Linking Input Inequality and Outcome Inequality

Inequality often appears in linked pairs of variables. Examples include schooling and income, income and consumption, and wealth and happiness. Consider the famous words of Veblen: “wealth confers honor.” Understanding inequality requires understanding input inequality, outcome inequality, and the relation between the two—in both inequality between persons and inequality between subgroups. This article contributes to the methodological toolkit for studying inequality by developing a framework that makes explicit both input inequality and outcome inequality and by addressing three main associated questions: (1) How do the mechanisms for generating and altering inequality differ across inputs and outcomes? (2) Which have more inequality—inputs or outcomes? (3) Under what conditions, and by what mechanisms, does input inequality affect outcome inequality? Results include the following: First, under specified conditions, distinctive mechanisms govern inequality in inputs and inequality in outcomes. Second, input inequality and outcome inequality can be the same or different; if different, whether inequality is greater among inputs or outcomes depends on the configuration of outcome function, types of inputs, distributional form of and inequality in cardinal inputs, and number of and associations among inputs. Third, the link between input inequality and outcome inequality is multiform; it can be nonexistent, linear, or nonlinear, and if nonlinear, it can be concave or convex. More deeply, this work signals the formidable empirical challenges in studying inequality, but also the fast growing toolbox. For example, even if the outcome distribution is difficult to derive, fundamental theorems on the variance make it possible to analyze the input–outcome inequality connection. Similarly, within specified distributions, the general inequality parameter makes it possible to express results in terms of both measures of overall inequality and measures of subgroup inequality.

Cumulative Subtraction Games

We study a variation of Nim-type subtraction games, called Cumulative Subtraction (CS). Two players alternate in removing pebbles out of a joint pile, and their actions add or remove points to a common score. We prove that the zero-sum outcome in optimal play of a CS with a finite number of possible actions is eventually periodic, with period $2s$, where $s$ is the size of the largest available action. This settles a conjecture by Stewart in his Ph.D. thesis (2011). Specifically, we find a quadratic bound, in the size of $s$, on when the outcome function must have become periodic. In case of exactly two possible actions, we give an explicit description of optimal play.

A model of electoral competition between national and regional parties

We consider a one-dimensional model of electoral competition with national and regional parties. There are two regions and three parties—one national party and one regional party for each region. We divide the paper into two parts— homogeneous and heterogeneous regions. In the former, the policy positions of the national party and the regional party of the region with the greater number of constituencies coincide with the favorite policy position of the region-wide median voter. In the latter, the national party chooses a policy position in a maximal isolation set, while the two regional parties choose policies on the same side of the national party’s policy as their own respective region-wide medians. For a given outcome function, the national party performs better when the regions are heterogeneous. In the homogeneous regions case, the national party can at best do as well as the regional party of the region with the greater number of constituencies. Our results are broadly consistent with intuition and evidence.

The Comparative Benefits and Hazards of EFBs and Paper Documents in the Cockpit

Electronic Flight Bags (EFBs) are replacing the traditional paper documents used by pilots for pre-flight planning and in-flight operations. Simulation studies comparing information retrieval times and error rates for EFBs and paper documents have found that pilots are faster and perform better with EFBs, but it is unclear whether this is true for all EFB systems. This study compared reports from the ASRS across categorical variables such as Human Factors Issue, Outcome, Function in Use, Operating Regulations and Phase of Flight. The most significant human factors issues relating to EFBs were lack of training, distractions/workload, and inhibited access to information. Crewmembers consistently ran into difficulty with the zooming/panning feature of EFBs, especially on multi-touch touchscreen displays.