative, but they provide a framework for understanding how individuals should compromise in different bargaining situations.This paper discusses proportional solutions to bargaining situations, focusing on interpersonal utility comparisons. The author, Ehud Kalai, presents a model where individuals must compare utilities to reach a cooperative outcome. The paper addresses the question of which cooperative outcome will be chosen in a bargaining situation, using a Nash-type approach. It shows that under plausible axioms, individuals must be doing interpersonal utility comparisons. The paper introduces two principles: monotonicity and negotiation by stages. Monotonicity states that if additional options are available, no one should lose utility. Negotiation by stages restricts solutions to those invariant under decomposition of the bargaining process into stages. The paper also discusses the Nash condition of independence of irrelevant alternatives and individual monotonicity, showing that these are compatible in the author's model and lead to interpersonal utility comparisons. The paper presents a solution that is proportional, meaning that individuals gain "equally" in the given situation. This is related to John Rawls' approach in "A Theory of Justice." The paper also addresses the difficulty of the indeterminacy of the scale of the utility functions, suggesting that agreement proportions can be left as open parameters. The paper concludes that proportional solutions are necessary for fair bargaining outcomes, and that these solutions can be derived from a "simple" game and applied to more complex games. The paper also discusses the connection between the proposed solution and Rawls' max-min approach to justice. The results show that proportional solutions are descriptive and not applicative, but they provide a framework for understanding how individuals should compromise in different bargaining situations.