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Öğe Mathematics and Economics, with Special Attention to Social Choice Theory(Springer International Publishing, 2021) Salles, M.The historical context of the usage of mathematics in economics and some other related social sciences is briefly described. This usage is then emphasized in three specific topics: (1) the analysis of a competitive market, regarding in particular the existence of equilibrium and the relations between the concepts of equilibrium and of optimality; (2) in social choice theory, Arrow’s theorem and results about the strategy-proofness of voting procedures; and (3) in game theory, focusing on cooperative games, the relations between the concepts of core and of competitive equilibrium, and an analysis of Shapley-Shubik voting power index in the case of the voting procedure used within the UN Security Council. The use of mathematics in economics has been questioned. Some responses to this questioning are provided. Finally, the thesis of the “indispensability of mathematics” is defended in the case of the social sciences. © Springer Nature Switzerland AG 2021.Öğe Öğe Social choice and the capability approach(Cambridge University Press, 2020) Salles, M.Social choice is concerned with the selection of an ideal (or social) option, which can be a so-called 'social state', or a social 'utility', or a social 'preference', or a social choice 'set', on the basis of individual utilities, or individual utility functions, or individual preferences, or individual choice sets, or individual choice functions. A number of scholars have outlined the limited aspect of the notion of utility, including, notably and pre-eminently, Amartya Sen and Martha C. Nussbaum. Although they did not put it in such a strong phrase, the basic idea is to replace the notion of utility by the notion of capability (leaving aside 'happiness', a notion which for many is hardly distinguishable from utility). As has been remarked by Mozaffar Qizilbash, the development of the capability approach has been focused on the capability of an individual; and the idea of amalgamating or aggregating individual data is consubstantial with social choice. The purpose of this text is to propose some preliminary ideas regarding the aggregation of individual capabilities. © 2021 Cambridge University Press.
