By A.K. Sen
This e-book is anxious with the learn of collective choice, particularly with the connection among the targets of social motion and the personal tastes and aspirations of societys participants.
Professor Sens technique is predicated at the assumption that the matter of collective selection can't be satisfactorily mentioned in the confines of economics. whereas collective selection types an important point of economics, the topic pertains additionally to political technology, the idea of the kingdom, and to the speculation of determination strategies. the writer has accordingly used fabric from those disciplines, plus philosophical points from ethics and the idea of justice.
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Additional resources for Collective Choice and Social Welfare
Nothing is specified about the genesis of the social ordering. Finally, on a rather technical point, the particular method of representation chosen is unnecessarily restrictive. For the purpose of being able to choose between alternative social states, it is not really necessary that a real-valued W function must exist. 4 For example, a complete "lexicographic ordering" over a two-dimensional real space cannot be represented by any real welfare function. 1 See Samuelson (1947), p. 222. The subject could end with these banalities were it not for the fact that numerous individuals find it of interest to specify the form of W, the nature of the variables, z, and the nature of the constraints.
But consider the choice over x and z. There each is "best," since each is as good as the other. Would it be right to describe a choice process as "rational" if it can choose either x or z given the choice between the two, but must choose specifically x if the choice is over the triple x, y, z? This is a violation of property ß (defined in Chapter 1*), which requires that if two alternatives are both best in a subset, then one of them should not be best in the whole set, without the other also being best in that set.
Condition U is also satisfied. This completes the proof. Note that the social preference relation R generated by the SDF defined above is merely quasi-transitive, and is not fully transitive. Suppose there are two individuals 1 and 2 and three alternatives jc, y, z, such that x Px y & y Pxz and z P2x & x P2y. We then have x Py, y I z and x I z. , a choice function will exist, no matter what the in dividual preferences are. We can strengthen Theorem 4*1 by strengthening the Pareto rule and the nondictatorship condition.