A decisiveness index for simple games |
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| Affiliation: | 3. Department of Biomaterial Sciences, Graduate School of Agricultural and Life Sciences, The University of Tokyo, Tokyo 113-8657, Japan;4. VTT Technical Research Centre of Finland, Espoo, FI-02044 VTT, Finland;5. Graduate School of Bioscience and Biotechnology, Tokyo Institute of Technology, Yokohama 226-8501, Japan;6. Department of Plant and Environmental New Resources, College of Life Sciences, Kyung Hee University, Giheung-ku, Yongin-si, Gyeonggi-do 446-701, Korea;3. Institute for Immunobiology and Department of Immunology, Shanghai Medical College, Fudan University, Shanghai 200032, China;4. Jiangsu Key Laboratory of Infection and Immunity, Institutes of Biology and Medical Sciences, Soochow University, Suzhou 215123, China;5. The State Key Laboratory of Medicinal Chemical Biology, College of Life Sciences, Nankai University, Tianjin 300071, China;1. Department of Economics, University of California, 508-1 Evans Hall #3880, Berkeley, CA 94720-3880, United States;2. Department of Economics, University of Essex, Wivenhoe Park, Colchester, CO4 3SQ, Essex, United Kingdom;3. Protein Science Key Laboratory of the Ministry of Education, School of Medicine, Tsinghua University, Beijing 100084, Peoples Republic of China;4. Department of Pharmacology, Okayama University Graduate School of Medicine, Dentistry & Pharmaceutical Sciences, Okayama 700-8558, Japan |
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| Abstract: | The decisiveness index introduced in this paper is designed to provide a normalized measure of the agility of all simple games, primarily viewed as collective decision-making mechanisms. We study the mathematical properties of the index and derive different axiomatic characterizations for it. Moreover, a close relationship is shown to the Banzhaf index of power––for which twice the decisiveness index plays the role of potential function––that gives rise to an effective computational procedure. Some real-world examples illustrate the usefulness of the decisiveness index, together with the Banzhaf power index, in applications to political science. |
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