Download e-book for iPad: Arrow Impossibility Theorems by Jerry S. Kelly and Karl Shell (Auth.)

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

ISBN-10: 0124033504

ISBN-13: 9780124033504

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By the first part of this proof, Property a holds, so that from C(v) ^ vwc can derive C(v) n C(v) Ç C(C(Ü)), so C(i;) = C(C(v)). ') = C{v), a contradiction. Therefore Property s is satisfied. 4 Property s has been called the superset property [45]. 30 CHAPTER 3 Finally, from Properties a and s we will obtain path independence. Suppose x E C(vl u v2). If x e vl9 then, by Property a , x e C(^1); if x G V2, then x G C(y2). u 1^2• By another application of Property a, x G Q Q I ^ ) u C(v2)). Thus, 5 C(Vl u i ; 2 ) ç C ( C W u C ( » 2 ) ) .

Theorem 5-5 (Blau and Deb [51], Sen [318]).

Iv) guarantees that F(x, y) is not empty. d) (b, c)B2(b', d) iff iff b5 V c 5 c' or or b = V and c 5 c', c = c' and fc 5 &'. ß j and ß 2 are transitive but not complete. Since A is finite we are assured that there exist 2^-maximal and jB2-maximal elements of nonempty subsets of A. We will be interested in local maximal sets Bx°{x, y) = {(b, c)I(b, c) e F(x,y) and there is no (b\ d) in F(x, y) such that (b\ d)B1(b, c)}, B2°(^ J;) = {(b, c) I(b, c) G F(x9y) and there is no (b\ d) in F(x,y) such that (b\ d)B2(b, c)}; and in global maximal sets B !

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

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