Normative and Descriptive Applications of the Concept of Degressive and Progressive Proportionality

The idea of “degressive proportionality” is associated primarily with the division of seats in the European Parliament, but this concept, after its clarification, may have much more universal applications. The precise definition of the class of digressively/progressively proportional apportionment methods as well as the definition of the "degressivity/progressivity" factor in the division of seats, allows both the strict design of allocation methods (eg in the European Parliament) to obtain an apportionment with precisely intended properties, and describe, in terms of the power of degression/progression, real divisions, e.g. resulting from specific parliamentary elections, or obtained as a result of the application of the analyzed division methods in simulation research. The paper contains: a proposal for the method of degressively/progressively proportional apportionment of mandates, referring to the formal definition of degressivity/progressivity, an example of its application in relation to the European Parliament ("normative application"), and examples of applying this concept in the analysis of the actual divisions of seats in national parliaments of European countries ('descriptive use'). The formal definition of "degressive / progressive proportionality" can be obtained by extending the concept of "proportionality". If A has twice the size of the entitlement than B, then the proportional allocation should give A twice as large a share as B. The "degressively proportional" allocation should instead allocate A share less than twice as large. The greater the degressivity strength is, the more the A share will be closer to the share of B. For example, in the European Parliament Romania, with 20 million inhabitants, obtained 32 seats, or 1.52 seats number of Hungary (9.9 million inhabitants, 21 seats). If we assume that such a ratio of the number of seats should be kept between all countries with twice the number of inhabitants, it can be easily demonstrated that the distribution of seats should not be proportional to the number of inhabitants, but to the number of inhabitants raised to the power of log2 (1.52) = 0.6. This value is a parameter or the factor of the degressivity strength of the division. Analyzing the proportions of the number of seats between EU countries, one can find the value of degressivity best suited to the actual division obtained through political agreement, and then propose a division that is closest to the political compromise and at the same time based on a strict and objective basis. An analogous method can be applied to the analysis of the distribution of seats in other parliamentary elections. However, because in most of the real election systems it is characterized by a certain privilege of large parties, the determined value of the degressiovity / progression factor will be greater than 1, which corresponds to a progressively proportional division. This value - calculated for elections in different countries, using different systems, can be used to characterize and compare them due to the empirical strength of the progressiveness of a given electoral system.