Knowledge that Transforms

ECONOMISTS OFTEN SUMMARIZE the income distribution by the Lorenz curve and Gini index. A variety of parametric methods (e.g., [1 and 8]) have been developed to estimate these measures from the grouped income data governments provide (e.g., [3 and 12]). Previously, one of the authors developed a distribution-free approach [5] which yielded accurate bounds on the Gini index. While analogous bounds on the Lorenz curve can be obtained [5 and 10], the resulting curve is not smooth so a method of interpolation is needed. The purpose of this paper is to adapt an old technique of numerical analysis, Hermite interpolation [7 and 13], to our problem and to show that it usually works in theory and in practice. Our paper was motivated by the work of Brittain [2] who also used numerical methods. Unfortunately, his procedure often resulted in estimates of the Gini index which were inconsistent with the above-mentioned bounds. Although the piecewise Hermite interpolation yielded accurate estimates of the Gini index, it is not always convex as the Lorenz curve must be. Section 5 states conditions for the interpolated curve to be convex or at least increasing over an interval. While these conditions are usually satisfied by real data, a theoretical example illustrates how an error may arise.

This paper seeks to prove that under a large class of group decision rules some sincere voting situations will be unstable because of strategic manipulation by single individuals. The concept of stability used is weaker than the stability concepts figuring in many earlier contributions in this area, insofar as under the concept used here any individual, while disrupting a given voting situation, considers the possibility of retaliation by other individuals. DUMMETT AND FARQUHARSON [2], Murakami [7], Farquharson [3], Sen [14], Gibbard [4], Satterthwaite [13], and Pattanaik [10, 11, and 12] have discussed various aspects of the problem of stability in voting. The general conclusion which emerges from these writings seems to be that stability of all possible sincere voting situations (which implies the absence of strategic distortion of preferences by voters) is an extremely rare feature of democratic group decision procedures. However, the notion of stability or equilibrium underlying many of these contributions is a simple one and does not take into account several phenomena usually associated with strategic voting such as the possibility of counter-coalitions when a coalition (of one or more individuals) threatens to disrupt a voting situation. The purpose of this paper is twofold. First, it introduces a less demanding notion of stability which takes into account the possibility of formation of countercoalitions when an individual seeks to influence the outcome in his own favor by strategic manipulations in voting. Secondly, using this very weak notion of stability, it is shown that, while under the changed definition the possibility of having unstable sincere voting situations because of strategic voting by single individuals is somewhat reduced, invulnerability of all possible sincere voting situations to voting maneuvres of single individuals still remains a very rare property among democratic group decision rules based on pairwise comparisons. We lay down the basic notation and some preliminary definitions in Section 1. In Section 2 we introduce a notion of stability taking into account the possibility of counter-coalitions. Using this very weak definition of stability, in Section 3 we show that under most democratic group decision rules based on pairwise comparisons, there is the danger of having unstable sincere voting situations owing to strategic manipulations by single individuals. We conclude in Section 4.

This paper is devoted to the analysis of the dynamic behavior of a sequence of temporary equilibria. The model chosen is a generalization of Samuelson's pure consumption loan model as introduced by J. M. Grandmont and G. Laroque in [5]. Three main results are given. First there is an open and dense subset U of economies for which, near stationary equilibria and cycles, the dynamics take the standard form of an ordinary difference equation. Then conditions are obtained so that, for an economy E in U, stationary equilibria are locally asymptotically stable; these conditions are discussed in the case where there is only one good in addition to money. Last, it is proven that the qualitative behavior of trajectories of E near stationary equilibria and cycles is preserved under small perturbations; i.e., one has a property of local structural stability; this is true in particular with respect to changes in the individual expectations of the agents.

The following sections are included:INTRODUCTIONSTABILITY OF DISTRIBUTED LAG MODELS IN THE MORISHIMA CASECONCLUSIONS AND EXTENSIONSREFERENCES(This abstract was borrowed from another version of this item.)

[A general equilibrium trade model with more produced commodities than factors is specified under the assumption that industry production functions are homothetic. The main issue under consideration is that of local and global determinateness of the economy's production pattern. The paper also examines the impact of exogenous commodity price and endowment changes on output levels and factor returns.]

Le but de ce papier est d'etendre les resultats de W. Hildenbrand relatifs aux production economy quand a chaque coalition est associe un vecteur (dans un espace de parametres biens non-marchands) qui determine son ensemble de production. Si cette dependance est a rendements constants, l'ensemble des equilibres de Walras de l'&conomie est non vide et (si chaque agent a une influence negligeable) egal au noyau. Nous donnerons aussi une condition necessaire et suffisante pour que l'ensemble des equilibres de Walras soit non vide mais dans ce cas un exemple montre que nous ne pouvons esperer avoir de theoreme d'egalite.