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     

Measures of Multigroup Segregation

In this paper we derive and evaluate measures of multigroup segregation. After describing four ways to conceptualize the measurement of multigroup segregation—as the disproportionality in group (e.g., race) proportions across organizational units (e.g., schools or census tracts), as the strength of association between nominal variables indexing group and organizational unit membership, as the ratio of between–unit diversity to total diversity, and as the weighted average of two–group segregation indices—we derive six multigroup segregation indices: a dissimilarity index (D), a Gini index (G), an information theory index (H), a squared coefficient of variation index (C), a relative diversity index (R), and a normalized exposure index (P). We evaluate these six indices against a set of seven desirable properties of segregation indices. We conclude that the information theory index H is the most conceptually and mathematically satisfactory index, since it alone obeys the principle of transfers in the multigroup case. Moreover, H is the only multigroup index that can be decomposed into a sum of between– and within–group components.     

Fire and restoration of the largest urban forest of the world in Rio de Janeiro City,Brazil

National Park of Tijuca in Rio de Janeiro (Brazil) is about 3,300 ha and considered the largest urban forest in the world. Its floristic composition is typical of Atlantic Rain Forest. The reserve is being altered because of fire occurrences and urban expansion. This study identified locations and causes of forest fires, and makes management recommendations to restore damaged areas. From 1991 to 2000, forest firefighters recorded an average of 75-fire occurrences/year. Identified causes included hot air balloons (24%), intentional (24%), rubbish burning (21%) and religious practices (17%). Primary fuels included invasive grasses and ferns. Although hot air balloons destroyed larger areas of forest in each occurrence, a greater number of fires started in the invasive vegetation along roads that bisect the forest. In response to recurrent forests, invasive vegetation has spread gradually into the forest increasing forest degradation. To decrease fire damage, sites with high fire frequencies and density of invasive vegetation were planted with less flammable species. Results indicate that fire frequency decreased and density of invasive vegetation declined. This approach appears to prevent fire incidence, reduce the need for fire fighting, and preserve existing biodiversity.     

Dairy Farm Survival in a Metropolitan Area: Dutchess County,New York, 1984–19901

Abstract The effect of nonfarm development on dairy farm survival in New York's highly developed lower Hudson Valley is analyzed. The major hypothesis is that significant losses of dairy farms during this period are the result of urban development pressures. Contrary to this hypothesis, however, the bivariate and multivariate analyses of data from a mail survey of all commercial dairy operators in Dutchess County as of 1984 and industry survivors, exiters, and new entrants through 1990 demonstrate that nonfarm development has a negligible effect on dairy farm survival; rather, survival is significantly affected by age of operator and by family disruption. Thus, demographic and family process factors are found to be more powerful determinants of dairy farm survival in this particular metropolitan context.     

Bayesian modelling of catch in a north-west Atlantic fishery

Summary. We model daily catches of fishing boats in the Grand Bank fishing grounds. We use data on catches per species for a number of vessels collected by the European Union in the context of the Northwest Atlantic Fisheries Organization. Many variables can be thought to influence the amount caught: a number of ship characteristics (such as the size of the ship, the fishing technique used and the mesh size of the nets) are obvious candidates, but one can also consider the season or the actual location of the catch. Our database leads to 28 possible regressors (arising from six continuous variables and four categorical variables, whose 22 levels are treated separately), resulting in a set of 177 million possible linear regression models for the log-catch. Zero observations are modelled separately through a probit model. Inference is based on Bayesian model averaging, using a Markov chain Monte Carlo approach. Particular attention is paid to the prediction of catches for single and aggregated ships.     

Bayesian analysis of mixture modelling using the multivariate t distribution

A finite mixture model using the multivariate t distribution has been shown as a robust extension of normal mixtures. In this paper, we present a Bayesian approach for inference about parameters of t-mixture models. The specifications of prior distributions are weakly informative to avoid causing nonintegrable posterior distributions. We present two efficient EM-type algorithms for computing the joint posterior mode with the observed data and an incomplete future vector as the sample. Markov chain Monte Carlo sampling schemes are also developed to obtain the target posterior distribution of parameters. The advantages of Bayesian approach over the maximum likelihood method are demonstrated via a set of real data.