Showing papers by "Graciela Chichilnisky published in 1982"

Social Aggregation Rules and Continuity

Abstract: It is shown that any continuous social aggregation rule for smooth preferences cannot simultaneously satisfy the properties of anonymity and respect of unanimity. This is true even when all individual preferences are linear. The relationship between the conditions on the social rule studied here and those of Arrow's paradox is discussed. The first result requires that the normalized gradient of the social choice rule be definable in the interior of the choice space, thus indicating a direction of increase of social preference. A second impossibility result extends the first to cases where the gradient of the social preference may vanish in the interior of the choice space.

The Topological Equivalence of the Pareto Condition and the Existence of a Dictator

Abstract: The paper studies two standard properties of rules for aggregating individual into social preferences: non-dictatorship and the Pareto condition. Together with the condition of independence of irrelevant alternatives, these are the three basic axioms of Arrow's social choice paradox. We prove the topological equivalence between the Pareto condition and the existence of a dictator for continuous rules. The axiom of independence of irrelevant alternatives is not required. The results use a topological framework for aggregation introduced in Chichilnisky (1980), but under different conditions. ln Chichilnisky (1980) rules are anonymous and respect of unanimity. Since anonymity is strictly stronger than the condition of non-dictatorship, while respeet of unanimity is strictly weaker than the Pareto conditions the two sets of conditions are nocomparable.

Structural Instability of Decisive Majority Rules

Abstract: We study social aggregation rules that satisfy a Pareto and a decisive majority condition. A rule satisfies the decisive majority condition if whenever the voters can be divided into two internally homogeneous groups (ie. groups within which all individuals agree about all possible choices) and these groups have opposite preferences, then the majority's preference is respected. No assumption are made about the outcome when the individuals have more than two different preferences even when a majority agree on a choice x being preferable to another y. Therefore a decisive majority condition does not imply, ie. is strictly weaker than, majority rules. The main result is that Pareto decisive majority rules are necessarily structurally unstable. in the tense that the outcome preference, which is a vector field, will undergo major changes in the structure in response to small change in the underlying parameters. The importance of structural instability derives from the fact that small errors of observation will lead to drastically different answers. An example of the result for three voters and with a two-dimensional choice space ia also given.

Basic Needs and the North/South Debate.

Abstract: This article re-examines the relationship between economic growth of the North and that of the South. It considers the implications of this relationship for two major issues within the current North-South debate: basic needs and exhaustible resources. The connections between international trade and national policies are explored on the basis of the theoretical research and empirical results of a United Nations Project on Technology, Distribution and North-South relations.