6,668 research outputs found

    Power Indices in Large Voting Bodies

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    There is no consensus on the properties of voting power indices when there are a large number of voters in a weighted voting body. On the one hand, in some real-world cases that have been studied the power indices have been found to be nearly proportional to the weights (eg the EUCM, US Electoral College). This is true for both the PenroseBanzhaf and the Shapley-Shubik indices. It has been suggested that this is a manifestation of a conjecture by Penrose (known subsequently as the Penrose limit theorem, that has been shown to hold under certain conditions). On the other hand, we have the older literature from cooperative game theory, due to Shapley and his collaborators, showing that, where there are a nite number of voters whose weights remain constant in relative terms, and where the quota remains constant in relative terms, while the total number of voters increases without limit - so called oceanic games - the powers of the voters with nite weight tend to limiting values that are, in general, not proportional to the weights. These results, too, are supported by empirical studies of large voting bodies (eg. the IMF/WB boards, corporate shareholder control). This paper proposes a restatement of the Penrose Limit theorem and shows that, for both the power indices, convergence occurs in general, in the limit as the Laakso-Taagepera index of political fragmentation increases. This new version reconciles the di erent theoretical and empirical results that have been found for large voting bodies

    Selfish Bin Covering

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    In this paper, we address the selfish bin covering problem, which is greatly related both to the bin covering problem, and to the weighted majority game. What we mainly concern is how much the lack of coordination harms the social welfare. Besides the standard PoA and PoS, which are based on Nash equilibrium, we also take into account the strong Nash equilibrium, and several other new equilibria. For each equilibrium, the corresponding PoA and PoS are given, and the problems of computing an arbitrary equilibrium, as well as approximating the best one, are also considered.Comment: 16 page

    On the voting power of an alliance and the subsequent power of its members

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    Even, and in fact chiefly, if two or more players in a voting game have on a binary issue independent opinions, they may have interest to form a single voting alliance giving an average gain of influence for all of them. Here, assuming the usual independence of votes, we first study the alliance voting power and obtain new results in the so-called asymptotic limit for which the number of players is large enough and the alliance weight remains a small fraction of the total of the weights. Then, we propose to replace the voting game inside the alliance by a random game which allows new possibilities. The validity of the asymptotic limit and the possibility of new alliances are examined by considering the decision process in the Council of Ministers of the European Union.

    Ready for the design of voting rules?

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    The design of fair voting rules has been addressed quite often in the literature. Still, the so-called inverse problem is not entirely resolved. We summarize some achievements in this direction and formulate explicit open questions and conjectures.Comment: 10 page

    On the Voting Power of an Alliance and the Subsequent Power of its Members

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    Even, and in fact chiefly, if two or more players in a voting gamehave on a binary issue independent opinions, they may haveinterest to form a single voting alliance giving an average gainof influence for all of them. Here, assuming the usualindependence of votes, we first study the alliance voting powerand obtain new results in the so-called asymptotic limit for whichthe number of players is large enough and the alliance weightremains a small fraction of the total of the weights. Then, wepropose to replace the voting game inside the alliance by a randomgame which allows new possibilities. The validity of theasymptotic limit and the possibility of new alliances are examinedby considering the decision process in the Council of Ministers ofthe European Union.Voting Power; Alliance
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