Sentencing Discretion. Suppose in the model above that the fact finder is free to choose the sentence length A. In this case, she necessarily evaluates the consequences of her verdict and sentence together. She anticipates that upon conviction she will choose the sentence that maximizes her expected utility.6 The expected utility from conviction, EUc = p · u(A; t) − (1 − p) · c1(A), is maximized according to the first-order condition: ∂u(A∗; t) = (1 − p)cj (A∗), (2.2) ∂A p 1 where A∗ is the optimal sentence length. Since c1j (A) > 0 ∀A, we have that ∂u(A∗; t)/∂A > 0, which by Assumption 1 implies A∗ < t. Instead of choosing t, the punishment that fits the crime, the fact finder chooses a more lenient sentence to mitigate the potential cost of a wrongful conviction. Note the importance of Assumption 1. The cost of making an incorrect decision cannot be the only thing motivating the fact finder, or else, if she chose to convict, she would always choose the lower bound on sentence length.7 Clearly, she must derive some utility from imposing a just punishment, and Assumption 1 fills that role. For (2) to define the optimal sentence length, the second-order condition must be 6The choice of A is presumably bounded, and information gathering may occur between the verdict and sentence, but neither of these features affect the main results below. 7This statement would remain true if the cost of a false acquittal depended on the sentence length. satisfied: ∂2u(A; t) jj p ∂A2 − (1 − p)c1 (A) < 0. (2.3) Assuming that ∂2u(A; t)/∂A2 ≤ 0, meaning that deviations from the target sentence length become more upsetting the farther away they are from the target, a sufficient condition for (3) is that the fact finder is risk-averse in the sentence of a wrongful conviction. (Since c1(A) is a loss, risk-aversion means that cj1j(A) > 0.) The fact finder can also be risk-loving provided she is especially sensitive to deviations from the target sentence. After choosing A∗, the threshold of reasonable doubt is p(A∗) = c1(A∗) . c1(A∗) + c2 + u(A∗; t) The key question is how this threshold compares to the one the fact finder would adopt without sentencing discretion, if she were required to impose the target sentence t. Section 2 presents the two main benchmarks for comparison. First consider the case of Section 2.1, where the fact finder weighs the consequences of her verdict both with and without sentencing discretion. Denoting by p(t) the threshold of reasonable doubt she would choose when required to...
