[Show abstract][Hide abstract] ABSTRACT: The later work of W.H. Riker (1921-93) has fervent admirers and fervent detractors. It has led to some extensions and qualifications. This review charts Riker's intellectual odyssey. Concentrating on his late works, it explores whether or not the characteristic methodology of these last two decades has the intrinsic strength necessary to survive and flourish.
[Show abstract][Hide abstract] ABSTRACT: In the conclusions of their clearly written paper the authors state precisely what they have achieved. (1) The (modified) paradox of redistribution occurs quite frequently in the German elections between 1949 and 2002: the frequency for the different power indices is always greater than 0.45. (2) The frequency of the paradox of new members in the German elections in the period just mentioned is 0.3409 for CDU/CSU and 0.0455 for the SPD. (3) From an empirical point of view, there is hardly any difference between the Shapley-Shubik index and the normalized Banzhaf index for the German case. (4) The redistribution paradox appears much more frequently (at least twice as much for each power index considered) in German politics than in Dutch politics, while the paradox of new members occurs much more frequently in the Dutch parliament than in the German one.
International Journal of Mathematics, Game Theory and Algebra. 01/2006; 6(6).
[Show abstract][Hide abstract] ABSTRACT: Manfred Holler introduced the Public Good index as a proposal to divide a
public good among players. In its unnormalized version, i.e., the raw measure,
it counts the number of times that a player belongs to a minimal winning
coalition. Unlike the Banzhaf index, it does not count the remaining winning
coalitions in which the player is crucial. Holler noticed that his index does
not satisfy local monotonicity, a fact that can be seen either as a major
drawback or as an advantage.
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