Knowledge that Transforms

The possible impact of autonomous (vs. the price mechanism and directive control) on the functioning of an economic system is studied. It sheds some light on similarities among economic systems that are quite different in their higher functioning. The survival and stability conditions for a Leontief-type economy demonstrate the role stock signals can play in controlling the behavior of producers and consumers. COMPLICATED SYSTEMS FULFILLING a number of duties are controlled, generally, by multi-stage regulators consisting of both simple and complex mechanisms. For example, some of the functions of the spaceship are controlled by simple, built-in servomechanisms; others are guided half-automatically from the earth; and still others are guided directly by handpower of the astronauts. Or let us take a higher living organism, the human body, say. Some of its functions, respiration, digestion, blood circulation, functioning of the heart, lungs, stomach, intestines, and kidneys are controlled by the autonomous (vegetative) nervous system; other functions by the central nervous system. An economy is also a complicated system, fulfilling a great number of functions. Its processes are controlled by several kinds of mechanisms of low and high degree. The low degree following the physiological analogy, is called autonomous (vegetative) control.2 The first section of our study explains the idea of the control mechanism, draws comparisons between the different mechanisms, and presents some empirical findings. Sections 2 and 3 analyze the autonomous theoretically, with the aid of a general and a special model. In the fourth section we draw conclusions and comment on the previous theoretical analysis.

First Interpretation: The game has a finite number of outcomes, but this set's distributions are also considered as outcomes of the game. These probability distribution outcomes are then points in a linear space. Second Interpretation: The game's outcome is a bundle of goods and, in our case, public goods. We shall give a version of the theory for private goods at the end of this paper. Let us now consider, like von Neumann and Morgenstern, a zero-sum twoperson game between a coalition S and its complement coalition I - S, using an arbitrarily chosen linear function defined on the vector space of outcomes. We denote the outcome by y and the linear function by q. Here S wants to maximize and I - S wants to minimize qy. According to von Neumann and Morgenstern, this game has a value called the characteristic function which is written as r(S, q). Using such a function calls for some explanation and comparison with the other methods employed in economic theory and game theory. The linear forms q

[It is known that prices only cannot usually be utilized to coordinate a linear economic system. This paper considers a linear economic system, formally represented as a linear programming model which is interpreted as a resource-allocation problem. An algorithm founded on the idea of associating with each resource a linearly increasing price schedule rather than a constant price is developed. The paper hence demonstrates that a mechanism rather similar to a pure price mechanism can be used both to find and sustain an optimal allocation of resources in a linear economic system.]

IN THIS PAPER we consider procedures for going from several individual preferences among several alternatives, called candidates, to something which may be called a collective preference. The individual preferences take the form of (total) orderings of the alternatives, and the collective preference is to take the form of a (total) weak ordering (i.e., ties allowed). We consider certain properties which seem desirable in such and investigate which have these properties. The of view taken here differs from that of other work in this area (e.g., [1, 2, 3, 4]) chiefly in asking that the procedure work for all possible sizes of the voting population, rather than for a fixed population, given in advance. This permits us to require, for example, that if each of two bodies of voters prefers candidate A to candidate B under a given procedure, then the combination of these bodies should prefer A to B under the same procedure. In Section 1 we give the formal definitions of an aggregation procedure and discuss certain desirable features, namely neutrality (treats candidates symmetrically), (the condition mentioned above), monotonicity, and an Archimedean property which says, roughly, that a sufficiently large body with a given distribution of preferences can impose its will on any body of fixed size. In Section 2 we introduce certain procedures: point systems and systems (roughly, allowing infinitesimal points), which are neutral and separable. They are monotonic if and only if the points are arranged in the natural order, and the are, in addition, Archimedean. In Section 3 we prove a converse, namely that any neutral and separable procedure can be realized by a generalized system and, if it is Archimedean, by a system. This part requires some familiarity with the notions of least upper bound of a set of real numbers and bases of vector spaces. In Section 4 (which is largely independent of Section 3), we consider point which use in a succession of eliminations. Such are neither separable nor monotonic but do satisfy some very weak separability and monotonicity conditions. While these probably do not characterize runoff systems, we know of no other satisfying them.

Donald H. Ebbeler, James B. McDonald, An Analysis of the Properties of the Exact Finite Sample Distribution of a Nonconsistent GCL Structural Variance Estimator, Econometrica, Vol. 41, No. 1 (Jan., 1973), pp. 59-65

[Transitivity-like properties for binary social choices on a triple of alternatives are shown to follow from simple conditions that apply within each voter preference profile, coupled with structural profile restrictions such as those used in single-peakedness. These results are compared to results obtained under the simple majority rule. The special intraprofile conditions used in the main theorem are related to interprofile conditions such as independence, neutrality, and monotonicity.]

[The paper deals with a measure theoretic model of a pure exchange economy. There are two kinds of traders: "big" traders, represented by atoms of the measure space, and "small" traders, represented by the atomless part of the measure space. The restriction of an allocation to the atomless sector is called competitive if there exists a price vector such that the consumption of every "small" trader is a maximal element (in terms of his preference) in the budget set defined by that price vector and by his initial endowment. We consider the set of allocations that are not blocked by any atomless coalition, or by the complement of any atomless coalition, and call it the extlesstex-math extgreater$ extbackslashscr\I\ extasciicircum\2\ extbackslashtext\-core$ extless/tex-math extgreater. The main results of the paper consist in defining sufficient conditions under which allocations in the extlesstex-math extgreater$ extbackslashscr\I\ extasciicircum\2\ extbackslashtext\-core$ extless/tex-math extgreater have a competitive restriction to the atomless sector, and vice versa. The economic implications and significance of the results are briefly discussed.]

A summation social choice function is a social choice function whose choice sets are determinable from maximum sums of utilities that preserve individual preference. Assuming the set of alternatives is finite and individual preferences are irreflexive and transitive, a unanimity-type condition is shown to be necessary and sufficient for a social choice function to be a summation social choice function. The effects of conditions of voter independence, anonymity, and neutrality are noted.

[It was suggested in [2] that an appropriate model for an oligopolistic economy is one in which the set of traders consists of some large traders and a continuum of small traders. The cores of such market models are analyzed here. Some of the results are as follows: A duopolistic market in which the duopolists are of the same type is "perfectly competitive," i.e., its core coincides with the set of competitive allocations. At any allocation in the core of any oligopolistic markets, the value of the bundle received by a small trader does not exceed the value of his initial bundle; that is, small traders can never "gain money." Conditions are given under which small traders will not "lose money" either. In addition to the case of duopoly, other conditions are given under which an oligopolistic market will be perfectly competitive.]