Voting power in the European Union enlargement |
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| Institution: | 1. Centre for Sports Business, Salford Business School, University of Salford, Salford M5 4WT, UK;2. Centre for Sports Business, Management School, University of Liverpool, L69 7ZH UK;1. Faculty of Natural Sciences, University of Zagreb, Croatia;2. Faculty of Electrical Engineering and Computing, University of Zagreb, Croatia;1. Research Group of Operations Research and Decision Systems, Laboratory on Engineering and Management Intelligence, Institute for Computer Science and Control (SZTAKI), Budapest, Hungary;2. Department of Operations Research and Actuarial Sciences, Corvinus University of Budapest (BCE), Budapest, Hungary;3. Department of Finance, Corvinus University of Budapest (BCE), Budapest, Hungary |
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| Abstract: | The Shapley–Shubik power index in a voting situation depends on the number of orderings in which each player is pivotal. The Banzhaf power index depends on the number of ways in which each voter can effect a swing. If there are n players in a voting situation, then the function which measures the worst case running time for computing these indices is in O(n2n). We present a combinatorial method based in generating functions to compute these power indices efficiently in weighted double or triple majority games and we study the time complexity of the algorithms. Moreover, we calculate these power indices for the countries in the Council of Ministers of the European Union under the new decision rules prescribed by the Treaty of Nice. |
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