[The fact that preference maximizing consumers generate aggregate excess demand is utilized to prove (i) a statement on the values of the excess demand correspondence and (ii) that the economies having an excess demand function are dense in the set of all economies. This is applied to get a straightforward proof for the existence of an equilibrium distribution.]
FOLLOWING ON SOME informal conjectures by Dummett and Farquharson [3] and Vickery [20] we now have independent proofs by Gibbard [7] and Satterthwaite [17 and 18] that no collective choice rule exists whose social choice functions are singlevalued, strategy-proof, nondictatorial and have a range containing at least three alternatives. Because strategy-proof ness seems desirable and because it is closely related to mainstream economic theory issues of evaluating resource allocation institutions with respect to incentive compatibility (cf. Hurwicz [9]), their theorem has excited considerable attention [5, 6, 10, 11, 12, 13, 14, 15, 16, 19, and 21]. In this paper, the requirement of singlevaluedness is dropped and explorations are made of the consequences this has on the Gibbard-Satterthwaite results. Let E be the set of all alternatives (which must, by assumption, be mutually incompatible) and N= {1, 2,.. ., n} be the set of individuals. A nonempty subset, v, of E (i.e., an element of 2E _-0}) is an agenda. RE is the set of all complete and transitive binary relations on E; RE is the n-fold Cartesian product of RE. An element, u, of RE is called a profile and if u = (R1, R2,... , Rn), we say that R, is the preference ordering for individual i in u. In the usual way, we use Ri to define strict preference, Pi, and indifference, Ii: xPiy if and only if xRiy and not yRix; xIiy if and only if xRiy and yRix. A social choice function (on V) is a function, C, on Vc2E _{0} into 2E _{0} satisfying C(v) c v. Here V is the set of admissible agenda. The set of all social choice functions on V is called ST. A collective choice rule (on V, U) is a function, F, on UcRE into c6. Here U is the set of admissible profiles. The first constraints on the social choice function in the Gibbard-Satterthwaite theorem are domain restrictions. They admit only one agenda, V= {E} and then require the collective choice rule to work for all societies, U = RE. The most important constraint they use is singlevaluedness: for each v in V, C(v) contains exactly one element. Of course, there is only one V, namely E, in the Gibbard-Satterthwaite theorem. The importance of this constraint stems from its use in all the rest of the problem; singlevaluedness is used in their method of formalizing both nondictatorship and strategy-proofness. Let us deal first with nondictatorship. Using singlevaluedness, let C(v) be the unique member of C(v). Then a collective choice rule, F, is nondictatorial if for no i, i = 1, ... , n, is it true that for all (R1,. . . , Rn) =uE U and for all x C(v) in the range of C = F(u), C(v)Pix. Finally, we turn to strategy-proofness. A collective choice rule is strategy-proof at (v, u) if it is not manipulable at (v, u). F is manipulable at (v, u) if, when u = (R1, R2, ... , Rn), there is a u'=
[A social decision function operates on individual weak orderings to produce acyclic social preference. The structure of a general neutral monotonic SDF is studied. It is shown to be characterized by the veto, if individual indifference is banned. With such indifference present, the characterization is by a veto structure, a hierarchy embracing all individuals. The reason for the interest in acyclicity [21, 22] is that it averts the voting paradox, permitting a choicefrom each subset of alternatives. This is for the finite case. When that assumption is dropped, an infinite ascending sequence of preferences prevents a choice. It is shown that this last phenomenon need not be prohibited along with cycles; the absence of such social sequences is implied by their absence from individual preferences.]
In analyzing the city as an economic institution, it seems reasonable to ask if the advantages of proximity are sufficient to assure that traders will form and maintain a market place. This process is called agglomeration. A general theorem concerning iterative spatial games is developed first. A spatial general equilibrium model comprised of a sequence of pure trade economies is proffered. Restrictions on transport technologies sufficient to assure agglomeration are determined. The possibility of a policy maker speeding the process of agglomeration is demonstrated. In conclusion, the optimality properties of the model are discussed. The research draws heavily on the works of A. Weber [8] and G. Debreu [2]. The model includes a dynamic adjustment process which is developed from individuals' maximizing behavior.
Sho-Ichiro Kusumoto, Global Characterization of the Weak Le Chatelier-Samuelson Principles and Its Applications to Economic Behavior, Preferences, and Utility-- "Embedding" Theorems, Econometrica, Vol. 45, No. 8 (Nov., 1977), pp. 1925-1955
[A treatment of taxation based on considerations of political and economic power in a majority-vote democratic context is the topic of this article. Agents are endowed with gross incomes and have concave von Neumann-Morgenstern utilities for money. Taxation policies are decided by majority vote, but each citizen retains a certain basic right that prevents the majority from arbitrarily expropriating his income. The resulting non-transferable utility cooperative game is analyzed by means of the Harsanyi-Shapley-Nash value.]
[Four conditions are shown to imply together that a solution function for two-person bargaining problems must equalize gains in some ordinal utility scales. These conditions are: weak Pareto optimality, strong individual rationality, composition, and uniformity. The composition condition relates to sequences of bargaining problems. The uniformity condition requires that the solution function must be invariant under enough ordinal utility transformationsto move any threat point to the origin.]