Consistency, Choice, and Rationality by Walter Bossert

By Walter Bossert

In Consistency, selection, and Rationality, fiscal theorists Walter Bossert and Kotaro Suzumura current an intensive mathematical therapy of Suzumura consistency, a substitute for proven coherence houses resembling transitivity, quasi-transitivity, or acyclicity. functions in person and social selection concept, fields vital not just to economics but additionally to philosophy and political technology, are mentioned. in particular, the authors discover issues reminiscent of rational selection and printed choice idea, and collective determination making in an atemporal framework in addition to in an intergenerational environment.

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According to Baigent and Gaertner (1996, p. 244), a choice function C is non-standard rationalizable if there exists a transitive relation R on X such that, for all feasible sets S, C(S) consists of the set of greatest elements of the subset of S that is obtained if the unique greatest element is removed; if there is no unique greatest element, the choice function selects all greatest elements according to R as in the traditional setting. The characterization of non-standard rationalizability established by Baigent and Gaertner (1996) applies to the extended domain consisting of all non-empty subsets of X and they assume X to be finite.

Although not transitive, the resulting relations are always quasi-transitive. Weymark (1984) retained transitivity of the social relation as a requirement but dropped completeness, thereby arriving at a characterization of the Pareto rule. However, replacing transitivity with quasi-transitivity does not help us much in finding an escape route from Arrow’s (1951, 1963) impasse as long as Arrow’s other assumptions are retained and slightly strengthened in certain ways; see Mas-Colell and Sonnenschein (1972), for instance.

1) immediately yields (x, y) ∈ tc(R). (ii) In view of part (i), it is sufficient to prove that tc(R) ⊆ R if R is transitive. Let (x, y) ∈ tc(R) for some x, y ∈ X . 1), there exist K ∈ N and x 0 , . . , x K ∈ X such that x = x 0 and (x k−1 , x k ) ∈ R for all k ∈ {1, . . , K } and x K = y. By (repeated if necessary) application of the transitivity of R, we obtain (x, y) = (x 0 , x K ) ∈ R. (iii) We begin by establishing the transitivity of tc(R). Let x, y, z ∈ X be such that (x, y) ∈ tc(R) and (y, z) ∈ tc(R).

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