Knowledge that Transforms

The concept of a dominance solvable voting scheme is presented as a weakening of the strategy-proofness requirement: it relies on successive elimination of dominated strategies and generalizes the well known concept of "sophisticated voting." Dominance solvable decision schemes turn out to contain many usual voting procedures such as voting by veto, kingmaker, and voting by binary choices. The procedure of voting by elimination is proved to be an anonymous dominance solvable voting scheme which always selects an efficient alternative.

This paper develops a matrix-measure of multivariate risk aversion which is related to a notion of risk premium and states the restrictions that must be imposed upon the matrix-measures of two utility functions in order that one require a higher risk premium than another for every small multivariate risk. A necessary and sufficient condition for comparability of global attitude towards risk is that the local restrictions hold over the entire domain. The usefulness of the measures of risk aversion is discussed within the context of a multivariate risk-sharing problem. UNIVARIATE MEASURES OF ABSOLUTE and relative risk aversion were introduced in the seminal works of Pratt [8] and Arrow [1], and have since become indispensable tools for the analysis of risk bearing in situations involving unidimensional risks. Recent years witnessed numerous attempts to generalize various aspects of the Pratt-Arrow notions to the case of multivariate risk (Kihlstrom and Mirman [6], Keeney [5], Duncan [2], Paroush [7], and Stiglitz [9]). The univariate case is qualitatively different from the multivariate case in that the ordinal preferences of all decision makers are identical, whereas in the multivariate case the preference orderings may differ among decision makers. This fact has two important consequences. First, while the analysis of risk bearing in situations involving univariate risks turns out to depend solely upon the cardinal properties of the function representing the ordinal preferences of the decision makers involved, in situations involving multivariate risks, the ordinal preferences themselves play an important role in addition to that of the function representing them. Second, in the univariate case the local measure of absolute risk aversion permits a complete ordering of individuals according to the relation least as risk averse as, whereas in the multivariate case such ordering is not in general independent of the specific risk under consideration. Pratt [8] has shown that the univariate measure of absolute risk aversion satisfies a formal relation to a number which has the interpretation of risk premium. In this study I introduce a matrix measure of absolute multivariate risk aversion which satisfies a similar formal criterion. It should be noted at the outset, however, that in the multivariate case the risk premium may be regarded as a vector of commodities (see, for example, Duncan [2, 3]), and interpersonal comparison of risk aversion is not directional independent. I.e., the ranking of risk

[This article considers an economy in which there is one public good financed by means of commodity taxes (lump sum transfers being not available). The first part of the paper is devoted to the study of tax equilibria. Sufficient conditions for the existence of an equilibrium with respect to a given tax system are given. When the tax system is modified, the structure of the corresponding set of tax equilibria is analyzed, and continuity properties of equilibria (with respect to the tax system) are stated. In the second part, attention is focused on the Pareto ranking of tax equilibria. In a given equilibrium, the directions of policy tools changes for a Pareto improvement (if any) are characterized. The "size" of the set of second best Pareto optima in the set of tax equilibria is evaluated.]

[Conventionally labor supply modeling has been dichotomized from consumption expenditure allocation. We estimate a model unifying both aspects of the consumer's decision problem, and we test for the two-stage decision implied by the conventional dichotomy. We investigate the gains from joint modeling. We use a version of the Rotterdam model recently shown by Barnett [6] to be derivable at the aggregate level under weaker assumptions than those needed to acquire empirically usable theoretical results at the aggregate level with other models; our results are not subject to the restrictiveness imputed to earlier uses of versions of the Rotterdam model.]

A. Holly, P. C. B. Phillips, A Saddlepoint Approximation to the Distribution of the k-Class Estimator of a Coefficient in a Simultaneous System, Econometrica, Vol. 47, No. 6 (Nov., 1979), pp. 1527-1547