One of the main problems of practical applications of degressively proportional allocations of goods and burdens is lack of uniqueness of this principle. Even under given boundary conditions of allocation, i.e. determined minimal and maximal amounts of a good that can be assigned in a given allocation, there are usually many feasible solutions. The lack of formal rules of allocation is the reason why the allocation is typically a result of negotiations among its agents. A number of allocations favor some of agents or their groups, therefore other agents cannot accept them. The aim of this paper is to indicate a way of reducing the set of all feasible solutions exclusively to those that are neutral to all agents. As a result of the term of lexicographic preference of allocation agents defined on the basis of the relation theory followed by a numerical analysis of sets of all feasible solutions, it is possible to determine a core of this set in the form of a subset of all feasible solutions that are acceptable by all agents. In addition, this subset can be further divided into smaller subsets with regard to the degree of acceptance of their elements. Theoretical analysis is complemented by case studies, one of which is application of this idea to the allocation of seats in the European Parliament among the member states of the European Union.

商品和负担递减比例分配的实际应用的主要问题之一是缺乏该原则的唯一性。即使在给定的分配边界条件下，即在给定分配中可以分配的物品的确定最小和最大数量，通常也有许多可行的解决方案。分配的正式规则的缺乏是分配通常是其代理之间协商的结果的原因。许多分配有利于某些代理或其组，因此其他代理无法接受它们。本文的目的是指出一种将所有可行解的集合专门化为对所有代理都是中性的解集的方法。由于基于关系理论定义的分配代理的词典偏好术语，然后对所有可行解的集合进行数值分析，因此可以以所有可行解的子集的形式确定该集合的核心所有代理都可接受的可行解决方案。此外，该子集还可以根据其元素的接受程度进一步划分为更小的子集。理论分析得到案例研究的补充，其中之一是将这一想法应用于欧盟成员国之间欧洲议会席位的分配。这个子集可以根据其元素的接受程度进一步划分为更小的子集。理论分析得到案例研究的补充，其中之一是将这一想法应用于欧盟成员国之间欧洲议会席位的分配。这个子集可以根据其元素的接受程度进一步划分为更小的子集。理论分析得到案例研究的补充，其中之一是将这一想法应用于欧盟成员国之间欧洲议会席位的分配。