# Approximating a Judge

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A judge's decision rule can be thought of as a mapping from facts to outcomes. And often, it is possible to approximate the facts as a set of binary values and the outcome as a binary value such as "affirmed" or "reversed", or a set of binary values. This Demonstration shows how an investigator can take a set of cases seen by a judge along with the associated outcomes and approximate the rule the judge must be applying.

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Contributed by: Seth J. Chandler (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The fact that outcomes can often take on more than two discrete values (, , and , for example) does not pose a significant limitation on the technique described in this Demonstration. In such cases one creates a binary representation of the outcome such as , , and and then uses the techniques described here to develop a rule that best computes each binary digit of the outcomes. Thus, if there are possible outcomes, there are rules that are required.

Facts that are not binary but that have either finite discrete values or can be approximated by finite discrete values likewise do not pose a significant limitation on the techniques described in this Demonstration. One simply takes the binary value of the fact and joins that to the other discrete facts of the case.

The technique described here may sometimes be an improvement over more typical techniques such as linear regression in predicting the behavior of judges if only a low-order combination of independent variables is used in the regression. By way of example, a probit or logit regression whose dependent variables were simply the binary values of the facts would likely have poor explanatory capability where the judge was basing his or her decision on various complex combinations of these variables. An ability to predict the behavior of judges is of great value in commercial cases and useful in advising clients on settlement offers.

## Permanent Citation

"Approximating a Judge"

http://demonstrations.wolfram.com/ApproximatingAJudge/

Wolfram Demonstrations Project

Published: March 7 2011