# ps1sol - Homework 1 Solution Preface To show a SWF satises...

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Homework 1 Solution Preface On the contrary, to show a SWF fails a certain property, it su¢ ces to give just ONE counter-example. 1. The easiest example is a Constant Rule. A Constant Rule is a Social Welfare Function (SWF) that generates the same societal ranking regardless of any individual±s preferences. Let±s check that all Constant Rules satisfy UD, IIA, and non-dictatorship, but violate Pareto: come before B in the societal ranking. Likewise, if everyone prefers B to A, B must come before A. A Constant Rule is independent of any individual rankings, so it gives the same ordering of A and B in both cases. Thus one of the two cases is a violation of Pareto. Non-Dictatorship: A Constant Rule is not a dictatorship because it is not in²uenced by any individual preferences. In fact, dictatorships satisfy Pareto. If all individuals prefer A to B, then the dictator must prefer A to B, so the social ranking will also put A above B. in-structions for generating a transitive societal ranking from the individual rankings (compare this to pairwise majority rule, which generates a ranking that may not be transitive, or the utilitarian SWF, which needs information about intensity of preferences). IIA: A Constant Rule satis&es IIA because the societal ranking of two alter-

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## This note was uploaded on 01/14/2012 for the course ECON 201 taught by Professor Witte during the Spring '08 term at Northwestern.

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ps1sol - Homework 1 Solution Preface To show a SWF satises...

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