A Nonlinear Model for the Analysis of Judicial Decisions

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Abstract
Various attempts have been made in recent years to analyze judicial decisions in selected areas of law as functions of controlling facts. At least two of these attempts have relied on systems of simultaneous equations. In both endeavors the assumption was made that the combination of facts on which the decisions depend is linear. In the absence of any clear indication of a nonlinear combination, as well as in view of the significant results that were obtained on the basis of a linear model, the initial approach was justified. The use of high speed digital computers has made it possible, however, to explore the existence of nonlinear relationships where the original assumption of linear relationships was made. The important feature in detecting nonlinear relationships is not primarily the greater accuracy of the results—the linear model has provided acceptable approximations—but the acquisition of new insights into how different facts combine in influencing judicial decisions.It is the purpose of this paper first to review the linear model, and then to show how it can be extended to a nonlinear model—in general terms as well as in the form of an actual application. Finally, limitations and implications of the nonlinear model will be indicated.

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