Arrow Impossibility Theorems - download pdf or read online

By Jerry S. Kelly and Karl Shell (Auth.)

ISBN-10: 0124033504

ISBN-13: 9780124033504

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All that remains is a demonstration that these local results can all be converted to global results. Still assuming xPDsy, let u be any profile with xPty for all i e S: S: xy, N-S: [xy]. Insert a z to get a u0 for which the restricted orderings are S: N-S: xzy, z[xy~]. By xPDsy we see from the first part of our proof that xPDsz. Therefore CMo({x,z}) = {x}. By the weak Pareto condition, CUo({y,z}) = {z}. Then, by base quasitransitivity, CUo({x,y}) = {x}. By independence of irrelevant alter­ natives, Cu({x, y}) = {x} as was to be shown.

Satisfies the weak Pareto condition. D Exercises 1. 2. 3. 4. Prove Theorem 3-3. Prove Property ß( + ) implies *PI. Show the need for Property a in each of Lemma 3-16, Theorem 3-17, and Theorem 3-18 by giving examples in which all assumptions but Property a hold and the conclusion fails. Prove the following result (similar to a theorem of Weldon [343]) which uses a property almost the opposite of liberalism. There does not exist a collective choice rule f on V, U satisfying (i) the standard domain constraint, (ii) for each S ç N = {1,2,.

SIMPLICITY : IMPOSSIBILITY THEOREMS 49 The condition of transitive rationality has not been the only object of criticism in Arrow's second theorem. Independence of irrelevant alternativeshas probably been the principle target of critics. Of course we already have Sen's theorem on the impossibility of a Paretian liberal which uses neither IIA nor any regularity condition. (B). Theorem 4-12 There is no collective choice rule / satisfying (i) the standard domain constraint, (ii) | £ | < o o , (iii) each Cu = f(u) has a complete, reflexive, and transitive rationaliza­ tion R(u), (iv) independence of single irrelevant alternatives, (v) the weak pairwise Pareto condition, (vi) general nondictatorship.

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Arrow Impossibility Theorems by Jerry S. Kelly and Karl Shell (Auth.)


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