Against the proportionality principle: Experimental findings on bargaining over losses

The outcomes of bargaining over losses, the subject of this paper, have rarely been studied. But experimental studies of related situations, such as those involving bankruptcies or bequests in which the sum of the legal claims that can be made against a bank or firm or estate are greater than their values, have produced strong support for the proportionality principle. To test whether this principle would find support in other situations involving losses we designed an experimental game in which four players start out with differing initial endowments of real money. They are then informed that a certain amount of this resource has to be given back to the experimenter. How should the loss be shared among the agents? This game was run at different locations and under different treatments over a period of almost three years. We found that the proportionality principle was rarely proposed and even less frequently accepted as a solution to this problem. One of the main reasons for this result was that the two players with the smallest endowments opposed most of the proposals which asked them to contribute at least some positive amount of their own initial resource.