Academic journal article Economic Inquiry

Optimal Deterrence with Legal Defense Expenditure

Academic journal article Economic Inquiry

Optimal Deterrence with Legal Defense Expenditure

Article excerpt


In this article we consider a justice system which makes both type I errors (sometimes convicting the innocent) and type II errors (sometimes acquitting the guilty) and in which legal defense expenditure on behalf of the accused can reduce their probability of conviction. Such expenditure has a private value, but its social value is less clear. We address two sets of issues. First, do individuals accused of crimes take socially optimal decisions about their expenditure on legal defense and, if not, what are the implications for public policy in terms of the regulation of defense expenditure or its provision by the state? Second, what are the implications of legal defense expenditure for optimal deterrence policy?

In much of the literature on optimal deterrence welfare is the unweighted sum of the expected utilities of honest and dishonest individuals (Becker, 1968; Polinsky and Shavell, 1979). With such an efficiency-oriented welfare function, the only socially relevant aspects of legal defense are its effect on deterrence and its cost.

Because defense expenditures reduce the probability of punishment of dishonest individuals, they reduce the expected sanction on dishonest individuals and thus reduce deterrence. However, when there are type I errors, honest individuals face the risk of wrongful arrest and conviction. (1) Defense expenditure by them increases the rewards for honesty. What matters for deterrence are the effects of defense expenditure on the difference between the expected utility of honest and dishonest individuals. We show that permitting defense expenditures may increase deterrence as compared with a system in which no such expenditure is permitted.

We also show that the level of defense expenditure chosen by accuseds is not efficient. The private value of legal defense expenditure is the reduction in the probability of conviction. Both honest and dishonest individuals choose their expenditure, when accused, to maximize their expected utility. The marginal effect of defense expenditure on the expected utility of honest and dishonest individuals at the privately optimal levels is zero. Consequently marginal changes in defense expenditure at the private optimum have no effect on deterrence because they do not change the difference between the expected utilities of honest and dishonest individuals. But defense expenditures do have a positive marginal social cost, so that the marginal private and social values of defense expenditure are different and there is scope for regulation to improve on the market equilibrium.

There is a commonly held view that type I and type II errors have a direct effect on social welfare, rather than an indirect one through their effect on deterrence. The view is reflected in Blackstone's remark that it is "better that ten guilty persons escape, than that one innocent suffer" (Volokh, 1997, 174). (2) With a justice-oriented welfare function reflecting concern with type I and II error, as well as with individuals' expected utilities, increases in defense expenditure by the honest reduce type I errors and thereby, ceteris paribus, increase welfare. Increases in defense expenditure by the dishonest increase type II errors and thereby directly reduce welfare. With a justice oriented welfare function honest individuals spend too little on defense if the social cost of a type I error is greater than the fine imposed if the individual is convicted. The marginal social value of defense expenditure by the dishonest is always negative at their privately optimal level.

The canonical result in efficient deterrence policy is the Becker (1968) demonstration that, because fines have a positive deterrent effect but a zero marginal social cost, the optimal policy is to increase them to a level that leaves convicted accused with zero wealth. There are few examples of deterrence regimes that use maximal fines, and the Becker result has generated a large literature that suggest reasons why the efficient fine should not bankrupt convicted accused (Garoupa, 1997; Polinsky and Shavell, 2000). …

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