Prof. Dr. Karol Zyczkowski, Jagiellonian Universität Krakau und Center for Theoretical Physics Warschau

Voting in the European Council: a mathematical approach

Termin: 08.04.2021

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Veranstalter: Dimitris-Tsatsos-Institut für Europäische Verfassungswissenschaften (DTIEV)

Der Vortrag wird in englischer Sprache gehalten.

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. 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 their representatives. They vote separately, so their votes can differ to optimally represent 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.

Karol Zyczkowski is Professor at Center for Theoretical Physics, Polish Academy of Sciences in Warsaw and Professor of Physics – Polish state title & position at the Jagiellonian University in Cracow. His research interests are: quantum theory, quantum information processing, quantum entanglement, classical and quantum chaos, nonlinear dynamics, random matrices, applied mathematics, applications of statistical physics in social sciences and economy, mathematical theory of social choice and voting theory.

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