Deterring repeat offenders with escalating penalty

Authors: Stan Miles Derek Pyne

Publish Date: 2015/02/26

Volume: 16, Issue: 3, Pages: 229-250

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Abstract

We model deterrence with costly punishment when criminals have different abilities Abilities are unobserved by both criminals and the courts Based on past successes criminals update their priors on being highability criminals Courts cannot observe a criminal’s total past offenses They do know that criminals with more convictions were undeterred by previous penalties Thus they must have had more successes resulting in higher posterior probabilities of being highability criminals Those with fewer convictions include more with lower posterior probabilities of being highability Since they know that they are relatively more likely to be caught they are deterred with lower penaltiesThis paper benefited from the comments of Marko Koethenbuerger Georgia Martin Peter Smoczynski two anonymous referees and participants at the 2013 Western Economic Association International conference and the 2013 Canadian Law and Economics conferencea Taking into account equation 1 and because q G q M it suffices to show that if k and n are fixed and 0le kle jn then PGOmega 1jk increases as j increases Thus it suffices to prove that the partial derivative of PGOmega 1jk with respect to j is positivec By equation 1 and because q G q M it suffices to show that if j and n are fixed and 0le kjn then PGOmega 1jk decreases as k increases That is it suffices to show that the partial derivative of PGOmega 1jk with respect to k is negativei Given that D 2 =fracBHPF 2 F 1 and D 1 =fracBLPF 1 we have fracD 2 D 1 =fracBHBLfracPF 1PF 2 F 1 Thus the inequality in 15 is more likely to hold the smaller the ratio of BH to BL It is also more likely to hold the greater the ratio of Pleft F 2 F 1 right to PF 1b If j ge 1 then for every value of k for which the expression above is nonnegative it is completely analogous to the expression on the lefthand side of inequality 13 Thus the proofs of the necessary and sufficient conditions for it to be efficient to use the value of D 2 that corresponds to some value of k with 1 le k le j rather than D 1 as the penalty for the second conviction are analogous as wellsquare

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