Leaky bucket paradoxes in income inequality perceptions : an experimental investigation

Leaky-bucket transactions can be regarded as a generalization of the transfer principle allowing for transaction costs. In its most rudimentary form, leaky-bucket transactions trace out the maximum leakage of transaction costs such that a transfer still pays at the margin. Yet "to pay at the margin" bears at least two different connotations: It could refer to the minimum transactions costs before a welfare loss is experienced, or before income inequality is exacerbated. These two aspects have not always be made explicit in earlier work. This notion suggests that a smaller, but positive amount of income has to reach the transferee in order to keep the degree of income inequality or the aggregate social welfare at the same level. However, this conjecture is theoretically wrong for the degree of income inequality, and partly wrong for aggregate social welfare. Rather there exists a unique benchmark such that the above holds only for transfers among income recipients below the benchmark. When they are both above the benchmark, then the transferee has to be given more than the amount taken from the transferor, and when they are on opposite sides of the benchmark, both should experience an income loss. Notice that these three cases cover only progressive transfers. Three more cases apply to regressive transfers, and six more cases apply to income donations. Each of these twelve cases ordains different theoretical results. Yet experimental research, calibrated against the Atkinson, generalized Gini, and entropy income inequality measures and their associated social welfare functions, shows that this generalized theory of the transfer principle is as poorly evidenced as is the plain transfer principle. This applies both to the income-inequality approach and to the social-welfare approach. At most one third of the subjects behave sometimes according to theory. The rest seems to follow some notion of compensating justice: If someone loses (gains) income, the other person involved should be negatively (positively) compensated to maintain the alleged degree of income inequality. This behavioral pattern is, however, at variance with theory.