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Abstract

The Human Development Index (HDI) is a measure of a country's development level that considers components that go beyond income. In this paper first we revise all past and present HDI together with their corresponding marginal rates of substitution (MRS). We find that according to the existing HDI the implementation of a certain health policy in a country is independent of its education level and vice versa. On the other hand, there is a literature indicating that education and health are complements in the production of the other. Motivated by these finding we propose an alternative HDI that complies with these findings and similarly as Herrero at al (2012), solves the problem of high discrepancy in the MRS found in the HDI of 2010.




Abstract

This paper identifies necessary and sufficient single-profile conditions for consistent decision under an supermajority rule. It is demonstrated that a preference profile generates a transitive supermajority rule relation if and only if it is not sufficiently balanced.




Abstract

In this paper we consider population rankings that are based on the opinion of the involved individuals. Each member of the society is asked to provide an ordered list of the population excluding himself. This information forms a profile of preferences that is used to decide what should be the population social ranking. Among all the possible aggregation methods, we are interested in the ones where each individual is impartial on his social position, i.e. any change of an individual initial preferences should not result with a variation of his own rank. Adding some additional monotonicity and unanimity requirements we show that such a social ordering does not exists.



Abstract

Many international organizations categorize populations with respect to their success on several qualities. In this spirit, the United Nations perform country classification relating to their accomplishment on Human Development. For that purpose, the UN combines each country's indicators of Income, Education Level and Life Expectancy into an overall index that represents its achieved Human Development. The idea behind Human Development is enriching people's choices and improving human capabilities. Therefore, the overall index objective is to provide governments with benchmarks for efficient development and motivate them to sustain Human Development by growth on every component. However, the methodology used by the UN allows countries to use trade-offs between different attributes and hence obtain higher level of Development by focusing for instance, on Income growth only. The paper reviews the classification techniques (rules) used when performing population categorization according to different attributes. We extend the standard classification procedures known in the literature and within this new family we characterize those rules that meet our axiom of no trade-offs among different attributes.



Abstract

We consider a preference relation over a finite set of alternatives that violates transitivity on the indifference part. Since there is no utility function representing this class of preferences, we derive a correspondence from the set of alternatives to Rn, that recovers the initial preference relation, by using coordinate-wise comparison. Moreover, we find an equivalent representation that employs strict set inclusion.




Abstract

Using the deconvolution theory, Fourier transformation and kernel estimation, we derive a procedure to consrtuct an estimator for the density of a multivariate volatility process. Having the estimator, we derive bounds for its bias and variance.