Dimension of the Lisbon voting rules in the EU Council: a challenge and new world record

Kurz, Sascha; Napel, Stefan

doi:10.1007/s11590-015-0917-0

Cited by 29 publications

(45 citation statements)

References 13 publications

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“…This leads direct enumeration to be the only feasible way of certifying which coalitions are winning and which ones are losing. The computational study by Kurz and Napel (2016) shows that dimension of the Lisbon voting system is at least seven, i.e. a combination of at least seven weighted voting games is needed to obtain the set of winning coalitions under the Lisbon voting system.…”

Section: Winning Coalitions and The Analysis Of Decision Efficiencymentioning

confidence: 99%

Vote Probabilities, Thresholds and Actor Preferences: Decision Capacity and the Council of the European Union

2018

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This paper studies how voting rules affect the ease with which decisions are made, basing the analysis on the key premise that ideology makes some coalitions more likely to form than others. Our study focuses on the Council of the European Union (EU), where member states hold different voting weights and ideological positions are strongly linked to the affiliation of actors to political parties. Accordingly, to explore the influence of ideology on the probability of coalition formation, and to thus formulate a 'decision probability', we incorporate ideological positions in the analysis of efficiency of the voting system. For the case of the EU, we particularly consider the transition from the triple-majority voting system of the Nice Treaty to the double-majority system incorporated into the Lisbon Treaty. The standard assumption that member states vote independently and affirmatively with a probability of 0.5 leads to a more pessimistic view of the Council's decisionmaking capacity than does the premise that member state votes are biased towards voting with the Council majority. The latter assumption is supported by voting data and anecdotal evidence on the 'consensus-seeking' culture in the Council. Hence, * Madeleine O. Hosli

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Section: Winning Coalitions and The Analysis Of Decision Efficiencymentioning

confidence: 99%

Vote Probabilities, Thresholds and Actor Preferences: Decision Capacity and the Council of the European Union

2018

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“…Freixas (2004) showed that the dimension of the European Union Council under the Nice rules had dimension 3. In a recent article Kurz and Napel (2015) have found that the revised voting rules of the Council of the European Union (EU Council) mean that a simple game representation of that voting body must have dimension at least 7. This is significantly larger than that of any other known simple game that occurs in the real world.…”

Section: Complete and Hierarchical Simple Gamesmentioning

confidence: 99%

“…To bound the dimension of a game from below we will use the following useful criterion, which is Observation 1 in Kurz and Napel (2015). It is so important that we call it a theorem.…”

Section: Complete and Hierarchical Simple Gamesmentioning

confidence: 99%

“…Freixas and Puente (2008) showed that complete games of arbitrary dimension exist and, in particular, their examples demonstrate that the worst-case growth of dimension in complete games is at least linear. In this paper, using a novel technique of Kurz and Napel (2015), we demonstrate that the growth of dimension in complete games can also be exponential in the number of players. …”

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confidence: 99%

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Growth of dimension in complete simple games

O'Dwyer

Slinko

2017

Mathematical Social Sciences

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The concept of dimension in simple games was introduced by Taylor and Zwicker (1993) as a measure of the remoteness of a given game from a weighted game. They demonstrated that the dimension of a simple game can grow exponentially in the number of players. However, the problem of worst-case growth of the dimension in complete games was left open. Freixas and Puente (2008) showed that complete games of arbitrary dimension exist and, in particular, their examples demonstrate that the worst-case growth of dimension in complete games is at least linear. In this paper, using a novel technique of Kurz and Napel (2015), we demonstrate that the growth of dimension in complete games can also be exponential in the number of players.

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“…Many theoretical results and examples about dimension and codimension [11,8,3,7,5,12,6] have been constantly appearing during the last years, as well as, computational complexity results [9,4,1]. We present some results that will be used in Section 2.…”

Section: Introductionmentioning

confidence: 99%