Voting over economic plans

We review and provide motivation for a one-sector model of economic growth in which decisions about capital accumulation are made by a political process. If it is possible to commit for at least three periods into the future, then for any feasible consumption plan, there is a perturbation that is majority-preferred to it. Furthermore, plans that minimize the maximum vote that can be obtained against them yield a political business cycle. If it is impossible to commit, voters select the optimal consumption plan for the median voter

A Multivariate Local Rational Modeling Approach for Detection of Structural Changes in Test Vehicles

A data driven structural change detection method is described and evaluated where the data are acceleration and force measurements from a mechanical structure in the form of a vehicle. By grouping the measured signals as inputs and outputs an hypothesized MIMO linear dynamic relation between the inputs and outputs is assumed. It is assumed that baseline data are available to build statistical models for the estimated frequency function of the baseline system at selected frequencies. When new data is available, the monitoring algorithm re-estimates the non-parametric frequency function and uses a test statistic based on the statistical distance to detect possible change. To generate the frequency function estimates a non-parametric MIMO frequency function estimator based on the local rational model (LRM) method is developed. A statistical analysis of the proposed test statistic shows that it has an F-distribution for data from the baseline case. The method is evaluated on simulated data from a high fidelity full scale vehicle simulation generating both baseline data and data from a structurally changed vehicle. In the evaluation, the frequency response functions were estimated by the non-parametric LRM method, the parametric ARX estimate and the non-parametric ETFE. The results show that all three methods can detect the structural change while the LRM method is more robust with respect to the selection of the hyperparameters. Copyright (C) 2021 The Authors

Hands-On Physical Science for In-Service Teachers

The initiation of the Virginia Commonwealth University B.S. in Science program was reported in this journal Fall 1999 as a program designed to meet the academic content major of a teacher preparation program for elementary and middle school mathematics and science teachers [1]. This paper reports the current status of the interdisciplinary B.S. in Science degree program including program enrollment data and trends. Also described are refinements in the required curriculum, which include a newly developed geometry, a mathematical computing course, and an emerging teaching technology course featuring graphing calculators, CBLs, and computer software applications

Covering, Dominance, and Institution Free Properties of Social Change

This paper shows that different institutional structures for aggregation of preferences under majority rule may generate social choices that are quite similar, so that the actual social choice may be rather insensitive to the choice of institutional rules. Specifically, in a multidimensional setting, where all voters have strictly quasi concave preferences, it is shown that the "uncovered set" contains the outcomes that would arise from equilibrium behavior under three different institutional settings. The three institutional settings are two candidate competition in a large electorate, cooperative behavior in small committees, and sophisticated voting behavior in a legislative environment where the agenda is determined endogenously. Because of its apparent institution free properties, the uncovered set may provide a useful generalization of the core when a core does not exist. A general existence theorem for the uncovered set is proven, and for the Downsian case, bounds for the uncovered set are computed. These bounds show that the uncovered set is centered around a generalized median set whose size is a measure of the degree of symmetry of the voter ideal points

Game Forms for Nash Implementation of General Social Choice Correspondences

Several game forms are given for implementing general social choice correspondences (SCC's) which satisfy Haskin's conditions of monotonicity and No Veto Power. The game forms have smaller strategy spaces than those used in previously discovered mechanisms: the strategy for an individual consists of an alternative, two subsets (of alternatives), and a player number. For certain types of economic and political SCC's, including a-majority rule, the Walrasian, and Lindahl correspondence, the strategy space reduces to an alternative and a vector, where the number of components of the vector is at most twice the dimension of the alternative space

Structural Instability of the Core

Let σ be a q-rule, where any coalition of size q, from the society of size n, is decisive. Let w(n,q)=2q-n+1 and let W be a smooth ‘policy space’ of dimension w. Let U〖(W)〗^N be the space of all smooth profiles on W, endowed with the Whitney topology. It is shown that there exists an ‘instability dimension’ w*(σ) with 2≦w*(σ)≦w(n,q) such that: 1. (i) if w≧w*(σ), and W has no boundary, then the core of σ is empty for a dense set of profiles in U(W)N (i.e., almost always), 2. (ii) if w≧w*(σ)+1, and W has a boundary, then the core of σ is empty, almost always, 3. (iii) if w≧w*(σ)+1, then the cycle set is dense in W, almost always, 4. (iv) if w≧w*(σ)+2 then the cycle set is also path connected, almost always. The method of proof is first of all to show that if a point belongs to the core, then certain generalized symmetry conditions in terms of ‘pivotal’ coalitions of size 2q-n must be satisfied. Secondly, it is shown that these symmetry conditions can almost never be satisfied when either W has empty boundary and is of dimension w(n,q) or when W has non-empty boundary and is of dimension w(n,q)+1

Generalized symmetry conditions at a core point

Previous analyses have shown that if a point is to be a core of a majority rule voting game in Euclidean space, when preferences are smooth, then the utility gradients at the point must satisfy certain restrictive symmetry conditions. In this paper, these results are generalized to the case of an arbitrary voting rule, and necessary and sufficient conditions, expressed in terms of the utility gradients of "pivotal" coalitions, are obtained

Public and Private Information: An Experimental Study of Information Pooling

This paper reports on an experimental study of-the way in which individuals make inferences from publicly available information. We compare the predictions of a theoretical model of a common knowledge inference process with actual behavior. In the theoretical model, "perfect Bayesians," starting with private information, take actions; an aggregate statistic is made publicly available; the individuals do optimal Bayesian updating and take new actions; and the process continues until there is a common knowledge equilibrium with complete information pooling. We find that the theoretical model roughly predicts the observed behavior, but the actual inference process is clearly less efficient than the standard of the theoretical model, and while there is some pooling, it is incomplete