Topological Social Choice Topological Social Choice
نویسنده
چکیده
The topological approach to social choice was developed by Graciela Chichilnisky in the beginning of the eighties. The main result in this area (known as the resolution of the topological social choice paradox) shows that a space of preferences admits of a continuous, anonymous, and unanimous aggregation rule for every number of individuals if and only if the space is contractible. Furthermore, connections between the Pareto principle, dictatorship, and manipulation were established. Recently, Baryshni-kov used the topological approach to demonstrate that Arrow's impossibility theorem can be reformulated in terms of the non-contractibility of spheres. This paper discusses these results in a self-contained way, emphasizes the social choice interpretation of some topological concepts, and surveys the area of topological aggre-gation. 1
منابع مشابه
Topological social choice
The topological approach to social choice was developed by Graciela Chichilnisky in the beginning of the 1980s. The main result in this area (known as the resolution of the topological social choice paradox) shows that a space of preferences admits of a continuous, anonymous, and unanimous aggregation rule for every number of individuals if and only if this space is contractible. Furthermore, c...
متن کاملOn the topological equivalence of the Arrow impossibility theorem and Amartya Sen's liberal paradox
We will show that the Arrow impossibility theorem for binary social choice rules that there exists no binary social choice rule which satisfies transitivity, Pareto principle, independence of irrelevant alternatives (IIA), and has no dictator, and Amartya Sen’s liberal paradox for binary social choice rules that there exists no binary social choice rule which satisfies acyclicity, Pareto princi...
متن کاملA topological approach to the Arrow impossibility theorem when individual preferences are weak orders
We will present a topological approach to the Arrow impossibility theorem of social choice theory that there exists no binary social choice rule (which we will call a social welfare function) which satisfies the conditions of transitivity, independence of irrelevant alternatives (IIA), Pareto principle and non-existence of dictator. Our research is in line with the studies of topological approa...
متن کاملResolving the Topological Social Choice Paradox
1.1. Topological Social Choice Theory. Social choice theory aims to understand the nature of, and provide methods for, the aggregation of individual preferences to yield a social preference which is fair and satisfactory to individual voters on an axiomatic ground. An important example of this is in popular elections. In the 1980s, Chichilnisky and colleagues developed a topological approach pi...
متن کاملTopological aggregation, the twin paradox and the no show paradox
Consider the framework of topological aggregation introduced by Chichilnisky (1980). We prove that in this framework the Twin Paradox and the No Show Paradox cannot be avoided. Anonymity and unanimity are not needed to obtain these results.
متن کامل