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We present a framework to assess the relative cognitive cost of alternative representational systems for problem solving.The framework consists of 19 cognitive properties of representational systems, which are distributed across 4 dimensions(registration, semantic encoding, inference, and solution) and three scales of granularity (symbol, expression, and sub-representations). It examines components and processes spanning the internal mental representation and external physicaldisplay, and also addresses heterogenous representations of problems. We provide functions to evaluate the cost of eachcognitive property by examining, for example, types of matches between display symbols and concepts, the arity ofrelations, or the depth of solution trees. The cognitive costs for each property are combined to estimate the overallcognitive cost, and hence the relative effectiveness, of a representation. The frameworks development is motivated byour goal of engineering an automated system that will select representations suited to specific classes of problems forindividual users.

In this paper, we evaluate income distributions in four European countries (Austria, Italy, Spain and Hungary) using two complementary approaches: a standard approach based on reported incomes in survey data, and a microsimulation approach, where taxes and benefits are simulated. These two approaches may be expected to generate slightly different results, particularly in respect of individuals on lower incomes, because benefit receipts tend to be under-reported in survey data, and over-estimated in microsimulation procedures. However, we find that the two approaches do in fact produce reasonably consistent results, in terms of both inequality measures and poverty rates. To the extent that the results differ, we explore the reasons why these differences arise, and suggest directions for future research, in which each approach may inform improvements in the other.

International comparisons of inequality based on measures of disposable income may not be valid if the size and incidence of publicly provided in-kind benefits differ across the countries considered. The benefits that are financed by taxation in one country may need to be purchased out of disposable income in another. We estimate the size and incidence of in-kind or "noncash" benefits from public housing subsidies, education, and health care for five European countries using comparable methods and data. Inequality in the augmented income measure is dramatically lower than in disposable income, with the effects of the three components varying in importance across countries. Adapting equivalence scales to take proper account of differences in needs for health care and education across population members reduces the scale of the effect, but does not eliminate it. (Contains 11 tables, 3 figures, and 15 footnotes.)