Domination and Balance of Degressively Proportional Allocations

According to the principle of degressively proportional allocation, if agents are ordered so that the sequence of their entitlements is increasing, then the quotients of goods apportioned to agents and entitlements of agents generate a nonincreasing sequence. In addition, an agent with a smaller entitlement cannot receive more goods than an agent with a greater entitlement and therefore degressive proportionality can be considered as a compromise between equality and proportionality. This compromise should guarantee that the interests of both low-entitlements and high-entitlements agents are protected. This paper considers the problem of domination of one group of agents over another in a degressively proportional allocation of goods. As a result, we conclude that there is no degressively proportional allocation rule such that its domination is finite with respect to both equal and proportional sequences of weight. However, it is possible to control both types of domination described.