This study investigates simple games. A fundamental research question in this field is to determine necessary and sufficient conditions for a simple game to be a weighted majority game. Taylor and Zwicker showed that a simple game is non-weighted if and only if there exists a trading transform of finite size. They also provided an upper bound on the size of such a trading transform, if it exists. Gvozdeva and Slinko improved that upper bound; their proof employed a property of (...) linear inequalities demonstrated by Muroga. In this study, we provide a new proof of the existence of a trading transform when a given simple game is non-weighted. Our proof employs Farkas’ lemma, and yields an improved upper bound on the size of a trading transform. We also discuss an integer-weight representation of a weighted simple game, improving the bounds obtained by Muroga. We show that our bound on the quota is tight when the number of players is less than or equal to five, based on the computational results obtained by Kurz. Furthermore, we discuss the problem of finding an integer-weight representation under the assumption that we have minimal winning coalitions and maximal losing coalitions. In particular, we show a performance of a rounding method. Finally, we address roughly weighted simple games. Gvozdeva and Slinko showed that a given simple game is not roughly weighted if and only if there exists a potent certificate of non-weightedness. We give an upper bound on the length of a potent certificate of non-weightedness. We also discuss an integer-weight representation of a roughly weighted simple game. (shrink)

This chapter contains sections titled: Preamble Introduction Three Historical Periods Contemporary Debate Virtue and Tradition in Japan Conclusion Acknowledgements Notes References.

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Reconfiguring Modernity: Concepts of Nature in Japanese Political IdeologyWilliam R. LaFleurReconfiguring Modernity: Concepts of Nature in Japanese Political Ideology. By Julia Adeney Thomas. Berkeley, Los Angeles, and London: University of California Press, 2001. Pp. xvi + 225.Books written by persons who self-identify as intellectual historians usually lend themselves more easily to review in history journals than in those that focus on philosophy. Reconfiguring Modernity: Concepts of Nature in (...) Japanese Political Ideology, Julia Adeney Thomas' study of certain Meiji period thinkers is such a book. In 2002 it was awarded the John K. Fairbank Prize in history. Taking a cue to step into her topic from an early essay by Robert Bellah, one in which he had written that "the concern for nature has been a pervasive one in much of modern Japanese thought,"1 Thomas specifies her own search: "It is now time to recover the historical mutability of that concept, and to describe precisely its politics at particular moments in Japan's confrontation with modernity, both within the dominant ideology of the moment and with the alternatives to it" (pp. 30-31).Thomas is among those American students of Japan apparently trained to challenge the massive amounts of excavational scholarship and mile-high reputations of Japanese scholars of Japan. She picks arguments with some of the most highly respected Japanese minds of the twentieth century: the late Maruyama Masao, the late Ienaga Saburō, and Matsumoto Sannosuke.Although Thomas' criticisms tend to focus on those portions of the works of these prolific scholars that have been translated into English,2 some of her criticisms are certainly interesting and possibly valid. For instance, Maruyama, "who repeatedly excoriated Japan's reliance on the political authority of nature (shizen) " (p. 16), envisioned modernity, surely desirable, as involving a move "against Chu Hsi Confucianism"—that is, "an inevitable turning away from nature (shizen) to invention (sakui)" (p. 17). Nevertheless, Maruyama's hero, Ogyū Sorai (1666-1728), had understood "the narrative of modernity" but, tragically, stepped "back from invention at the critical moment, unable, it would seem, to embrace it as the culmination of the historical process" (p. 19).Thomas, rightly I think, indicates that most left and liberal thinkers in Europe and America in the early and mid-twentieth century were skeptical of an invocation of the "natural" in the making of political theory.3 However, she stakes a claim to being part of a different generation, one that rejects the old binary opposition between nature and culture—as well as the further assumption that Western political thinking had successfully disengaged itself from invoking the category of what is natural. Taking a cue from Stephen Toulmin's demonstration of how many of Europe's modernizers embraced and used, rather than rejected, concepts of nature,4 Thomas claims that, at least for us who now live "'on the far side of modernity,' nature can be seen [End Page 172] as multivalent rather than the antonym in a series of binary opposites." In practice this means that for us now, "nature can no longer appear synonymous with the anti-modern, the past, the oppressive, or the Orient" (p. 25).I ask that the reader highlight the sentences above. They constitute what in my view is the most important and by far the most interesting move made in Refiguring Modernity. I will return to them below. First, however, I will recapitulate the progression of the book's chapters. They move in the pattern of linear history. The first, discussed already and titled "The Trouble with Nature," introduces the problem. The second, "The Topographical Imagination of Tokugawa Politics," deals with thinkers of the Tokugawa (Edo) period (1600-1868). Theirs was an era during which, although Chinese claims to being both topographically and morally central had long been dutifully accepted in Japan, strong-thinking Japanese argued that China's frequent dynastic changes demonstrated that "centralness need not be possessed physically to be enacted morally" (p. 42). By outdoing contemporaneous Chinese in terms of being Confucian, Neo-Confucian, or whatever it was that had its origins in China, Japanese and in some sense Japan as a whole were imagined to be the "real China."5... (shrink)