Chapter Eighteen - Topological Theories of Social Choice
Chapter 18 in Handbook of Social Choice and Welfare, 2011, vol. 2, pp 301-334 from Elsevier
This chapter presents a simple introduction to the main results in topological social choice theory. Given a continuous social welfare function, these results show the following: (i) Unanimity and Anonymity are incompatible; (ii) Weak Pareto and No Veto are incompatible; and (iii) Weak Pareto implies the existence of a Strategic Manipulator. Given the role of continuity in all these results, its justification is critically discussed. Finally, a remarkable proof of Arrow's theorem using topological methods is presented.
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