In a two-tier decision-making system such as the EU Council of Ministers, if the number of constituencies (member-states) is sufficiently large (say, 15 or more), Penrose’s Square-Root rule can be implemented to a high level of approximation by a simple weighted decision rule at the top level (the Council) with any given quota q smaller than the total weight. This leaves one degree of freedom: the value of q as a free parameter, to be determined by some additional condition. I (...) propose to survey and discuss critically the most important considerations for fixing this value – some of which have actually been used by theoreticians or practitioners: efficiency, transparency, sensitivity (total voting power of citizens), mean majority deficit, giving certain ‘privileged’ coalitions blocking status. Some of these considerations are reasonably compatible; others less so. Some kind of compromise is clearly needed. But which? This is essentially a political matter; but a political decision ought to be made in a theoretically enlightened way. (shrink)

We analyse the projected future evolution of the distribution of voting power and related quantities under the qualified majority decision rule for the Council of Ministers of the EU, prescribed by the forthcoming EU Reform Treaty. Our projections are based on the demographic changes forecast by eurostat [4] for the period stretching from the present to the middle of the 21st Century. We use a method similar to the one we used in [6], [7], [8] and [9].

This is an introduction to set theory and logic that starts completely from scratch. The text is accompanied by many methodological remarks and explanations.

The hope of this work is that these notes will help to convince more mathematicians that non-standard analysis can make a useful addition to the tools of their trade.

This collection addresses a post-WWII shift in the hierarchy of scientific explanations, where the highest goal moves from reductionism towards some ...

We address simple voting games as mathematical objects in their own right, and study structures made up of these objects, rather than focusing on SVGs primarily as co-operative games. To this end it is convenient to employ the conceptual framework and language of category theory. This enables us to uncover the underlying unity of the basic operations involving SVGs.

For the theorists of crisis, the revolutionary state comes into existence through violence, and due to its inability to provide an authoritative katechon (restrainer) against internal and external violence, it perpetuates violence until it self-destructs. Writing during extreme economic depression and growing social and political violence, the crisis theorists––Joseph de Maistre, Juan Donoso Cortés, and Carl Schmitt––each sought to blame the chaos of their time upon the Janus-faced postrevolutionary ideals of liberalism and socialism by urging a return to pre-revolutionary moral (...) and religious values. They are united by three counterrevolutionary principles, all of which are purported to remedy revolutionary violence: traditional constitutional fidelity, the philosophy of the decision, and opposition to bourgeois liberalism. This essay is followed by the first complete English translation and publication of Donoso’s letter of October 24, 1851, which contains Donoso’s only reference to the “discussing class,” a political entity later popularized by Schmitt in his 1922 work Political Theology. (shrink)

I propose a twofold classification of the main considerations underlying the choice of an election procedure: political criteria on the one hand, and social-choice criteria on the other. I formulate political dichotomies, each combination of which narrows down the choice of procedure to a sub-class of the class of all procedures. I discuss what social-choice theory has to offer in each of these.

If K is an index of relative voting power for simple voting games, the bicameral postulate requires that the distribution of K -power within a voting assembly, as measured by the ratios of the powers of the voters, be independent of whether the assembly is viewed as a separate legislature or as one chamber of a bicameral system, provided that there are no voters common to both chambers. We argue that a reasonable index – if it is to be used (...) as a tool for analysing abstract, ‘uninhabited’ decision rules – should satisfy this postulate. We show that, among known indices, only the Banzhaf measure does so. Moreover, the Shapley–Shubik, Deegan–Packel and Johnston indices sometimes witness a reversal under these circumstances, with voter x ‘less powerful’ than y when measured in the simple voting game G1 , but ‘more powerful’ than y when G1 is ‘bicamerally joined’ with a second chamber G2 . Thus these three indices violate a weaker, and correspondingly more compelling, form of the bicameral postulate. It is also shown that these indices are not always co-monotonic with the Banzhaf index and that as a result they infringe another intuitively plausible condition – the price monotonicity condition. We discuss implications of these findings, in light of recent work showing that only the Shapley–Shubik index, among known measures, satisfies another compelling principle known as the bloc postulate. We also propose a distinction between two separate aspects of voting power: power as share in a fixed purse (P-power) and power as influence (I-power). (shrink)

In much of the current academic and public discussion, conspiracy theories are portrayed as a negative phenomenon, linked to misinformation, mistrust in experts and institutions, and political propaganda. Rather surprisingly, however, philosophers working on this topic have been reluctant to incorporate a negatively evaluative aspect when either analyzing or engineering the concept conspiracy theory. In this paper, we present empirical data on the nature of the concept conspiracy theory from five studies designed to test the existence, prevalence and exact form (...) of an evaluative dimension to the ordinary concept conspiracy theory. These results reveal that, while there is a descriptive concept of conspiracy theory, the predominant use of conspiracy theory is deeply evaluative, encoding information about epistemic deficiency and often also derogatory and disparaging information. On the basis of these results, we present a new strategy for engineering conspiracy theory to promote theoretical investigations and institutional discussions of this phenomenon. We argue for engineering conspiracy theory to encode an epistemic evaluation, and to introduce a descriptive expression—such as ‘conspiratorial explanation’—to refer to the purely descriptive concept conspiracy theory. (shrink)

LS Penrose was the first to propose a measure of voting power (which later came to be known as ‘the [absolute] Banzhaf index’). His limit theorem – which is implicit in Penrose (1952) and for which he gave no rigorous proof – says that, in simple weighted voting games, if the number of voters increases indefinitely while the quota is pegged at half the total weight, then – under certain conditions – the ratio between the voting powers (as measured by (...) him) of any two voters converges to the ratio between their weights. We conjecture that the theorem holds, under rather general conditions, for large classes of variously defined weighted voting games, other values of the quota, and other measures of voting power. We provide proofs for some special cases. (shrink)

This wide-ranging volume presents an in-depth picture of adolescent sexuality and behavior. As perhaps the most vital period in human development, adolescence is a time of complex, often difficult interactions between diverse influences. Here, nineteen scientists representing ten disciplines explore the biological, psychological, and cultural factors involved in the onset of puberty and its associated emotional changes. Patterns of adolescent sexual behavior are viewed in cross-cultural perspective, psychiatric disorders are considered, and trends in adolescent sexual activity, contraception, and pregnancy are (...) described. Key legal and social dilemmas are also explored. This is the third volume in a groundbreaking series from the Kinsey Institute, which has as its aim the study of topics relating to sex, gender, and reproduction that require an interdisciplinary approach. Previous volumes in the series include Homosexuality/Heterosexuality and Masculinity/Femininity. (shrink)

Bioethics has paid surprisingly little attention to the special problems faced by women and to feminist analyses of current health care issues other than ...