Thanks are due to Hendrik Houthakker and Christopher Sims, for both encouragement and advice in developing this paper. As usual, all remaining errors are my own. This research was supported by a Harvard Dissertation Fellowship, NSF grant 33-708, and the
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.]
[This paper simplifies and extends some previous work on domain restriction. With the help of an easy arithmetical result, two types of necessary and sufficient conditions are established for transitivity and quasi-transitivity under majority rule and transitivity under non-minority rule.]
In most empirical work, the investigator's understanding of the economic process under study is only minimally reflected in the econometric methodology. This paper suggests that in many cases, the construction of a small-scale simulation can prepare the data for regression in a manner which takes cognizance of the theory of the process. Regression is then used to scale the output of the simulation up to observed magnitudes of the variable to be predicted. The simulation has the function of exploring for the nature of the nonlinearities and interactions and thus replaces the usual search for a form which maximizes R2. The simulation may also be helpful where colinear data are a problem. An example is presented in which the effects of wages, unemployment rates, and labor turnover on poverty are studied through a prepared regression. IN THE LAST three decades, regression analysis has become the Procrustean bed into which all economic data are fitted. In the usual empirical paper by an economist, the obligatory theoretical discussion which precedes the description of the regressions generally contributes little more to the empirical methodology than an indication of which variables ought to be included in which equation, what the signs of the coefficients might be expected to be, and whether the regressions should be run in linear or logarithmic form. One reaction to this state of affairs has been the commencement of construction of large systems of microsimulation, notably one at the Urban Institute emphasizing demography and the distribution of income [6], one at the National Bureau of Economic Research on urban problems [4], and one at the University of Maryland featuring money flows [2]. While these big microsimulations are designed to describe the processes of the economy in a more natural way than can be done exclusively by usual regression methods, they tend to take years to build and tend to be unavailable to economists not involved in their building. It is possible, however, to occupy a middle ground between the regression runners and the large-model microsimulators. In many cases, improvement over the usual regression procedures can be gained by a combination of a very simple do-it-yourself simulation model with regression. The simulation model has the function of preparing the data for regression, in the sense of exploring for the nonlinearities and variable interactions inherent in the phenomenon under study. The regression, which uses the output of the simulation as an explanatory variable, has the function of scaling the simulation results up to observed magnitudes of the variable under study.
[The paper proves the asymptotic normality of a generalized least squares estimator utilizing estimated autocovariances of the residual in a regression equation having a residual following a mixed autoregressive, moving-average process. It also proves the asymptotic normality of the best linear unbiased estimator and shows that the two asymptotic distributions are the same.]