A majorization comparison of apportionment methods in proportional representation

From the inception of the proportional representation movement it has been an issue whether larger parties are favored at the expense of smaller parties in one apportionment of seats as compared to another apportionment. A number of methods have been proposed and are used in countries with a proportional representation system. These apportionment methods exhibit a regularity of order, as discussed in the present paper, that captures the preferential treatment of larger versus smaller parties. This order, namely majorization, permits the comparison of seat allocations in two apportionments. For divisor methods, we show that one method is majorized by another method if and only if their signpost ratios are increasing. This criterion is satisfied for the divisor methods with power-mean rounding, and for the divisor methods with stationary rounding. Majorization places the five traditional apportionment methods in the order as they are known to favor larger parties over smaller parties: Adams, Dean, Hill, Webster, and Jefferson. Received: 5 August 2000/Accepted: 24 October 2001     

Worlds come apart: Systems theory versus critical theory. Drama in the history of sociology in the twentieth century

This article places an episode in the history of sociological theory into intellectual history in the twentieth century. The perspective is chronological as well as contextual. The themes are two theoretical approaches, both embedded in both American and German history, Parsonian Systems Theory and “Frankfurt School” Critical Theory. The chronology shown spanned mainly from the 1940s to the 1960s. The context of the two theories is a period that is crucial in twentieth century history. The protagonists of the two approaches were, in the 1940s, Americans and Germans exiled in the United States. In the 1950s, both approaches were affected by McCarthyism in different ways. The 1960s, however, were the culmination. The dynamics of the two approaches led into a schism which came into the open on the occasion of the 1964 German Sociology Conference in Heidelberg celebrating Max Weber. The article shows the stages in the evolution of the schism, emulating three acts in a drama. The final split was over whether Weber or Marx should be the classic whose oeuvre was to influence sociological thinking today. My aim is to exemplify how these two authoritative approaches in sociological theory, far from escaping the vagaries and vicissitudes of their times, were embedded in twentieth-century history.     

Partial strikes under the railway labor act: The need for a doctrine of unprotected concerted activity

In light of use by airline unions of partial-strike tactics, such as concerted refusals to bid for overtime work and so-called ” CHAOS” tactics involving unannounced refusals to fly after passengers have been ticketed and are ready to board, the authors examine whether the Railway Labor Act (RLA) should be interpreted to permit employers to discipline employees for engaging in such tactics, or whether these are a protected form of economic pressure. Although in many respects bargaining duties and economic weapons under the RLA are read consonant with precedents under the National Labor Relations Act (NLRA) (which governs all industries other than rail and air transport), there are a few decisions suggesting that during the period when self-help may be resorted to, employees can engage in partial strike activities as long as they violate no court order but are subject to permanent replacement in limited circumstances. These decisions, the authors submit, fail to take account of Supreme Court decsions since the 1930s that some economic pressures by unions, such as slowdowns and sitins, may not violate the labor laws but nor are they protected by those laws so as to immunize partial strikers from employer discipline. These decisions are not based on unique features of the NLRA. Rather, they give recognition to the background assumptions of Congress that employers may act to protect their property interests as long as they do not run afoul of NLRA or RLA protections and that employees who engage in partial-strike activities are subject to employer discipline even where not strictly necessary to maintain operations. Moreover, these tactics skew the bargaining process by giving employees an essentially risk-free gambit to pressure their economic position through planned disruption of carrier operations. Professor Estreicher is also labor and employment counsel to O’Melveny & Myers, LLP. The views expressed herein are the authors’ and should not be attributed to any organization. Hannah Breshin and Tom Jerman of O’Melveny & Myers, assisted the authors with this article. We also thank Professor Herbert Northrup for his helpful comments.     

Adolescent Protective Factors Promoting Resilience in Young Adults at Risk for Depression

In a longitudinal, community-based study, adolescent protective factors for those at risk for depression were identified that were associated with resilient outcomes in young adulthood. For those with childhood risk factors for major depression, significant protective factors included family cohesion, positive self appraisals, and good interpersonal relations. Findings may help inform the development of prevention and treatment programs for adolescents vulnerable to depression. Implications for future research and clinical practice are discussed.     

Luxembourg's Foreign Policy: Does Small Size Help or Hinder?

As a very small state, Luxembourg would not appear to qualify as an influential foreign policy actor either in Europe or the world. Yet the country's international influence has long belied its reputation as a small state. This article reviews the literature on small-state foreign policy and finds that it offers numerous contradictory conclusions. As a case study it then addresses Luxembourg in the 1990s, with particular attention to two themes: its active participation in the European Union (EU) and its policies directed at maintaining economic prosperity. The paper goes on to explain Luxembourgish foreign policy behaviour through three levels of analysis and assesses to what extent smallness is a benefit or a hindrance to Luxembourg's success in meeting its international goals.     

A NOTE ON EVANESCENT PROCESSES

This note examines the connection between μ-invariant measures for the transition function of a continuous-time Markov chain and those of its q-matrix, Q. The major result establishes a necessary and aufficient condition for a convergent μ-invariant measure for Q to be μ-inhant for the minimal transition function, P, under the assumption that P is honest. This corrects Theorem 6 of Vere-Jones (1969) and the first part of Corollary 1 of Pollett (1986), both of which assert that the above conclusion holds in the absence of this condition. The error was pointed out by E.A. van Doom (1991) and the counterexample which be presented provides the basis for the present arguments. In determining where the error occurred in the original proof, we are able to identify a simple sufficient condition for μ-invariance.