Prasanta K. Pattanaik

On Ranking Opportunity Sets in Terms of Freedom of Choice

The paper explores the notion of freedom of choice which is of considerable importance in welfare economics and the theory of social choice. Three plausible axioms are introduced for ranking alternative opportunity sets in terms of the degrees of freedom that they offer to the agent making choices. It is shown that, under these axioms, judgements about degrees of freedom of choice have to be based on the naive principle of simply counting the number of available options.

Individual Rights Revisited

Since Sens contribution on the impossibility of a Paretian liberal, his formulation of libertarian rights has been under debate. In this paper, we highlight some important strands in this debate, and achieve some conceptual clarification of the different and often incompatible views of individual rights. We demonstrate in terms of a counter-example and general reasoning that Sens concept can, more often than not, be inconsistent with our intuitive view of rights and fails to capture important categories of rights. An alternative formulation in terms of game form is introduced, and its relative merit vis-a-vis Sens formulation is discussed.

On choosing rationally when preferences are fuzzy

Abstract In real life, exact choices are induced by fuzzy preferences. These choices eventually satisfy certain plausible rationality properties. Several alternative rules for generating exact choices from fuzzy weak preference relations are introduced and the extent to which exact choice sets generated by these rules satisfy fairly weak rationality conditions is studied. Max-min transitivity is shown to be crucial for obtaining a positive result.

On Ranking Opportunity Sets in Economic Environments

Abstract This paper examines how freedom of choice as reflected in an agents opportunity sets can be measured in economic environments where opportunity sets are non empty and compact subsets of the non-negative orthant of the n -dimensional real space. Several plausible axioms are proposed for this purpose. It is then shown that, under different sets of axioms, one can represent the ranking of compact opportunity sets by different types of real-valued functions with intuitively plausible properties. Journal of Economic Literature Classification Numbers: D63, D70.

On diversity and freedom of choice

Abstract We discuss how information about diversity of alternatives may affect our judgments about an individual’s freedom of choice as reflected in the available set of alternatives. We provide an axiomatic characterization of a similarity-based rule for ranking alternative opportunity sets in terms of the individual’s freedom of choice.

Choice under complete uncertainty: axiomatic characterizations of some decision rules*

Summary. We provide characterizations of four new rules for individual decision-making under complete uncertainty. They are what we call the min-max rule, the max-min rule, the lexicographic min-max rule and the lexicographic max-min rule. These rules provide orderings of the sets of possible outcomes associated with uncertain prospects. They provide significant alternatives to commonly-used rules that focus on worst outcomes or best outcomes only, and lexicographic versions of those rules.

Extending an order on a Set to the power set: Some remarks on Kannai and Peleg's approach

Abstract Kannai and Peleg have shown that given an ordering over a set, it is impossible to induce an ordering over the power set satisfying certain plausible axioms. We prove an impossibility and also a possibility result in this context with closely related sets of axioms, and argue that the dividing line between impossibility and possibility here is rather thin. Also, we distinguish three possible intuitive interpretations for the formal framework of Kannai and Peleg, and argue that the acceptability of specific formal axioms may crucialy depend on the particular interpretation that one chooses to adopt.

Rationality and aggregation of preferences in an ordinally fuzzy framework

Abstract The paper explores the problem of aggregating ordinally fuzzy individual preferences into ordinally fuzzy social preferences. Using Goguens ordinal formulation of fuzziness, it is shown that, given certain plausible conditions, the requirement that the societys preferences should satisfy any of several alternative transitivity conditions creates a dilemma: either power in the society is rather unevenly distributed, or the society tends to be indecisive. The problem increases as weaker transitivity conditions are replaced by stronger ones.

Choice, welfare, and development : a Festschrift in honour of Amartya K. Sen

Professor Amartya Sen has been a distinguished and influential scholar in development economics for over twenty years, and this edited volume seeks to reflect his interests, and the inspiration he has provided for others. The editors have succeeded in creating a coherent and stimulating set of papers from well-known contributors. The volume deals with the enduring themes of Amartya Sens work, ranging through theoretical issues of development economics to the philosophical foundation of welfare systems, and ethics in society. Contributors: Kenneth Arrow, A. B. Atkinson, Pranab Bardhan, J. L. Coles, Rajat Deb, Jean Dreze, Louis Gevers, Peter Hammond, Ravi Kanbur, Eric Maskin, Robert Nozick, Siddiq Osmani, Martin Ravallion, Kevin Roberts, Robert Solow, S. Wibaut

Median-based extensions of an ordering over a set to the power set: An axiomatic characterization

Abstract In this paper we consider the problem of inducing an ordering over the set of all non-empty subsets of a finite set X of alternatives, given an ordering R over X . Assuming R to be antisymmetric and X to have at least six elements, we provide a set of independent, necessary, and sufficient conditions for the induced ordering to be “median-based” (so that every non-empty subset of X is “indifferent” to its own median set defined in terms of R ).