Voting power on a graph connected political space with an application to decision-making in the Council of the European Union
Bibliographic Data
| ID | 21470546 |
|---|---|
| Authors | Stefano Benati (0000-0002-1928-5224, University of Trento, corresponding author), Giuseppe Vittucci Marzetti (0000-0003-3093-8000, University of Milano-Bicocca) |
| Year | 2021 |
| Volume | 57 |
| Issue | 4 |
| Pages | 733-761 |
| Publication date | 2021-11-01 |
| Peer Reviewed | Yes |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | Social Choice and Welfare (JOURNAL) |
| Journal identifiers | ISSN: 0176-1714 • E-ISSN: 1432-217X |
| Publisher | Springer Science and Business Media LLC (PUBLISHER) |
| DOI | 10.1007/s00355-021-01339-6 |
| OpenAlex | W3159606244 |
| Language | EN |
| Citations received | 1 |
| References cited | 47 |
We analyze the problem of computing the Banzhaf and Shapley power indices for graph restricted voting games, defined in a particular class of graphs, that we called line-clique. A line-clique graph is a model of a uni-dimensional political space in which voters with the same bliss point are the connected vertices of a clique and then other arcs connect nodes of consecutive cliques. The interest to this model comes from its correspondence to the spatial voting game: a model that has been proposed and used by political analysts to understand nations’ behavior and the political outcome of the bargaining process within the EU Council. Broadly speaking, the computation of a power index of a graph restricted game is strongly #P-complete, as it includes the enumeration of all winning coalitions. Nevertheless, we show that in this special class of graph coalitions can be enumerated by dynamic programming, resulting in a pseudo-polynomial algorithm and proving that the problem only weakly #P-complete. After implementing our new algorithms and finding that they are very fast in practice, we analyze the voting behavior in the EU Council, as for this application previous research compiled a large data set concerning nations’ political positions and political outcomes. We will test whether voting power has an effect on the political outcome, more precisely, whether nations that are favored by their weight and position can influence the political outcome to their advantages. Using linear regressions, we will see that unrestricted power indices are not capable of any predictive property, but graph restricted indices are. The statistic evidence shows that the combination of voting weight and network position is a source of power that affects the political outcome to the advantage of a country
Cardinal voting systems · Graph · Mathematical economics · Political science · Politics · Voting · Voting behavior · Computer Science · Electoral Systems and Political Participation · Game Theory and Applications · Game Theory and Voting Systems · Law · Mathematics · Theoretical Computer Science
Mathematical Properties of the Banzhaf Power Index
Graphs and Cooperation in Games
The Elementary Statistics of Majority Voting
The modified Banzhaf value for games with coalition structure
The complexity of power indexes with graph restricted coalitions
Who has the power in the EU
The Owen and Shapley spatial power indices
Voting power and voting blocs
Why Resist the Temptation to Apply Power Indices to the European Union
Bargaining Power in the European Union
The Impossibility of a Preference-Based Power Index
The Possibility of a Preference-Based Power Index
Strategic Power in the European Union
A new dataset on decision-making in the European Union before and after the 2004 and 2007 enlargements (Deuii)
Is it Better to Be Powerful or Lucky
Is it Better to Be Powerful or Lucky? Part 2
Power Measurement as Sensitivity Analysis
Testing models of legislative decision-making with measurement error
A Priori versus Empirical Voting Power in the EU Council of Ministers
A Method for Evaluating the Distribution of Power in a Committee System
| Unique citing works | 1 |
|---|---|
| Citations per year | 1 |
| Citation span | 2026 - 2026 (1) |
| Citation velocity | current |
| Highly cited | No |
| Citation types | Neutral: 1 |