Abstract: In apportionment problems, allocation rules are often defined using real-valued functions. When defining such a rule, one typically considers the values of a selected function at points corresponding to the sequence of entitlements of agents participating in the division, and uses appropriately chosen rounding to determine the allocation. This idea is characteristic, for example, of all divisor methods widely used in practical electoral problems. However, this is not the only possible construction. In discussions regarding degressively proportional seat allocation in the European Parliament, other methods of using real functions to construct allocation rules are also known. This paper presents a classification of these methods, taking into account current practices and substantive differences between the various concepts. This allowed for a clear distinction between two types of functions, namely adjustment functions and allocation functions.

Keywords: apportionment problem, degressive proportionality, fair division, elections, European Parliament, voting

Pages: 2536-2543