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8 pages, 255 KiB

Open AccessArticle

A Note on Time Inconsistency and Endogenous Exits from a Currency Union

by Yuta Saito

Games 2022, 13(2), 21; https://doi.org/10.3390/g13020021 - 23 Feb 2022

Viewed by 2380

This paper investigates the effects of members’ exits from a currency union on the credibility of the common currency. In our currency union model, the inflation rate of the common currency is determined by majority voting among N member countries that are heterogeneous [...] Read more.

This paper investigates the effects of members’ exits from a currency union on the credibility of the common currency. In our currency union model, the inflation rate of the common currency is determined by majority voting among N member countries that are heterogeneous with respect to their output shocks. Once an inflation rate of the common currency has been selected, each member decides whether to remain in the currency union or not. If a member decides to exit, it has to pay a fixed social cost and individually chooses the inflation rate of its currency. Unlike previous research on this topic, we focus on the possibility of achieving an optimal outcome, which generates no inflation bias, when more than one member is expected to leave the currency union. We show that the optimal outcome can only be achieved if no members leave the currency union. Full article

(This article belongs to the Special Issue Weighted Majority Voting Games)

25 pages, 307 KiB

Open AccessArticle

Exits from the European Union and Their Effect on Power Distribution in the Council

by Dóra Gréta Petróczy, Mark Francis Rogers and László Á. Kóczy

Games 2022, 13(1), 18; https://doi.org/10.3390/g13010018 - 7 Feb 2022

Viewed by 3362

Abstract

Debates on an EU-leaving referendum arose in several member states after Brexit. We want to highlight how the exit of an additional country affects the power distribution in the Council of the European Union. We inspect the power indices of the member states [...] Read more.

Debates on an EU-leaving referendum arose in several member states after Brexit. We want to highlight how the exit of an additional country affects the power distribution in the Council of the European Union. We inspect the power indices of the member states both with and without the country which might leave the union. Our results show a pattern connected to a change in the number of states required to meet the 55% threshold. An exit that modifies this number benefits the countries with high population, while an exit that does not cause such a change benefits the small member states. According to our calculations, only the exit of Poland would be supported by the qualified majority of the Council. Full article

(This article belongs to the Special Issue Weighted Majority Voting Games)

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25 pages, 1819 KiB

Open AccessArticle

Gender and Nominal Power in Multilateral Bargaining

by Nicola Maaser, Fabian Paetzel and Stefan Traub

Games 2022, 13(1), 11; https://doi.org/10.3390/g13010011 - 17 Jan 2022

Viewed by 2861

Abstract

In many bargaining situations, the distribution of seats or voting weights does not accurately reflect bargaining power. Maaser, Paetzel and Traub (Games and Economic Behavior, 2019) conducted an experiment to investigate the effect of such nominal power differences in the classic Baron–Ferejohn model. [...] Read more.

In many bargaining situations, the distribution of seats or voting weights does not accurately reflect bargaining power. Maaser, Paetzel and Traub (Games and Economic Behavior, 2019) conducted an experiment to investigate the effect of such nominal power differences in the classic Baron–Ferejohn model. This paper re-analyzes the data from that experiment, looking at gender differences in bargaining behavior and in the effect of nominal weights. We find that women and men differ in particular with respect to the proposed distribution of payoffs and coalition size. By contrast, nominal weights have only minor gender-specific effects. Full article

(This article belongs to the Special Issue Weighted Majority Voting Games)

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17 pages, 341 KiB

Open AccessArticle

Dynamic Programming for Computing Power Indices for Weighted Voting Games with Precoalitions

by Jochen Staudacher, Felix Wagner and Jan Filipp

Games 2022, 13(1), 6; https://doi.org/10.3390/g13010006 - 26 Dec 2021

Cited by 3 | Viewed by 3021

Abstract

We study the efficient computation of power indices for weighted voting games with precoalitions amongst subsets of players (reflecting, e.g., ideological proximity) using the paradigm of dynamic programming. Starting from the state-of-the-art algorithms for computing the Banzhaf and Shapley–Shubik indices for weighted voting [...] Read more.

We study the efficient computation of power indices for weighted voting games with precoalitions amongst subsets of players (reflecting, e.g., ideological proximity) using the paradigm of dynamic programming. Starting from the state-of-the-art algorithms for computing the Banzhaf and Shapley–Shubik indices for weighted voting games, we present a framework for fast algorithms for the three most common power indices with precoalitions, i.e., the Owen index, the Banzhaf–Owen index and the symmetric coalitional Banzhaf index, and point out why our new algorithms are applicable for large numbers of players. We discuss implementations of our algorithms for the three power indices with precoalitions in C++ and review computing times, as well as storage requirements. Full article

(This article belongs to the Special Issue Weighted Majority Voting Games)

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17 pages, 324 KiB

Open AccessArticle

An Adaptive Model of Demand Adjustment in Weighted Majority Games

by Maria Montero and Alex Possajennikov

Games 2022, 13(1), 5; https://doi.org/10.3390/g13010005 - 26 Dec 2021

Cited by 1 | Viewed by 2617

Abstract

This paper presents a simple adaptive model of demand adjustment in cooperative games and analyzes this model in weighted majority games. In the model, a randomly chosen player sets her demand to the highest possible value subject to the demands of other coalition [...] Read more.

This paper presents a simple adaptive model of demand adjustment in cooperative games and analyzes this model in weighted majority games. In the model, a randomly chosen player sets her demand to the highest possible value subject to the demands of other coalition members being satisfied. This basic process converges to the aspiration set. By introducing some perturbations into the process, we show that the set of separating aspirations, i.e., demand vectors in which no player is indispensable in order for other players to achieve their demands, is the one most resistant to mutations. We then apply the process to weighted majority games. We show that in symmetric majority games and in apex games, the unique separating aspiration is the unique stochastically stable one. Full article

(This article belongs to the Special Issue Weighted Majority Voting Games)

17 pages, 2136 KiB

Open AccessArticle

Weighted Scoring Committees

by Alexander Mayer and Stefan Napel

Games 2021, 12(4), 94; https://doi.org/10.3390/g12040094 - 14 Dec 2021

Cited by 1 | Viewed by 2239

Abstract

Weighted committees allow shareholders, party leaders, etc. to wield different numbers of votes or voting weights as they decide between multiple candidates by a given social choice method. We consider committees that apply scoring methods such as plurality, Borda, or antiplurality rule. Many [...] Read more.

Weighted committees allow shareholders, party leaders, etc. to wield different numbers of votes or voting weights as they decide between multiple candidates by a given social choice method. We consider committees that apply scoring methods such as plurality, Borda, or antiplurality rule. Many different weights induce the same mapping from committee members’ preferences to winning candidates. The numbers of respective weight equivalence classes and hence of structurally distinct plurality committees, Borda commitees, etc. differ widely. There are 6, 51, and 5 plurality, Borda, and antiplurality committees, respectively, if three players choose between three candidates and up to 163 (229) committees for scoring rules in between plurality and Borda (Borda and antiplurality). A key implication is that plurality, Borda, and antiplurality rule are much less sensitive to weight changes than other scoring rules. We illustrate the geometry of weight equivalence classes, with a map of all Borda classes, and identify minimal integer representations. Full article

(This article belongs to the Special Issue Weighted Majority Voting Games)

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25 pages, 352 KiB

Open AccessArticle

A Disproportionality Bias in the Bureau of the Regional Assembly of Madrid

by Omar de la Cruz Vicente, Fernando Tomé Bermejo and Rafael Ramiro Moreno

Games 2021, 12(4), 92; https://doi.org/10.3390/g12040092 - 7 Dec 2021

Viewed by 2759

Abstract

This paper analyses the voting behavior of the parliamentary groups in the Regional Assembly of Madrid to appoint the Bureau, its representative body, in all the legislatures since its inception (1983–2021). To this end, the actual result of the voting is compared with [...] Read more.

This paper analyses the voting behavior of the parliamentary groups in the Regional Assembly of Madrid to appoint the Bureau, its representative body, in all the legislatures since its inception (1983–2021). To this end, the actual result of the voting is compared with the mock result attained by following a Nash equilibrium (NE) and a d’Hondt (d’H) allocation in each vote. But the result of a d’Hondt allocation varies based on the number of stages in which the voting is performed (President, Vice-President, and Secretaries), so a bias towards disproportionality could exist as measured by the absolute index of disproportionality which calculates the number of seats non-proportionally allocated. The results show that, in view of the hypothesis on the importance of the number of seats, the NE was only followed in four of the 12 Legislatures for Vice-Presidents (it was always followed for Secretaries). Thus, parliamentary groups could gain more seats by modifying their strategies. Additionally, the absolute rate of disproportionality and the number of seats non-proportionally allocated indicate that, in general, parliamentary groups obtain voting results that are less disproportionate than they could be (due to the number of voting stages). Full article

(This article belongs to the Special Issue Weighted Majority Voting Games)

25 pages, 432 KiB

Open AccessEditor’s ChoiceArticle

On Weights and Quotas for Weighted Majority Voting Games

by Xavier Molinero, Maria Serna and Marc Taberner-Ortiz

Games 2021, 12(4), 91; https://doi.org/10.3390/g12040091 - 6 Dec 2021

Cited by 1 | Viewed by 3266

Abstract

In this paper, we analyze the frequency distributions of weights and quotas in weighted majority voting games (WMVG) up to eight players. We also show different procedures that allow us to obtain some minimum or minimum sum representations of WMVG, for any desired [...] Read more.

In this paper, we analyze the frequency distributions of weights and quotas in weighted majority voting games (WMVG) up to eight players. We also show different procedures that allow us to obtain some minimum or minimum sum representations of WMVG, for any desired number of players, starting from a minimum or minimum sum representation. We also provide closed formulas for the number of WMVG with n players having a minimum representation with quota up to three, and some subclasses of this family of games. Finally, we complement these results with some upper bounds related to weights and quotas. Full article

(This article belongs to the Special Issue Weighted Majority Voting Games)

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10 pages, 340 KiB

Open AccessArticle

The Number of Parties and Decision-Making in Legislatures

by Marina Bannikova, Artyom Jelnov and Pavel Jelnov

Games 2021, 12(4), 76; https://doi.org/10.3390/g12040076 - 12 Oct 2021

Viewed by 2735

Abstract

This paper proposes a model of a legislature, formed by several parties, which has to vote for or against a certain bill in the presence of a lobbyist interested in a certain vote outcome. We show that the ease with which the lobbyist [...] Read more.

This paper proposes a model of a legislature, formed by several parties, which has to vote for or against a certain bill in the presence of a lobbyist interested in a certain vote outcome. We show that the ease with which the lobbyist can manipulate a legislature decision increases with the number of elected parties, and, consequently, decreases with an electoral threshold. On the other hand, a lower electoral threshold increases the representativeness of a legislature. We combine these two effects in a notion of fairness. We show the existence of an electoral threshold that optimizes the fairness of a political system, which is close to 1–5%. Namely, the optimal threshold (in our sense) is close to thresholds that exist in most parliamentary democracies. Full article

(This article belongs to the Special Issue Weighted Majority Voting Games)

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18 pages, 2581 KiB

Open AccessArticle

Simple Voting Games and Cartel Damage Proportioning

by Stefan Napel and Dominik Welter

Games 2021, 12(4), 74; https://doi.org/10.3390/g12040074 - 1 Oct 2021

Cited by 3 | Viewed by 2807

Abstract

Individual contributions by infringing firms to the compensation of cartel victims must reflect their “relative responsibility for the harm caused” according to EU legislation. Several studies have argued that the theoretically best way to operationalize this norm is to apply the Shapley value [...] Read more.

Individual contributions by infringing firms to the compensation of cartel victims must reflect their “relative responsibility for the harm caused” according to EU legislation. Several studies have argued that the theoretically best way to operationalize this norm is to apply the Shapley value to an equilibrium model of cartel prices. Because calibrating such a model is demanding, legal practitioners prefer workarounds based on market shares. Relative sales, revenues, and profits however fail to reflect causal links between individual behavior and prices. We develop a pragmatic alternative: use simple voting games to describe which cartel configurations can(not) cause significant price increases in an approximate, dichotomous way; then compute the Shapley-Shubik index. Simulations for a variety of market scenarios document that this captures relative responsibility better than market share heuristics can. Full article

(This article belongs to the Special Issue Weighted Majority Voting Games)

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10 pages, 819 KiB

Open AccessEditor’s ChoiceArticle

Brexit and Power in the Council of the European Union

by László Á. Kóczy

Games 2021, 12(2), 51; https://doi.org/10.3390/g12020051 - 21 Jun 2021

Cited by 7 | Viewed by 3764

Abstract

The exit of the United Kingdom from the European Union has had profound economic and political effects. Here, we look at a particular aspect, the power distribution in the Council of the European Union. Using the Shapley–Shubik power index, we calculate the member [...] Read more.

The exit of the United Kingdom from the European Union has had profound economic and political effects. Here, we look at a particular aspect, the power distribution in the Council of the European Union. Using the Shapley–Shubik power index, we calculate the member states’ powers with and without the United Kingdom and update earlier power forecasts using the Eurostat’s latest population projections. There is a remarkably sharp relation between population size and the change in power: Brexit increases the largest members’ powers while decreasing the smallest ones’ powers. Full article

(This article belongs to the Special Issue Weighted Majority Voting Games)

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