Knowledge that Transforms

Recent developments in social theory are critically surveyed in the light of a categorization of interpersonal aggregation problems into four distinct types that seem to require varying treatment but typically do not receive it. Informational inadequacy of the usual social framework is discussed in this context. A fairly thorough exploration of the correspondences between consistency conditions for functions and regularity properties of the binary relation of preference leads to a re-examination of the class of impossibility results in social theory, necessitating reinterpretations of various theorems (including Arrow's). SOCIAL CHOICE THEORY is concerned with relationships between individuals' preferences and social choice (Fishburn (1973, p. 3)). But a great many problems fit this general description and they can be classified into types that are fundamentally different from each other. It can be argued that some of the difficulties in the general theory of social arise from a desire to fit essentially different classes of group aggregation problems into one uniform framework and from seeking excessive generality. An alternative is to classify these problems into a number of categories and to investigate the appropriate structure for each category. In a small way, this is what will be done in this paper, and some of the recent developments in the theory of social will be examined in that light.

[This paper proposes a simple and straightforward method of finding a consistent and efficient set of sectoral capacity growth rates and output and investment levels in a dynamic input-output (IO) model with given production capacities at a certain "base period" of time and given consumption targets for a later "terminal period." The basic problem is that terminal capacities have to be consistent with terminal production requirements as given by the consumption targets, intermediate input requirements, and investment, where both the latter are treated endogenously. The basis for endogenous investment is (a) the assumption that the planning period as a whole is characterized by a set of constant sectoral growth rates and (b) the assumption that investment does not create any excess capacity. These two assumptions form the core of the notions of consistency and efficiency respectively. The method proposed is an integrated iterative procedure with endogenous revision of the division of sectors between those operating at full capacity (bottleneck) and the rest, output and investment levels, and rates of growth. The method is, in fact, a straightforward adaptation of the standard method of solving an IO model by power series expansion. The paper also discusses the method of target revision taken in conjunction with prior bounds on growth rates and certain aspects of the relation between investment and technology in the frame of the model proposed. It ends with a brief review of the literature, criticizing, in particular, the methods and approaches followed in a large number of applied planning models to tackle the set of issues discussed.]

[A kernel of a set of alternative actions over which there is a partial order is defined in terms of optimality properties. It is shown to be the same as the generalized efficient set. A variety of theorems such as uniqueness, existence, and composition in terms of other sets are established. Related sets, such as quasi kernels and weak kernels, are also considered.]

Michael J. Hartley, Parthasaradhi Mallela, The Asymptotic Properties of a Maximum Likelihood Estimator for a Model of Markets in Disequilibrium, Econometrica, Vol. 45, No. 5 (Jul., 1977), pp. 1205-1220

[A decision scheme makes the probabilities of alternatives depend on individual strong orderings of them. It is strategy-proof if it logically precludes anyone's advantageously misrepresenting his preferences. It is unilateral if only one individual can affect the outcome, and duple if it restricts the final outcome to a fixed pair of alternatives. Any strategy-proof decision scheme, it is shown, is a probability mixture of schemes each of which is unilateral or duple. If it guarantees Pareto optimal outcomes, it is a probability mixture of dictatorial schemes. If it guarantees ex ante Pareto optimal lotteries, it is dictatorial.]

[A limiting feature of several theoretically superior "shrinkage" estimators for the linear regression model lies in the fact that there must be a certain degree of orthogonality in regressors in order for them to dominate the ordinary least squares estimator. In this paper we apply variants of pre-test and Stein estimators to data on international trade, and discuss their merits in light of the limitations imposed by the non-orthogonality of these and other sets of economic data.]