The convex combination rule and its relationship to Gini coefficient in the problem of degressively proportional allocation

Depending on the extent of agents’ entitlements, their desires about the outcome of the allocation of goods are distinct and asymmetric. Based on egalitarian concepts, agents with smaller entitlements tend to perceive equality as absolute equality, whereas those with larger entitlements tend to perceive it as equality of representation, i.e., proportionality. A concept which conciliates these asymmetric desires is the principle of degressively proportional goods allocation. Under this principle, both the interests of agents with small and large entitlements are protected. However, this is only a general principle and not a definite rule that allows for an unambiguous solution for each allocation problem. The following paper indicates a family of allocation rules, which, through a direct relationship with the Gini coefficient, allows for inequality control in the received allocation. Additionally, an allocation was shown in this family which reflects, as much as possible, the diversification of allocation satisfaction regarding the entitlements of all agents.