We are now ready to resume our review of Anarchy, State, and Utopia. The fourth subsection of Chapter 4 (pp. 59-63) contains an extended digression into retributive and deterrence theories of punishment. Nozick takes a probabilistic approach to punishment (pp. 59-60), an approach which is music to our ears: “A person’s option of crossing a [moral] boundary is constituted by a (1 – p) chance of gain G from the [wrongful] act, where p is the probability he is apprehended, combined with the probability p of paying various costs of the act [if caught].” According to Nozick (p. 60), these costs include C, the payment of compensation to the victim; D, the emotional costs to the wrongdoer of being caught and tried; and E, the financial costs of getting caught and going to trial. As Nozick notes (p. 60): “Prospects for deterrence look dim if the expected costs of a boundary crossing are less than its expected gain; that is, if p times (C + D + E) is less than (1 – p) times G.” (Being the mathematical geeks we are, we really loved this simple model.)

After building his probabilistic model, Nozick identifies some problems with both retributive and deterrence theories of punishment. One problem with deterrence theories is that they are useless in practice, or in Nozick’s words (p. 61, emphasis in original): “[the maxim] ‘the penalty for a [wrongful act] should be the minimal one necessary to deter commission of it’ provides no guidance until we’re told how much commission of it is to be deterred.” In other words, we need to know what the “optimal level” of wrongdoing is! More fundamentally (p. 61), another problem with deterrence theories “of the utilitarian sort” (but what other kind is there?) is that they tend to “equate[] the unhappiness the criminal’s punishment causes him with the unhappiness a [wrongful act] causes its victim.” (Note that we have replaced the word “crime” in the above quotations with the words “wrongful act” since we don’t want to prejudge whether a wrongful act (i.e. a moral boundary crossing) should be treated as a public crime or a private tort, the central question of Chapter 4.)

By contrast, the main problem with retributive theories, as Nozick nicely points out, is that they set an upper limit to the penalty that may be inflicted on a wrongdoer, since a retributive penalty must be based on the wrongdoer’s degree of responsibility and the degree of harm inflicted. (See Nozick, p. 60: “Let us suppose … that R, the retribution deserved, equals r times H; where H is a measure of the seriousness of the harm of the [wrongful] act, and r (ranging between 0 and 1 inclusive) indicates the person’s degree of responsibility for H.”) But if this upper limit of r times H is set below (1 – p) times G — the expected gain to the wrongdoer — then no deterrence will be achieved. At the same time, however, the retributive approach sheds new light on the right to self-defense and the rule of proportionality. Recall that, under a retributive theory of punishment, H is a measure of the seriousness of the harm of a wrongful act, while r (ranging between 0 and 1) is a measure of the person’s degree of responsibility for H. As a result (p. 62), the retribution model “makes the upper magnitude of permissible defensive harm some function f of H, which varies directly with H — the greater H is, the greater f(H) — and such that f(H) > H.” Furthermore, as Nozick himself notes (p. 62), the variable r — the wrongdoer’s degree of responsibility — is completely irrelevant to this rule of proportionality. (What an original and fascinating insight, by the way.)

Now, let’s return to the central question of Chapter 4: (i) should wrongful acts be prohibited and punished as crimes or (ii) should they be allowed so long as compensation is paid to the victim (i.e. should wrongful acts be treated as torts)? Notice that Nozick’s simple models do not provide a definitive answer to this question. Neither the retributive model nor the deterrence model tell us how to classify boundary crossings, i.e. as a crime or a tort. Worse yet, Nozick’s models yield different ways of calculating the level of compensation to be paid under the permissive or tort approach, since the formula for compensation could be made equal either to r times H or to (1 – p) times G, depending on which theory of punishment we prefer.