Knowledge that Transforms

[This paper examines a notion of coalitional fairness for exchange allocations. An allocation is "c-fair" if no coalition of traders could benefit from achieving the net trade of some other coalition. Properties of c-fair allocations are studied both in exchange economies with a finite number of traders and with an atomless sector.]

THIS NOTE SUGGESTS that the components models employed in [2, 3, 10, 11, 12 and 17] may be usefully analyzed within the state space framework found in the literature of control engineering. Such a formulation has the distinct advantage that a large corpus of filtering and estimation theory may then be brought to bear upon such models and has secondary benefits in the form of a greater lucidity of, and flexibility in, the exposition of the extraction problem. Further, by relating such models to a format that has widespread use in other fields, it is possible to exploit any future computational and theoretical advances therein.

Under the assumption of single peaked preferences, the majority rule equilibrium considered as a correspondence from the voters' preference is shown to be continuous. We also complement the work of Fishburn [6], who first presented a general location theorem for majority rule equilibriums, by dropping the assumptions that the alternative set is finite and that voters' preferences are strict partial orders. SINCE THE WORK of Black [3] on simple majorities and single-peaked preferences, much work has been done in deriving conditions for which some state achieves a majority over all other states. It is also well known that the equilibrium in many cases is the median of the distribution of most preferred states of the voters. (See [3, pp. 14-18].) We present here a result concerning the continuity of the majority rule equilibria. Specifically, we show that in the case of single-peaked preferences, the majority rule equilibrium depends only on the peaks of the voters' preferences and not on the transitivity properties of these preferences. We then show that the equilibrium, viewed as a correspondence of these peaks, is continuous (i.e., both upper and lower semicontinuous). This result is especially important when one tries to prove the existence of an equilibrium in a political-economic system. Most existence theorems are based on fixed point theorems which require at least upper semicontinuity of the correspondences being studied. The theorem proved here shows that the majority rule equilibrium is continuous in voters' peaks. If these are in turn continuous functions of other parameters such as prices, then our result might aid one in deriving general existence theorems for social equilibria. (See [3 or 4].) The only related work seems to be that of Kelly [10] who investigates the existence of a continuous numerical representation of the social preference relation generated by majority rule. He shows that one cannot expect continuity even if the social preference relation has other properties, such as transitivity. Specifically, he presents a case in which a majority of voters are indifferent between two points. In a neighborhood of one of these points, this majority rules between points in the neighborhood and the other point, but a minority (since the majority is indifferent) rules between the two given points. Hence one cannot expect continuity of the

[This paper considers the estimation of a simultaneous equations model in which the dependent variables are qualitative. The model is a simultaneous version of the multivariate logit model, and can be estimated by maximum likelihood. An example is presented, dealing with the prediction of occupation and industry of employment of a worker based on certain demographic variables.]

[In this paper we analyze implications of a singular contemporaneous disturbance covariance matrix for the estimation and hypothesis testing of systems of equations with autoregressive disturbances. We find that this singularity imposes restrictions on the parameters of the autoregressive process. When these restrictions are not imposed, the specification, maximum likelihood estimates, and likelihood ratio test statistics are conditional on the equation deleted. Furthermore, singularity of the contemporaneous disturbance covariance matrix raises issues concerning identification of parameters of the autoregressive process. This identification problem complicates the interpretation of likelihood ratio statistics. The above results are illustrated with an empirical example.]

[The purpose of this paper is to set forth a general theorem on the shape of free spatial market demand curve and on the shape of the spatial competitive market demand curve. It is demonstated that the free spatial demand curve is necessarily convex to the origin regardless of the shape of the shape of the individual demands which comprise it. But the shape of the spatial competitive market deamnd curve is shown to depend upon the behavioral assumptions used in the competitive. Three basically different competitive models are presented with contrasting results. Elasticity and price effects under each type of competition are determined and evaluated as is the effect of spatial competition on prices. Different interpretations of price data tend to result from conceptions of aggregate spatial demand curves vis a vis the classical spaceless demand curve.]

[This paper is concerned with clarifying the relationship between the certainty equivalence and first order certainty equivalence results. The effects of applying the first order certainty equivalence result are examined by analyzing the effects on the control vector of a one period stochastic control problem of a change in elements of the covariance matrix of parameters.]

Linear decision rules for controlling complex systems are often obtained by matrix inversion, but transform methods offer an alternative approach that yields insights into the structure of the decision problem of maximizing expected payoffs under constraints.