# Against Prediction: Profiling, Policing, and Punishing in An Actuarial Age

By Bernard E. Harcourt | Go to book overview

Appendix B

MATHEMATICAL PROOFS REGARDING THE ECONOMIC MODEL OF RACIAL PROFILING

To make these proofs as accessible as possible to a general audience, I discuss elasticity in terms of changes in magnitude rather than derivatives. This allows me to present the equations using simple algebra instead of calculus. The logic and results, however would be identical using derivatives and point elasticity. For the most precise model using derivatives, see pages 132–33 above.

Under Conditions of Equal and Constant Elasticity of Offending to Policing

Assuming resource constraint, racial profiling will decrease the profiled crime under conditions of equal and constant elasticity of offending to policing if the minoritymotorist offending rate is greater than the white-motorist offending rate. This can be derived from the definition of elasticity.

For purposes of notation, let r ∈{M, W}denote the race of the motorists, either minority or white. Let Poprdenote the representation of each racial group in the total population. Let Ordenote the offending rate of each racial group. Let Or denote the absolute valueof the change in the offending rate of the racial group from Time 1 (no racial profiling) to Time 2 (racial profiling). Let Irdenote the internal search group rate for each racial group. Let Irdenote the absolute value of the change in the internal search rate for each racial group from Time 1 to Time 2. Let Sdenote the search rate for the total population.

From the definition of elasticity, if minority and white motorists have the same and constant elasticity, then the following is true:

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