Comparing influence theories in voting games under locally generated measures of dissatisfaction |
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Authors: | L. Diffo Lambo B. Tchantcho J. Moulen |
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Affiliation: | 1. Department of Mathematics, ENS Yaounde, Yaound??, Cameroon 2. University of Cergy Pontoise, THEMA, Cergy Pontoise, France
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Abstract: | The Isbell desirability relation (I), the Shapley?CShubik index (SS) and the Banzhaf?CColeman index (BC) are power theories that grasp the notion of individual influence in a yes?Cno voting rule. Also, a yes?Cno voting rule is often used as a tool for aggregating individual preferences over any given finite set of alternatives into a collective preference. In this second context, Diffo Lambo and Moulen (DM) have introduced a power relation which ranks the voters with respect to how ably they influence the collective preference. However, DM relies on the metric d that measures closeness between preference relations. Our concern in this work is: do I, SS, BC and DM agree when the same yes?Cno voting rule is the basis for collective decision making? We provide a concrete and intuitive class of metrics called locally generated (LG). We give a characterization of the LG metrics d for which I, SS, BC and DM agree on ranking the voters. |
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