New trends on the numerical representability of semiordered structures

[EN] We introduce a survey, including the historical back-ground, on different techniques that have recently been issued in the search for a characterization of the representability of semiordered structures, in the sense of Scott and Suppes, by means of a real-valued function and a strictly positive threshold of discrimination.This work has been supported by the research projects MTM2007-62499, ECO2008-01297, MTM2009-12872-C02-02 and MTM2010-17844 (Spain)Abrísqueta, F.; Campión, M.; Catalán, R.; De Miguel, J.; Estevan, A.; Induráin, E.; Zudaire, M.... (2012). New trends on the numerical representability of semiordered structures. Mathware & Soft Computing Magazine. 19(1):25-37. http://hdl.handle.net/10251/57632S253719

On the use of Cost-Benefit Analysis and Multi-Criteria Evaluation in ex-ante Impact Assessment

When a public administration wishes to implement policies, there is a need of comparing different options and valuating and evaluating them to assess their social attractiveness. Traditionally, welfare economics has used cost-benefit analysis based on the Kaldor-Hicks compensation principle, which was invented to achieve two clear objectives: 1) To compare individuals’ preferences according to the efficiency oriented utilitarian calculus, explicitly avoiding the principle one individual, one vote. 2) To implement an objective evaluation criterion, that could be accepted in the framework of the positivistic philosophical paradigm. A relevant question now is: are these objectives still relevant in the 21st Century? This article aims at presenting a structured comparison of the main distinguishing features of monetary and non-monetary methods useful in the assessment of public policy options. In particular, cost-benefit analysis (CBA) and multi-criteria evaluation (MCE) are discussed according to the following ten comparison criteria: efficiency, fairness, democratic basis, effectiveness, problem structuring, alternatives taken into account, policy consequences, comprehensiveness, transparency and mathematical aggregation rule. A conclusion is that regarding public policy problems, CBA and MCE can be considered as competitive methods only if all consequences of a policy decision can be correctly transformed into monetary values and efficiency is the only relevant policy objective. In all other cases, CBA can be used as a criterion in a MCE framework; thus in general terms, CBA and MCE are complementary in nature. MCE seems to be an appropriate public policy framework to integrate different scientific languages, when concerns about civil society and future generations have to be considered along with policy objectives and market conditions.JRC.I.1-Modelling, Indicators and Impact Evaluatio

Comparison of random variables from a game-theoretic perspective

This work consists of four related parts, divided into eight chapters. A ¯rst part introduces the framework of cycle-transitivity, developed by De Baets et al. It is shown that this framework is ideally suited for describing and compar- ing forms of transitivity of probabilistic relations. Not only does it encompass most already known concepts of transitivity, it is also ideally suited to describe new types of transitivity that are encountered in this work (such as isostochas- tic transitivity and dice-transitivity). The author made many non-trivial and sometimes vital contributions to the development of this framework. A second part consists of the development and study of a new method to compare random variables. This method, which bears the name generalized dice model, was developed by De Meyer et al. and De Schuymer et al., and can be seen as a graded alternative to the well-known concept of ¯rst degree stochastic dominance. A third part involves the determination of the optimal strategies of three game variants that are closely related to the developed comparison scheme. The de¯nitions of these variants di®er from each other solely by the copula that is used to de¯ne the payo® matrix. It turns out however that the characterization of the optimal strategies, done by De Schuymer et al., is completely di®erent for each variant. A last part includes the study of some combinatorial problems that orig- inated from the investigation of the transitivity of probabilistic relations ob- tained by utilizing the developed method to compare random variables. The study, done by De Schuymer et al., includes the introduction of some new and interesting concepts in partition theory and combinatorics. A more thorough discussion, in which each section of this work is taken into account, can be found in the overview at the beginning of this manuscript. Although this work is oriented towards a mathematical audience, the intro- duced concepts are immediately applicable in practical situations. Firstly, the framework of cycle-transitivity provides an easy means to represent and compare obtained probabilistic relations. Secondly, the generalized dice model delivers a useful alternative to the concept of stochastic dominance for comparing random variables. Thirdly, the considered dice games can be viewed in an economical context in which competitors have the same resources and alternatives, and must choose how to distribute these resources over their alternatives. Finally, it must be noted that this work still leaves opportunities for future research. As immediate candidates we see, ¯rstly the investigation of the tran- sitivity of generalized dice models in which the random variables are pairwisely coupled by a di®erent copula. Secondly, the characterization of the transitivity of higher-dimensional dice models, starting with dimension 4. Thirdly, the study of the applicability of the introduced comparison schemes in areas such as mar- ket e±ciency, portfolio selection, risk estimation, capital budgeting, discounted cash °ow analysis, etc