A symmetric network consists of a set of positions and a set of bilateral links between these positions. For every symmetric network we define a cooperative transferable utility game that measures the “power” of each coalition of positions in the network. Applying the Shapley value to this game yields a network power measure, the β-measure, which reflects the power of the individual positions in the network. Applying this power distribution method iteratively yields a limit distribution, which turns out to be (...) proportional to the well-known degree measure. We compare the β-measure and degree measure by providing characterizations, which differ only in the normalization that is used. (shrink)

A situation, in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A (point-valued) solution for TU-games assigns a payoff distribution to every TU-game. In this article we discuss a class of equal surplus sharing solutions consisting of all convex combinations of the CIS-value, the ENSC-value and the equal division solution. We provide several characterizations of this class of solutions on variable and fixed (...) player set. Specifications of several properties characterize specific solutions in this class. (shrink)

Digraph games are cooperative TU-games associated to domination structures which can be modeled by directed graphs. Examples come from sports competitions or from simple majority win digraphs corresponding to preference profiles in social choice theory. The Shapley value, core, marginal vectors and selectope vectors of digraph games are characterized in terms of so-called simple score vectors. A general characterization of the class of (almost positive) TU-games where each selectope vector is a marginal vector is provided in terms of game semi-circuits. (...) Finally, applications to the ranking of teams in sports competitions and of alternatives in social choice theory are discussed. (shrink)

A symmetric network consists of a set of positions and a set of bilateral links between these positions. For every symmetric network we define a cooperative transferable utility game that measures the “power” of each coalition of positions in the network. Applying the Shapley value to this game yields a network power measure, the β-measure, which reflects the power of the individual positions in the network. Applying this power distribution method iteratively yields a limit distribution, which turns out to be (...) proportional to the well-known degree measure. We compare the β-measure and degree measure by providing characterizations, which differ only in the normalization that is used. (shrink)

We introduce a family of proportional surplus division values for TU-games. Each value first assigns to each player a compromise between her stand-alone worth and the average stand-alone worths over all players, and then allocates the remaining worth among the players in proportion to their stand-alone worths. This family contains the proportional division value and the new egalitarian proportional surplus division value as two special cases. We provide characterizations for this family of values, as well as for each single value (...) in this family. (shrink)

A situation, in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A (point-valued) solution for TU-games assigns a payoff distribution to every TU-game. In this article we discuss a class of equal surplus sharing solutions consisting of all convex combinations of the CIS-value, the ENSC-value and the equal division solution. We provide several characterizations of this class of solutions on variable and fixed (...) player set. Specifications of several properties characterize specific solutions in this class. (shrink)

It is known that peer group games are a special class of games with a permission structure. However, peer group games are also a special class of digraph games. To be specific, they are digraph games in which the digraph is the transitive closure of a rooted tree. In this paper we first argue that some known results on solutions for peer group games hold more general for digraph games. Second, we generalize both digraph games as well as games with (...) a permission structure into a model called games with a local permission structure, where every player needs permission from its predecessors only to generate worth, but does not need its predecessors to give permission to its own successors. We introduce and axiomatize a Shapley value-type solution for these games, generalizing the conjunctive permission value for games with a permission structure and the β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document}-measure for weighted digraphs. (shrink)

We deal with the ranking problem of the nodes in a directed graph. The bilateral relationships specified by a directed graph may reflect the outcomes of a sport competition, the mutual reference structure between websites, or a group preference structure over alternatives. We introduce a class of scoring methods for directed graphs, indexed by a single nonnegative parameter α. This parameter reflects the internal slackening of a node within an underlying iterative process. The class of so-called internal slackening scoring methods, (...) denoted by λα, consists of the limits of these processes. It is seen that λ0 extends the invariant scoring method, while λ∞ extends the fair bets scoring method. Method λ1 corresponds with the existing λ-scoring method of Borm et al. (Ann Oper Res 109(1):61–75, 2002) and can be seen as a compromise between λ0 and λ∞. In particular, an explicit proportionality relation between λα and λ1 is derived. Moreover, the internal slackening scoring methods are applied to the setting of social choice situations where they give rise to a class of social choice correspondences that refine both the Top cycle correspondence and the Uncovered set correspondence. (shrink)

The Shapley value is the unique value defined on the class of cooperative games in characteristic function form which satisfies certain intuitively reasonable axioms. Alternatively, the Banzhaf value is the unique value satisfying a different set of axioms. The main drawback of the latter value is that it does not satisfy the efficiency axiom, so that the sum of the values assigned to the players does not need to be equal to the worth of the grand coalition. By definition, the (...) normalized Banzhaf value satisfies the efficiency axiom, but not the usual axiom of additivity. (shrink)

A cooperative game with transferable utility–or simply a TU-game– describes a situation in which players can obtain certain payoffs by cooperation. A value function for these games assigns to every TU-game a distribution of payoffs over the players. Well-known solutions for TU-games are the Shapley and the Banzhaf value. An alternative type of solution is the concept of share function, which assigns to every player in a TU-game its share in the worth of the grand coalition. In this paper we (...) consider TU-games in which the players are organized into a coalition structure being a finite partition of the set of players. The Shapley value has been generalized by Owen to TU-games in coalition structure. We redefine this value function as a share function and show that this solution satisfies the multiplication property that the share of a player in some coalition is equal to the product of the Shapley share of the coalition in a game between the coalitions and the Shapley share of the player in a game between the players within the coalition. Analogously we introduce a Banzhaf coalition structure share function. Application of these share functions to simple majority games show some appealing properties. (shrink)

Is knowledge possible? If so, what can we know and how do we come to know it? What degree of certainty does our knowledge enjoy? In these two powerful works, Descartes, the seventeenth-century philosopher considered to be the father of modern philosophy, outlines his philosophical method and then counters the skeptics of his time by insisting that certain knowledge can be had. He goes on to address the nature and extent of human knowledge, the distinction between mind and body, the (...) existence of God, and the existence of external objects. (shrink)

In this paper, I defend a representationalist account of the phenomenal character of color experiences. Representationalism, the thesis that phenomenal character supervenes on a certain kind of representational content, so-called phenomenal content, has been developed primarily in two different ways, as Russellian and Fregean representationalism. While the proponents of Russellian and Fregean representationalism differ with respect to what they take the contents of color experiences to be, they typically agree that colors are exhaustively characterized by the three dimensions of the (...) color solid: hue, saturation, and lightness. I argue that a viable version of representationalism needs to renounce this restriction to three dimensions and consider illumination to be a genuine phenomenal dimension of color. My argument for this thesis falls into two parts. I first consider the phenomenon of color constancy in order to show that neither Russellian nor Fregean representationalism can do justice to the phenomenal significance of local illumination. I subsequently formulate a version of representationalism that accounts for illumination by taking it as a phenomenal dimension of color. (shrink)

In this paper I explore, in sections 2 and 3, respectively, Herman Dooyeweerd’s notion of naive experience and the notion of common sense as found in the writings of Thomas Reid and G. E. Moore. I argue in section 4 that naive experience and common sense are assigned a structurally similar functional role by their advocates—viz., the role of touchstone for philosophy. In the final section I stage a conversation between Dooyeweerd and Reid about the touchstones they adopt.

Discourse on the method of rightly conducting the reason and seeking truth in the field of science -- The meditations concerning first philosophy -- Rules for the direction of the mind.

These two 1985 volumes provide a translation of the philosophical works of Descartes, based on the best available Latin and French texts. They are intended to replace the only reasonably comprehensive selection of his works in English, by Haldane and Ross, first published in 1911. All the works included in that edition are translated here, together with a number of additional texts crucial for an understanding of Cartesian philosophy, including important material from Descartes' scientific writings. The result should meet the (...) widespread demand for an accurate and authoritative edition of Descartes' philosophical writings in clear and readable modern English. (shrink)

Le problème de l'être-avec et de la socialité chez Heidegger a déjà une longue tradition de commentateurs. Ceux-ci se distinguent par la pluralité de leurs approches: se situant parfois à l'opposé de la méthode d'Être et temps, ils se portent alors à la défense d'autrui, insistent sur l'aspect dialogique et sur l'importance de la rationalité du discours dans le monde de la vie. D'autres encore, sans nécessairement remettre en question la méthodologie heideggérienne, défendent ou réinterprètent autrement sa phénoménologie de l'existence (...) d'autrui: parmi eux, certains s'en tiennent uniquement à l'analytique existentiale, tandis que d'autres élargissent l'horizon de leurs critiques en tenant compte du projet global de la pensée de Heidegger. Il y a enfin les commentateurs pour lesquels cette question n'est abordée que dans le contexte politique de sa pensée. (shrink)

Why do creationists persist in rejecting the evidence for Darwin’s theory of evolution? This paper explores longstanding disagreements among Christians over the epistemic status of evolution. Like other studies that have tried to define the evidence for evolution, a recent analysis by Gijsbert van den Brink, Jeroen de Ridder, and René van Woudenberg does not adequately face up to antecedent commitments that play into any assessment of evolution. The scientific theory of evolution involves higher-level models that are associated (...) with a range of non-scientific factors, including theological judgments. In light of these realities, an emphasis on mutual dialogue and understanding offers promising opportunities for Christians trying to discover the truth about God’s creation. (shrink)

This paper is a contribution to the debate on epistemic foundationalism. Section I expounds and criticises Hans Albert's critical rationalist antifoundationalism position. Section I1 discusses Karl‐Otto Apel's ‘transcendental pragmatic’ argument for ultimate epistemic foundations. Section III suggests how the latter argument can be restated so as to avoid ambiguity and yield a plausible case for epistemic foundationalism.

Les problèmes de la vie commençante et ceux de la vie finissante déterminent deux secteurs importants de la bioéthique. La démarche éthique de toutes les personnes concernées par ces problèmes commence par une information sérieuse sur les données scientifiques, biologiques ou médicales, sur les situations des personnes et leurs implications anthropologiques et sociales. Elle requiert ensuite, mais toujours en lien étroit avec ces approches technologiques, l'analyse, principalement philosophique, des concepts de personne et de corps humain, de dignité et de respect (...) de la personne, analyse attentive à la fragilité de l'être humain et aux conflits qui peuvent surgir entre valeurs humaines et procédures médicales comme entre les situations individuelles et les impératifs de la loi. A la « morale commune », élaborée par le discours philosophique, la théologie ajoute son intuition propre de la gratuité de l'amour et de la responsabilité d'autrui, puisée dans la révélation de l'Alliance et de l'identification du Christ aux personnes les plus fragiles et aux conditions de plus grande précarité. Elle n'entre pas en concurrence avec la morale commune ni ne se substitue à la décision éthique qui incombe à chacun, mais elle apporte aux croyants des motivations plus pressantes et un regard plus ouvert et plus compréhensif sur le prochain et sur l'humain.Bioethics can be divided into two sectors, problems in the first stages of life and problems near the end of life . The etbical steps taken by the people concerned by these problems begin with a serious study of the scientific, biological, or medical facts. They must also consider the situation of the individual's case as well as the anthropological and social implications, The ethical steps to be taken require, but always in close connection with technological approaches, the analysis of the concepts of person and the human body. Tbey also require respect for the dignity elabored by pbilosopbical discourse, theology adds its own intuition on the gratuitousness of love and responsibility for the other. Its sources are found in the revelation of the Covenant and the identification of Christ with the weakest persons and to conditions that are the most precarious. Theology does not enter into competition witb common morality, nor put itself in the place of the ethical decision that eacb person must make. Rather it brings strong motives to believers and a more open and more understanding look at one’s neighbour and humanness. (shrink)

The view that theology represents the highest level of academic learning and the summit of human knowledge has a long history. In this article, starting from Aristotle, the genealogy of this view is excavated. Second, it is examined how and why theology lost this special status in modernity, as this appears in Immanuel Kant’s The Conflict of the Faculties (1798). Third, it is shown in which way and for what reasons theology continued to have a place of its own in (...) the modern university since the founding of the University of Berlin (1810). In particular, the crucial role of Friedrich Schleiermacher’s proposal is highlighted. Fourth, it is suggested that, under certain conditions, theology can still be conceived as a proper university discipline in contemporary pluralistic societies. (shrink)

So simple and imperfect as it may appear this book has made use of knowledge on invention and discovery accumu lated during a lifetime. Those persons who would be tempted to emphasize only its imperfections should read the correspondence exchanged between Cantor and Dedekind at the end of the nineteenth century; they would then realize how difficult it was, even for an outstanding man, the creator of the set theory, to propose impeccable results in a completely new field. The field (...) I have chosen here is plausibility. I have proposed an intuitive, some would say a naive, presentation as I want to reach as large an audience as possible and because I personally believe that it is easier to axiomatize a mathematical theory precisely than to dis cover it and enunciate its key theorems. Professor Polya said: "The truly creative mathematician is a good guesser first and a good prover afterward. " For centuries a formalized generalized logic was found necessary and many attempts have been made to build it. vi Preface Mine is based on plausibility which covers with precision a wider field than probability and makes the formalization of analogy and generalization possible. As Laplace said: "Even in the mathematical sciences, our principal instru ments to discover the truth are induction and analogy. "* The examples of application I have chosen are not des cribed in detail. (shrink)