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.     

GENDER AND RACE PATTERNS IN THE PATHWAYS FROM SPORTS PARTICIPATION TO SELF-ESTEEM

Athletics is the most prominent extracurricular activity in U.S. secondary schools in terms of student participation and school budgets. The latter is often justified on the grounds that healthy bodies produce healthy minds, that school sports boost school spirit, and that participation in school-based sports increases students' self-esteem. In this article we examine the interrelationships among participation in a school-based sport and the benefits assumed to be associated with it. Specifically, we test a model that postulates that school spirit, operationalized as attachment to school, and healthy bodies, operationalized as a sense of physical well-being, mediate the relationship between school sports and self-esteem. Data from the National Longitudinal Study of Adolescent Health on Caucasian and African American girls and boys were employed to test the model. School attachment and physical well-being absorbed the statistical effect of participating in a sport for all four gender-by-race groups. Among Caucasian girls a negative residual effect of sports participation was observed, which suggests that sports participation encapsulates multiple effects with contradictory influences. For African American girls school attachment by itself was not a significant mediator of the effect of sports participation on self-esteem. For all groups a sense of physical well-being was the more powerful mediator.     

Child Characteristics,Parenting Stress,and Parental Involvement: Fathers Versus Mothers

This study examined variations in the relationships among child characteristics, parenting stress, and parental involvement. Participants were 100 two‐parent families with preschool‐aged children. Self‐report and interview data were collected to measure parental involvement, as well as perceptions of child temperament and parental stress. Analyses revealed significant, yet somewhat different, associations between child temperament and parental stress for mothers and fathers. More significant associations were found between perceptions of child temperament and involvement for fathers than for mothers. The associations between child temperament and parental stress and involvement differed on the basis of child and parent gender. Results are discussed in terms of future research on father involvement, as well as programs designed to encourage fathers to assume more active parental roles.     

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.     

Peer Crowd Affiliation and Internalizing Distress in Childhood and Adolescence: A Longitudinal Follow‐Back Study

Concurrent and longitudinal associations between peer crowd affiliation and internalized distress were examined in a sample of 246 youth (148 girls, 98 boys). Children completed measures of depression, social anxiety, loneliness, and self‐esteem when they were in grades 4 to 6 (Time 1), and again 6 years later during adolescence (grades 10 – 12; Time 2). At Time 2, adolescents also reported their self‐concept and their identification with reputation‐based peer crowds, including Populars, Jocks, Brains, Burnouts, Non‐Conformists, and None/Average crowds. Results indicated that adolescents' report of peer crowd affiliation was concurrently associated with self‐concept and levels of internalizing distress. Follow‐back analyses of internalizing trajectories revealed that Populars/Jocks had experienced significant declines in internalizing distress across development, whereas Brains exhibited some increases in internalizing distress between childhood and adolescence.     

THE EAST END, THE WEST END, AND KING'S CROSS: ON CLUSTERING IN THE FOUR-PLAYER HOTELLING GAME

We study experimentally a standard four-player Hotelling location game with a uniform density of consumers and inelastic demand. The pure strategy Nash equilibrium configuration consists of two firms located at one quarter of the "linear city," and the other two at three quarters. We do not observe convergence to such an equilibrium. In our experimental data we find three clusters. Besides the direct proximity of the two equilibrium locations, this concerns the focal midpoint. Moreover, we observe that whereas this midpoint appears to become more notable over time, other focal points fade away. We explain how these observations are related to best-response dynamics, and to the fact that the players rely on best-responses in particular when they are close to the equilibrium configuration.