Abstract:

Two major mathematical issues related to the governance in European Union are discussed:

a) Voting rules in the European Council,

b) Allocation of seats in the European Parliament.

Each member state is represented in the European Council by a single representative, which takes part in weighted voting with a qualified majority. We review the theory of Penrose, according to which the voting power of any citizen of any state is equal, if the voting weights are proportional to the square root of the population of each Member State. The proposed voting system, called Jagiellonian Compromise (JagCom), is based on the Penrose law. For EU-27 the value of the optimal threshold of qualified majority is around 61%.

In the case of the European Parliament, each Member State sends several of their representatives. They vote separately, so their votes can differ to optimally represent the point of views of their electorate. This assumption leads to the linear dependence between the population of a given state and the number of Parliament members representing this state. We review certain apportionment functions and show that the constitutional constraints are so strong that admissible functions lead to rather similar solutions. In particular, we discuss the partition of 705 MP adopted by the European Parliament after Brexit in January 2020, equivalent to a fixed base plus a term proportional to the population.

Public talk within the QIM (Quantum Information Malta) Workshop Malta 2023, organised by the University of Malta, with the financial support of the Malta Council for Science and Technology (MCST).