Showing papers by "Melvin J. Hinich published in 1983"

Voting One Issue at a Time: The Question of Voter Forecasts

Abstract: When issues (i.e., dimensions) are voted on one at a time, a voter whose preferences are not separable across issues must forecast the outcome of later issues in order to know how to vote in the present. This is the problem of expectations. In this article, we develop a general theory designed to handle this problem. Assuming that voters are risk averse and maximize expected utility, we demonstrate that a random variable forecast of how later issues will be decided reduces to a point forecast, which is the mean of the multidimensional random variable. We also show that single-peaked preferences are induced on each issue, and consequently there exists an equilibrium across issues.

Voter Expectations in Multi-Stage Voting Systems: An Equilibrium Result

Abstract: Recent work by Shepsle (1979) on structure-induced equilibrium has been challenged by Denzau and Mackay (1981), who show that voter expectations about the outcome of future votes can upset the stability induced by voting on issues one at a time. We show that under a politically informed model of voter expecations, risk aversion on each issue is necessary and sufficient for equilibrium under all voter forecasts when issues are voted on one at a time. This result gives an important insight into the role played by risk aversion in ensuring stability in real world voting systems.

Estimating the gain of a linear filter from noisy data

Abstract: Publisher Summary This chapter presents an asymptotically unbiased estimator of filter gain for a certain class of filters. Measuring the gain and phase of a linear relationship between two signals is an important task in a variety of scientific investigations. In some applications, one signal called the “input” is controlled. For example, various test input signals are used to measure the response of a linear amplifier. In other applications, the two signals—input and output—are stochastic and it is arbitrary to decide the signal that is called the input.

Tracking a moving vessel from bearing measurements

Abstract: This paper presents a method for tracking a distant moving target using only bearing measurements obtained from a tracking platform. The method is an improvement of the Hinich-Bloom passive tracking approach presented in [1]. The target is assumed to be moving at constant speed on a fixed heading, whereas the platform maneuvers during the measurement period. The direction cosines of the bearings are computed with respect to a rotation of the coordinate system that places 0° at the mean estimated target bearing. This is done to minimize the approximation bias due to the linearization of sine bearing as a function of inverse range and time. The coordinate system is rotated back to estimate the target coordinates. When the noise is Gaussian, the estimates of target range and heading are approximately maximum likelihood when the target's relative range is slowly varying during the observation period. In this case the mean square errors of the target parameter estimates are the smallest achievable within the order of the approximation.

Bearing Estimation using Random Arrays

Abstract: A sonobuoy field is a random two dimensional array if the signals from the sensors are coherently processed. The sensor position coordinates must be estimated to a fraction of a wavelength in order to coherently process the signals, which is a separate processing task since the field has a changing random pattern due to drifting of the buoys. This paper reviews the statistical properties of the maximum likelihood bearing estimator computed from coherent summation of output signals from randomly deployed sensors. It is shown that the approximate mean-square bearing error for a small random array favorably compares with that for a square array of equally spaced sensors with about one-half the aperture. The random array is not subject to the aliasing (grating lobes) problem of an equally spaced array, and a great deal of array gain can be achieved from a large array of randomly placed sensors. Serious consideration should be given to tracking the locations of drifting sonobuoys so as to coherently process them as an array.