Abstract
In the case of the proportional allocation of goods and burdens, the shares of all agents with respect to their values are equal, i.e., they form a constant sequence. In a degressively proportional allocation this sequence is nondecreasing when agents are increasingly ordered according to their values. The division performed according to this principle is ambiguous, and its selection requires many negotiations among participants. The aim of this paper is to limit the range of such negotiations when the problem is complex, i.e., the set of feasible solutions has high cardinality. It can be done thanks to a numerical analysis of the set of all feasible solutions, and eliminating allocations favoring or disfavoring some coalitions of agents. The problem is illustrated by the case study of allocating seats in the European Parliament in its 2019–2024 term.
Highlights
The problem of allocation of gains and burdens emerges in many aspects of social life
Local government entities and management boards of large corporations decide about fair distribution, while entire societies participate in general elections to allocate seats in collegial bodies to their representatives
A natural and widely applied principle of fair distribution is the rule of proportionality that originated from Aristotle
Summary
The problem of allocation of gains and burdens emerges in many aspects of social life. Local government entities and management boards of large corporations decide about fair distribution, while entire societies participate in general elections to allocate seats in collegial bodies to their representatives. In most cases the fair allocation depends on the values representing the respective participants in the division. Those values are sometimes called entitlements and are typically expressed by numbers. A natural and widely applied principle of fair distribution is the rule of proportionality that originated from Aristotle. According to this principle, the share of each agent in the distributed good should be equal to the quotient of its value to the total value of all contenders
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