Many bodies around the world make their decisions through voting systems in which voters have several options and the collective result also has several options. Many of these voting systems are anonymous, i.e., all voters have an identical role in voting. Anonymous simple voting games, a binary vote for voters and a binary collective decision, can be represented by an easy weighted game, i.e., by means of a quota and an identical weight for the voters. Widely used voting systems of (...) this type are the majority and the unanimity decision rules. In this article, we analyze the case in which voters have two or more voting options and the collective result of the vote has also two or more options. We prove that anonymity implies being representable through a weighted game if and only if the voting options for voters are binary. As a consequence of this result, several significant enumerations are obtained. (shrink)

The work on set theory made by A. Tarski in the years 1924-1950 is very interesting, but little know.We develope partial questions in set theory in the moment that A. Tarski intervenes and his contributionsand also influences.The principals aims in this development are:1. The axiom of choice [A.C.] and his equivalents;2. the general continuum hypothesis [G.C.H.] and the A.C.;3. the dual trichotomy principle;4. the inaccessible cardinals and his relation with the A.C. and the G.C.H.;5. the notion of finite set and (...) his relation with the A.C and the G.C.H.;6. the almost disjoint set and their relation with the G.C.H.;and finally,7. the results in Berkeley. (shrink)

La Misericordia de Dios lo abarca todo. Los atributos de Dios referidos a su Misericordia y Munificencia vienen reflejados en los nombres Ar-Rahman y Ar-Rahim. El primero es la cualidad exclusiva de Dios y se refiere a las gracias sobrenaturales y el segundo a las gracias naturales. En cuanto al siervo del Misericordioso. Abd Ar-Rahman, resume este nombre y es una gracia para todo el mundo en general. Abd Ar-Rahim, el siervo del Generoso, ejemplifica a la persona piadosa que practica (...) la compasión pero sobre todo con aquellos en los que Dios se complace.The Mercy of God includes all His creatíon. The Divine Qualities refered to the Compassionate and the Merciful are reflected in the names Ar-Rahman and Ar-Rahim. The first one is an exclusiva quality of God and it is refereá to the supernatural Grace and the second one to the natural Grace. As for the servant of the Compassionate epitomises this name and is a mercy to all the world in general. 'Abd Ar-Rahim, the servant of the Merciful exemplifies the pious that bestows his mercy particularly upon those with whom God is pleased. (shrink)

The moral pedagogy in the fairy tales is simple but powerful. It is concentrated in the lesson -according to the message of Aristotle- about the finalism sense of action: it makes the child understand that the human answer is an action with sense. Everything in the fairy tale leads to this perspective. Moreover, it exemplifies MacIntyre's opinion which says that current people tend to be proto-aristotelian and to understand their own life and the other's in narrative terms.

The topos of jews’ blindness, recurrent in adversos iudaeos literature, embodies in the image of blindfold Synagoga in medieval visual arts. The first part of this paper focuses on its integration in different contexts of medieval Spanish art. Diferent, but not less interesting, is the way caecitatis iudeorum is illustrated in some illuminated manuscripts of Breviari d’Amor by Matfre Ermengaud and Fortalitium Fidei by Alonso de Espina, also subject of study throughout these pages.

A previous work by Friedman et al. (Theory and Decision, 61:305–318, 2006) introduces the concept of a hierarchy of a simple voting game and characterizes which hierarchies, induced by the desirability relation, are achievable in linear games. In this paper, we consider the problem of determining all hierarchies, conserving the ordinal equivalence between the Shapley–Shubik and the Penrose–Banzhaf–Coleman power indices, achievable in simple games. It is proved that only four hierarchies are non-achievable in simple games. Moreover, it is also proved (...) that all achievable hierarchies are already obtainable in the class of weakly linear games. Our results prove that given an arbitrary complete pre-ordering defined on a finite set with more than five elements, it is possible to construct a simple game such that the pre-ordering induced by the Shapley–Shubik and the Penrose–Banzhaf–Coleman power indices coincides with the given pre-ordering. (shrink)