This paper, authored by Ehud Kalai, explores the concept of proportional solutions in bargaining situations, focusing on interpersonal utility comparisons. The author describes a bargaining situation as a set of feasible outcomes when individuals cooperate and an outcome when they do not. The paper aims to determine which cooperative outcome will be chosen, using a Nash-type approach to prove that under plausible axioms, individuals must compare their utilities interpersonally. The model and solution proposed in the paper address some difficulties highlighted by Nydegger and Owen. The solution differs from Harsanyi's interpersonal utility comparison in that it suggests maximizing utilities while ensuring equal gains for all players, rather than maximizing the sum of individual utilities. The paper introduces two principles: monotonicity and step-by-step negotiation. Monotonicity ensures that no player loses utility due to new options, while step-by-step negotiation restricts solutions to those that are invariant under decomposing the bargaining process into stages. The author shows that both principles imply interpersonal utility comparisons. The main results of the paper are: 1. A solution is monotonic if and only if it is proportional. 2. A solution satisfies the step-by-step negotiation condition if and only if it is proportional. 3. A solution satisfies the conditions of independence of irrelevant alternatives (IIA), individual monotonicity (IM), and continuity if and only if it is proportional. The paper concludes by discussing the implications of these results, including the difficulty of determining the specific proportions of utility gains and the connection to Rawls' max-min approach to justice. The proportional solution suggests that all individuals should receive equal utility gains in every bargaining situation. The paper also raises questions about the applicability of these findings to n-person cooperative games without sidepayments.This paper, authored by Ehud Kalai, explores the concept of proportional solutions in bargaining situations, focusing on interpersonal utility comparisons. The author describes a bargaining situation as a set of feasible outcomes when individuals cooperate and an outcome when they do not. The paper aims to determine which cooperative outcome will be chosen, using a Nash-type approach to prove that under plausible axioms, individuals must compare their utilities interpersonally. The model and solution proposed in the paper address some difficulties highlighted by Nydegger and Owen. The solution differs from Harsanyi's interpersonal utility comparison in that it suggests maximizing utilities while ensuring equal gains for all players, rather than maximizing the sum of individual utilities. The paper introduces two principles: monotonicity and step-by-step negotiation. Monotonicity ensures that no player loses utility due to new options, while step-by-step negotiation restricts solutions to those that are invariant under decomposing the bargaining process into stages. The author shows that both principles imply interpersonal utility comparisons. The main results of the paper are: 1. A solution is monotonic if and only if it is proportional. 2. A solution satisfies the step-by-step negotiation condition if and only if it is proportional. 3. A solution satisfies the conditions of independence of irrelevant alternatives (IIA), individual monotonicity (IM), and continuity if and only if it is proportional. The paper concludes by discussing the implications of these results, including the difficulty of determining the specific proportions of utility gains and the connection to Rawls' max-min approach to justice. The proportional solution suggests that all individuals should receive equal utility gains in every bargaining situation. The paper also raises questions about the applicability of these findings to n-person cooperative games without sidepayments.