The Gini index and the consistent measurement of inequality among the poor

In several economic fields, such as those related to health, education or poverty, the individuals' characteristics are measured by bounded variables. Accordingly, these characteristics may be indistinctly represented by achievements or shortfalls. A diculty arises when inequality needs to be assessed. One may focus either on achievements or on shortfalls but the respective inequality rankings may lead to contradictory results. Specifically, this paper concentrates on the poverty measure proposed by Sen. According to this measure the inequality among the poor is captured by the Gini index. However, the rankings obtained by the Gini index applied to either the achievements or the shortfalls do not coincide in general. To overcome this drawback, we show that an OWA operator is underlying in the definition of the Sen measure. The dual decomposition of the OWA operators into a self-dual core and anti-self-dual remainder allows us to propose an inequality component which measures consistently the achievement and shortfall inequality among the poor

Characterizing best-worst voting systems in the scoring context

An increasing body of theoretical and empirical work on discrete choice considers a choice design in which a person is asked to select both the best and the worst alternative in an available set of alternatives, in contrast to more traditional tasks, such as where the person is asked to: select the best alternative; select the worst alternative; rank the alternatives. Here we consider voting systems motivated by such “best–worst” choice; characterize a class of “best–worst” voting systems in terms of a set of axioms in the context of scoring rules; and discuss briefly possible extensions to approval–disapproval systems.

Thermoresponsive gold polymer nanohybrids with a tunable cross-linked meo 2 ma polymer shell

Gold nanoparticles (AuNPs) are functionalized with a thermoresponsive polymer shell of a cross-linked poly(2-(2-methoxyethoxy)ethyl methacrylate) (P(MEO 2 MA)). To provide a covalent attachment of the polymer to the NP surface, AuNPs are fi rst modifi ed using butanoic acid to develop the encapsulation with the biocompatible thermoresponsive polymer formed by free-radical precipitation polymerization. Both the MEO 2 MA concentration and the shell cross-linking density can be varied and, in turn, the thickness and the shells' free volume can be fi ne-tuned. By downscaling the size of the polymeric shell, the lower critical solution temperature (LCST) is decreased. The LCST in the nanohybrids changes from 19.1 to 25.6 °C when increasing the MEO 2 MA content; it reaches almost 26 °C for P(MEO 2 MA) (bulk). The maximum decrease in the volume of the nanohybrids is around 40%, resulting in a modifi cation of the light scattering properties of the system and causing a change in the turbidity of the gel network. The sizes of the nanohybrids are characterized using both transmission electron microscopy and dynamic light scattering measurements. Optical properties of the colloidal systems are determined using the derived count rate measurements as an alternative to absorbance or transmittance measurements, confi rming the colloidal stability of the nanohybrid systems.Peer Reviewe

Numerical representability of fuzzy total preorders

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