The shape of incomplete preferences

Incomplete preferences provide the epistemic foundation for models of imprecise subjective probabilities and utilities that are used in robust Bayesian analysis and in theories of bounded rationality. This paper presents a simple axiomatization of incomplete preferences and characterizes the shape of their representing sets of probabilities and utilities. Deletion of the completeness assumption from the axiom system of Anscombe and Aumann yields preferences represented by a convex set of state-dependent expected utilities, of which at least one must be a probability/utility pair. A strengthening of the state-independence axiom is needed to obtain a representation purely in terms of a set of probability/utility pairs.Comment: Published at http://dx.doi.org/10.1214/009053606000000740 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A behaviorally-based approach to measuring inequality

The measurement of inequality is often made using observed population-based distributions, such as the distribution of income or the distribution of members of different groups across neighborhoods. Unfortunately, such distributions confound the behavior of a given year with earlier events that influence the composition of the population. Here, we advocate measuring inequality using current behavioral measures and their compositional implications, and show how such measures may be obtained from frequently available data. The approach is then applied to trends in inequality between men and women in the distribution of ages at death. Observed death distributions indicate that, since 1970, mortality in 4 Western countries experienced increases in inequality that recently leveled off. In contrast, life table death distributions, which solely reflect the implications of a given year’s mortality rates, reveal a peak in inequality followed (in 3 of the 4 countries) by appreciable declines. The results are insensitive to whether inequality is measured by entropy, the Gini Index, or the Index of Dissimilarity. However, the type of distribution analyzed---whether observed or behaviorally derived---can make a significant difference in the results obtained. Because behaviorally derived distributions reflect the inequality implications of actual behavior, they are recommended for greater use in analyses of inequality.behaviorally-based, entropy, Gini Index, index of dissimilarity, inequality, measurement

Global Strong Solutions for a Class of Heterogeneous Catalysis Models

We consider a mathematical model for heterogeneous catalysis in a finite three-dimensional pore of cylinder-like geometry, with the lateral walls acting as a catalytic surface. The system under consideration consists of a diffusion-advection system inside the bulk phase and a reaction-diffusion-sorption system modeling the processes on the catalytic wall and the exchange between bulk and surface. We assume Fickian diffusion with constant coefficients, sorption kinetics with linear growth bound and a network of chemical reactions which possesses a certain triangular structure. Our main result gives sufficient conditions for the existence of a unique global strong $L^2$-solution to this model, thereby extending by now classical results on reaction-diffusion systems to the more complicated case of heterogeneous catalysis.Comment: 30 page

Strain Limits for Concrete Filled Steel Tubes in AASHTO Seismic Provisions

INE/AUTC 13.1

Foreign Policy Views and U.S. Standing in the World

What do Americans think about the US role in world affairs and why do they think the way they do? Americans typically do not think about foreign policy most of the time, and, as a consequence, know relatively little about it (Almond 1950, Lippmann 1955, Converse 1964, Erskine 1963, Edwards 1983, Sobel 1993, Holsti 2004, Canes-Wrone 2006, Page and Bouton 2006, Berinsky 2007). While foreign policy issues can become salient when major international events (like 9/11 and the Iraq War) arise or when political candidates focus on foreign policy (Aldrich, Sullivan and Borgida 1989), ceteris paribus, Americans know and care more about domestic politics (Delli-Carpini and Keeter 1996, Holsti 1994, Canes-Wrone 2006, Converse 1964). Consequently, typical Americans are broadly aware of foreign policy, and have some available attitudes about it (Page and Bouton 2006, Aldrich et al. 1989). However, except in the face of political priming by elites or exogenous shocks, such attitudes may not be broadly accessible when making political decisions, like voting.