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     

Territorial Modernity and Public Space: Lessons from the Politics of Water Conflict Along the US/Canadian Border

Conflict over water resources is a major problem throughout the world. This essay describes the long-standing and often successful effort to insulate decisions on how to allot water among contending users, and how to reduce water pollution along a 5000-mile international border. The effort has been fraught with political and scientific complexity. Yet, after more than 90 years of experience, it provides a model that other nations are beginning to examine as relevant to their own efforts to find solutions.     

On the run length of a Shewhart chart for correlated data

We consider an extension of the classical Shewhart control chart to correlated data which was introduced by Vasilopoulos/Stamboulis (1978). Inequalities for the moments of the run length are given under weak conditions. It is proved analytically that the average run length (ARL) in the in-control state of the correlated process is larger than that in the case of independent variables. The exact ARL is calculated for exchangeable normal variables and autoregressive processes (AR). Moreover, we compare this chart with residual charts. Especially, in the case of an AR(1)—process with positive coefficient, it turns out that the out-of-control ARL of the modified Shewhart chart is smaller than that of the Shewhart chart for the residuals.     

Binding the Generations: Household Formation Patterns among Vietnamese Refugees1

Much of the analysis of refugee and immigrant adaptation has stressed the interaction of prior experience with the requirements of life in a new country. For refugees, that interaction has often been jarring because of the after‐effects of their flight and their relative inability to prepare for a new life in a new country. Yet refugees have often done rather well in economic terms in that new country. The reasons for that relative success have been phrased in cultural terms (e.g., the predisposition toward education) and in general socioeconomic terms (e.g., refugees as educated and skilled). This article examines a set of factors that lie between these customary cultural and socioeconomic categories. Specifically, the paper examines key features of household formation among Vietnamese refugees. An examination of historical data from southern Vietnam indicates patterns in household formation that appear durable over time yet are not shared across the breadth of Vietnam and cannot thus be viewed as “cultural” in the usual sense. A comparison of the historical data with recent national survey data on refugees in the United States indicates that these patterns continue among Vietnamese refugees and are ‐ as compared to other refugees ‐ distinctive to them. These patterns of household formation provide Vietnamese refugees with important options in adaptation to a new country.     

Open Road or Blind Alley? Welfare Reform, Mothers, and Children with Disabilities

Welfare reform was examined for 39 Michigan families whose children have significant health or intellectual and behavioral disabilities. As a group, these families received little specialized assistance or services to address their unique needs. Family-cited barriers to self-sufficiency included poorly trained welfare caseworkers, limited public transportation, and inadequate child care. Having an older child was the only discriminating variable between working and non-working mothers. However, working mothers only had temporary positions with no benefits and low pay. All families, whether employed or not, lived below the poverty line.