Friedman, Harsanyi, Rawls, Boulding – or somebody else? An experimental investigation of distributive justice

This paper investigates distributive justice using a fourfold experimental design: The ignorance and the risk scenarios are combined with the self-concern and the umpire modes. We study behavioral switches between self-concern and umpire mode and investigate the goodness of ten standards of behavior. In the ignorance scenario, subjects became, on average, less inequality-averse as umpires. A within-subjects analysis shows that about one half became less inequality-averse, one quarter became more inequality-averse and one quarter remained unchanged as umpires. In the risk scenario, subjects became on average more inequality-averse in their umpire roles. A within-subjects analysis shows that about half became more inequality-averse, one quarter became less inequality-averse, and one quarter remained unchanged as umpires. As to the standards of behavior, several prominent ones (leximin, leximax, Gini, Cobb-Douglas) were not supported, while expected utility, Boulding’s hypothesis, the entropy social welfare function, and randomization preference enjoyed impressive acceptance. For the risk scenario, the tax standard of behavior joins the favorite standards of behavior.Financial Support of the European Commission under TMR Contract No. ERBFMRXCT98-0248 is gratefully acknowledged. We are indebted to Serge-Christophe Kolm, Alf Erling Risa, Peter Zweifel, two anonymous referees and an editor of Social Choice and Welfare for helpful comments. We thank Marc Paolella for improving our English writing style. The usual disclaimer applies. The experimental data can be obtained from the authors (e-mail: traub@bwl.uni-kiel.de).     

Thinning operations for modeling time series of counts—a survey

The analysis of time series of counts is an emerging field of science. To obtain an ARMA-like autocorrelation structure, many models make use of thinning operations to adapt the ARMA recursion to the integer-valued case. Most popular among these probabilistic operations is the concept of binomial thinning, leading to the class of INARMA models. These models are proved to be useful, especially for processes of Poisson counts, but may lead to difficulties in the case of different count distributions. Therefore, several alternative thinning concepts have been developed. This article reviews such thinning operations and shows how they are successfully applied to define integer-valued ARMA models.     

Probability and statistics: A tale of two worlds?

This comparative study of research productivity and publication habits in probability and statistics completes the paper that was published in this Journal at the end of 1997. It is based on a ten-year survey of eighteen international journals, half of which are specialized in probability theory and the other half in statistics. Paper, author and adjusted page counts yield cursory measures of productivity for countries and institutions that contributed to fundamental research in these two related fields during the period 1986-1995. These data also reveal significant cultural differences between probabilists and statisticians in the volume of research, the length of papers, coauthorship practices, etc. Canada is seen to be one of the strongest contributors to the development of these two disciplines.     

Shape analysis for automated sulcal classification and parcellation of MRI data

We describe geometric invariants that characterize the shape of curves and surfaces in 3D space: curvature, Gauss integrals and moments. We apply these invariants to neuroimaging data to determine if they have application for automatically classifying and parcellating cortical data. The curves of sulci and gyri on the cortical surface can be obtained by reconstructing cortical surface representations of the human brain from magnetic resonance imaging (MRI) data. We reconstructed gray matter surfaces for 15 subjects, traced 10 sulcal curves on each surface and computed geometric invariants for each curve. These geometric features were used classify the curves into sulcal and hemispheric classes. The best classification results were obtained when moment-based features were computed on the sulcal curves in native space. Gauss integral measures showed that they were useful for differentiating the hemispheric location of a single sulcus. These promising results may indicate that moment invariants are useful for characterizing shape on a global scale. Gauss integral invariants are potentially useful measures for characterizing cortical shape on a local, rather than global scale. Gauss integrals have found biological significance in characterizing proteins so it is worthwhile to consider their possible application to neuroscientific data.     

The Joy of Copulas: Bivariate Distributions with Uniform Marginals

We describe a class of bivariate distributions whose marginals are uniform on the unit interval. Such distributions are often called “copulas.” The particular copulas we present are especially well suited for use in undergraduate mathematical statistics courses, as many of their basic properties can be derived using elementary calculus. In particular, we show how these copulas can be used to illustrate the existence of distributions with singular components and to give a geometric interpretation to Kendall's tau.