Antonio Villar

Multidimensional Social Evaluation: An Application to the Measurement of Human Development

This paper deals with the axiomatic derivation of social evaluation indices in a multidimensional context. The resulting evaluation formula is the geometric mean of the egalitarian equivalent values of the different characteristics under consideration. We provide an application to the measurement of human development and compare the results obtained with those corresponding to the standard (additive) index.

On the Comparison of Group Performance with Categorical Data

There are many different evaluation problems that involve several groups (societies, firms or institutions) whose members can be classified into ordered categories, pursuant to their characteristics or their achievements. This paper addresses these types of problems and provides an evaluation criterion based on the distribution of the agents across categories. The starting point is that of dominance relations in pair-wise comparisons. We say that group i dominates group j when the expected category of a member of i is higher than the expected category of a member of j. We introduce the notion of relative advantage of a group to extend this principle to multi-group comparisons and show that there is a unique evaluation function that ranks all groups consistently in terms of this criterion. This function associates to each evaluation problem the (unique) dominant eigenvector of a matrix whose entries describe the dominance relations between groups in pair-wise comparisons. The working of the model is illustrated by means of three different applications.

On the existence of Pareto optimal allocations when individual welfare depends on relative consumption

Abstract In this paper we analyze the existence of Pareto optimal allocations of k goods among n agents, when individual welfare depends on relative consumption. Under rather mild assumptions we show that for any predetermined vector of utility values we can find the amounts of goods, and their corresponding distribution, so that those target utility values are efficiently achieved. Then we prove that in the case where utility functions are interpersonally comparable (in ordinal terms), there exists a Pareto optimal allocation of any given bundle of goods that equalizes all agents welfare levels (what we call a welfare-fair allocation).

The Herrero-Villar approach to citation impact

This paper focuses on the evaluation of research institutions in terms of size-independent indicators. There are well-known procedures in this context, such as what we call additive rules, which provide an evaluation of the impact of any research unit in a scientific field based upon a partition of the field citations into ordered categories, along with some external weighting system to weigh those categories. We introduce here a new ranking procedure that is not an additive rule – the HV procedure, after Herrero & Villar (2013) – and compare it those conventional evaluation rules within a common setting. Given a set of ordered categories, the HV procedure measures the performance of the different research units in terms of the relative probability of getting more citations. The HV method also provides a complete, transitive and cardinal evaluation, without recurring to any external weighting scheme. Using a large dataset of publications in 22 scientific fields assigned to 40 countries, we compare the performance of several additive rules – the Relative Citation Rate, four percentile-based ranking procedures, and two average-based high-impact indicators – and the corresponding HV procedures under the same set of ordered categories. Comparisons take into account re-rankings, and differences in the outcome variability, measured by the coefficient of variation, the range, and the ratio between the maximum and minimum index values.

The rights egalitarian solution for NTU sharing problems

The purpose of this paper is to extend the rights egalitarian solution (Herrero etxa0al. in Math Soc Sci 37:59–77, 1999) to the context of non-transferable utility sharing problems. Such an extension is not unique. Depending on the kind of properties we want to preserve we obtain two different generalizations. One is the “proportional solution”, that corresponds to the Kalai–Smorodinsky solution for surplus sharing problems and the solution in Herrero (Soc Choice Welf 15:113–119, 1998) for rationing problems. The other is the “Nash solution”, that corresponds to the standard Nash bargaining solution for surplus sharing problems and the Nash rationing solution (Mariotti and Villar in Int J Game Theory 33:367–377, 2005) for the case of rationing problems.

Who Meets the Standrads: A Multidimensional Approach

We consider here the evaluation of the performance of a society with respect to a given set of targets. We provide a characterization of an intuitive evaluation formula that consists of the mean of the shares of the achievements in the targets. The criterion so obtained permits one not only to endogenously determine who meets the standards and who does not, but also to quantify the degree of fulfilment. Two empirical illustrations are provided: the compliance of the European Union Stability and Growth Pact, on the one hand, and the evaluation of research excellence in the Spanish universities, on the other hand.

Inequality and Welfare

This chapter provides an integrated way of approaching inequality measurement from a normative viewpoint, by using the notion of social evaluation function, instead of that of social welfare function. A social evaluation function is a mapping that is defined directly on the space of income distributions, without going through the intermediate step of individual utilities. This notion permits extending the standard normative approach to inequality and provides a general framework in which all the inequality indices can be confronted in terms of the properties that imply on this social evaluation function. Besides, we introduce here the notion on multidimensional inequality and welfare, that applies when more than one relevant dimension is involved. We illustrate this venue by means of the Human Development Index.

Positive Inequality Indices

This chapter discusses positive inequality measures, as functions that try to provide descriptive estimates of the variability of income distributions that satisfy most of the properties presented in Chap. 2 and are compatible with our intuitions about what inequality means. There are no explicit references to social welfare even though different measures incorporate implicitly different value judgements. Indeed, one can think of those measures as particular ways of aggregating the differences between individual incomes and a reference value, most of the times the mean income. We review here four different ways of comparing income distributions from a descriptive point of view: the Lorenz curve, the Gini index, the Theil’s family of indices and the Palma ratio. We shall check the properties that those measures satisfy in order to illustrate the different ways of valuing inequality. There are many other ways of measuring inequality, but these are the most common ones.

Multidimensional Poverty and Welfare

This chapter develops an approach to poverty measurement based on the interpretation of poverty as a welfare loss. Following the standard approach in the normative theory of income inequality, poverty indices are derived here from a social evaluation function and some poverty thresholds. A welfare poverty index is defined as the relative welfare loss due to the insufficient welfare of those agents whose achievements do not reach the minimum established. The construction of those indices is formulated in a multidimensional context. We show that, under conventional assumptions, those indices can be expressed as the product of the incidence and the inequality-adjusted intensity of poverty. We include an application to the measurement or educational poverty using the data from PISA.

Normative Inequality Indices

This chapter describes the standard approach to normative inequality measurement. The key idea is to interpret inequality as a welfare loss, when social welfare is measured by a conventional social welfare function. We focus on the of Atkinson family of inequality indices, which extends the initial ideas of Dalton by applying some of the notions that are common in expected utility theory. Atkinson uses the notion of equally distributed equivalent income to evaluate the actual distribution and to assess the size of the welfare loss. Those inequality indices are derived from a utilitarian social welfare function applied to individuals with identical cardinal utility functions. Atkinson generates a family of indicators that depend on a single parameter, to be understood as a measure of inequality aversion.