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This study is theoretically anchored in the office-seeking approach and coalition theory of political science. It is based on the most widespread theories of portfolio distribution in executive and legislative bodies (proportionality, power index, voting weights), and it tests these theories using data related to coalition negotiations in the Czech Republic for the new 2021 government coalition, a case of a surplus majority government. The study investigates the distribution of ministerial positions in the government, the office of President (Speaker) of the Chamber of Deputies, and the chairs of permanent parliamentary committees. The analysis also explores the types of electoral coalitions formed; the SPOLU coalition was a superadditive coalition, while the PirSTAN coalition was only an additive coalition. Grounded in the theory of electoral games, the Shapley-Shubik and Banzhaf power indices and the theory of coalition formation are applied in order to analyse the possible minimal winning coalitions that could be formed following the 2021 elections to the Chamber of Deputies. [ABSTRACT FROM AUTHOR]

In this paper, we extend the Banzhaf–Coleman–Dubey–Shapley sensitivity index to the class of dichotomous voting games with several levels of approval in input, also known as (j, 2)-simple games. For previous works, on classical simple games ((2, 2)-simple games), a sensitivity index reflects the volatility or degree of suspense in the voting body. Using a set of independent axioms, we provide an axiomatic characterization of that extension on the class of (j, 2)-simple games. [ABSTRACT FROM AUTHOR]

In this paper, we propose an axiomatization of the totally critical raw Banzhaf index (TCRBI). In the literature, the TCRBI was introduced as a generalization of the Banzhaf power index on the class of yes–no voting games with several ordered levels of approval in input ((j, 2)-simple games). Its principal strength, compared to earlier generalizations of the Banzhaf power index, is the fact that it preserves the desirability relation regardless of the number of input levels of approval. Our main result is that, up to a multiplicative positive real number, the TCRBI is the only power index on the class of (j, 2)-simple games, satisfying the following set of axioms : Equal treatment, Positivity, Null Player, and Linear Transfer. [ABSTRACT FROM AUTHOR]

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The power of individual EU Member States has been changing over the past decades as a result of revisions to the voting systems and the enlargements of the European Union. The present article analyses the development of the voting power of individual Member States in the Council of the European Union before and after the withdrawal of the United Kingdom of Great Britain and Northern Ireland from the European Union. We use the calculation of the standardized Banzhaf power index to calculate the legislative power of the Member States. The calculations recorded in the table point to changes in the weights of national votes caused by Brexit. The article pays special attention to the Visegrad Group, which we define within the European Union as an informal group consisting of four Central European states - the Czech Republic, Hungary, Poland, and the Slovak Republic. The results indicate a significant growth of the voting power in Poland and more moderate growth in the other three Visegrad Group countries which contributes to the shift in the voting equilibrium within the ordinary legislative procedure of the European Union.

The power of individual EU Member States has been changing over the past decades as a result of revisions to the voting systems and the enlargements of the European Union. The present article analyses the development of the voting power of individual Member States in the Council of the European Union before and after the withdrawal of the United Kingdom of Great Britain and Northern Ireland from the European Union. We use the calculation of the standardized Banzhaf power index to calculate the legislative power of the Member States. The calculations recorded in the table point to changes in the weights of national votes caused by Brexit. The article pays special attention to the Visegrad Group, which we define within the European Union as an informal group consisting of four Central European states - the Czech Republic, Hungary, Poland, and the Slovak Republic. The results indicate a significant growth of the voting power in Poland and more moderate growth in the other three Visegrad Group countries which contributes to the shift in the voting equilibrium within the ordinary legislative procedure of the European Union. [ABSTRACT FROM AUTHOR]