Approximations of rational criteria under complete ignorance and the independence axiom

Rational decision making under complete ignorance, a limit case of uncertainty, is defined. Through a concept of approximation, a meaning is given to a criterion almost possessing a property. Rational criteria depend almost on the sole bounds of the outcome range of each decision, they are almost continuous, they can almost possess a transitive indifference relation; however, under Savage's Independence Axiom, this last property restricts possible criteria to those which can be approximated, at least partly, by either the Maximin or the Maximax criterion.     

Contents Volume 54

Volume Contents

Contents Volume 54     

Polarization: Concepts,Measurement, Estimation

We develop the measurement theory of polarization for the case in which income distributions can be described using density functions. The main theorem uniquely characterizes a class of polarization measures that fits into what we call the “identity‐alienation” framework, and simultanously satisfies a set of axioms. Second, we provide sample estimators of population polarization indices that can be used to compare polarization across time or entities. Distribution‐free statistical inference results are also used in order to ensure that the orderings of polarization across entities are not simply due to sampling noise. An illustration of the use of these tools using data from 21 countries shows that polarization and inequality orderings can often differ in practice.     

Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality

We derive the asymptotic sampling distribution of various estimators frequently used to order distributions in terms of poverty, welfare, and inequality. This includes estimators of most of the poverty indices currently in use, as well as estimators of the curves used to infer stochastic dominance of any order. These curves can be used to determine whether poverty, inequality, or social welfare is greater in one distribution than in another for general classes of indices and for ranges of possible poverty lines. We also derive the sampling distribution of the maximal poverty lines up to which we may confidently assert that poverty is greater in one distribution than in another. The sampling distribution of convenient dual estimators for the measurement of poverty is also established. The statistical results are established for deterministic or stochastic poverty lines as well as for paired or independent samples of incomes. Our results are briefly illustrated using data for four countries drawn from the Luxembourg Income Study data bases.     

Biomechanical analysis of older adults stepping up: a method of evaluating balance

The aim of this study was to analyze differences in biomechanical parameters between elderly and control participants when stepping up, to evaluate control of balance. Eleven control and 14 elderly participants performed a step from an initial static posture onto a 7-cm-high force plate. For the spontaneous-velocity condition, elderly participants performed a slower progression velocity than control participants. Elderly participants spent proportionally more time in stance phase, with a corresponding decrease in swing phase, than the control participants, irrespective of movement velocity. In contrast, at spontaneous velocity the parameters related to ground-reaction force (GRF) showed that anteroposterior and mediolateral forces at toe-off of the support limb and the slope of vertical force during weight transfer were significantly smaller for the elderly than for control participants. These GRF parameters depended on the stepping-up velocity. The elderly develop a spatiotemporal strategy and reduced movement velocity to control support balance.     

Intergenerational reliance on social assistance: Evidence from Canada

This paper provides the first analysis of the intergenerational transmission of participation in a Canadian social assistance program. Two sources of intergenerational transmission are taken into account: one that is due to a possible causal link between parents' and children's participation, and one that is due to a correlation between individual and environment specific characteristics across generations. The basic data come from the Québec government's administrative records and cover 17,203 young people who were 18 years old in 1990 and whose parents were recipients of social assistance during at least one month between 1979 and 1990. The results reveal that, on average, a one-percentage unit increase in parental participation during the youth's pre-adult years (age 7–17) raises the youth's participation rate by 0.29 percentage unit during early adulthood (age 18–21). This impact is stronger during the early stages of childhood (age 7–9) and during late adolescence (age 16–17).