This chapter reviews the SWFL approach to social choice. It does not attempt to be a complete and systematic survey of existing results, but to give a critical assesment of the main axioms and their role in filtering the ethically relevant information, in particular the measurability and comparability properties of individual evaluation functions. Social welfare functionals are defined formally together with closely related concepts. After adducing a good number of examples, we elaborate on the meaning of the SWFL domain of definition and we sketch some alternative approaches. Several types of axioms are considered; some of them are used to filter the relevant information while others express collective efficiency or equity requirements. Then, to illustrate the various tradeoffs among these axioms, selected characterisation results are presented; most of them are cast in what we call the formally welfarist framework. Finally, we have assembled some other characterisations which eschew either invariance properties or the formally welfarist framework. We discuss the treatment of two sets of social alternatives endowed with an enriched structure, viz. the set of classical exchange economies and the complete set of lotteries one can define on an abstract set of pure alternatives. As an introduction to the latter discussion, we elaborate on the difficulties raised by social evaluation when risks and uncertainty are taken explicitly into account.
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ReDIF This chapter was published in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.) Handbook of Social Choice and Welfare, , chapter 10, pages 459-541, 2002.