Deterrent Punishment in Utilitarianism

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January, 2019

Deterrent Punishment in Utilitarianism

This document explains some of the basic features of the utilitarian theory of punishment. It focuses especially on the use of punishment to deter potential criminals from breaking the law. It does not discuss the punishment of any one crime, but rather the general principles that utilitarians believe should regulate the punishments of various crimes. The theory was first developed in the 1760’s by the Italian philosopher Cesare Beccaria. Jeremy Bentham, the pioneering utilitarian, took it a good bit further in 1789. A distinguishing feature of Bentham’s work is the fact that he combines the moral theory of utilitarianism with a comprehensive psychological theory of human decision-making. We will examine both. I use Bentham and Beccaria’s writings in this document, especially Bentham’s, but at a number of points I extend or modify them in order to make them clearer or more plausible. And I consider a few problems that their thinking encounters. But this is mainly meant to be a careful presentation of the utilitarian approach to the use of punishment as a deterrent to criminal activity. It is not an evaluation of its plausibility in moral terms.

A legislator who followed Bentham’s guidance in designing a system of punishments would, he believed, help to produce the most happiness for her society. The guiding moral principle in all of Bentham’s philosophy is the Principle of Utility. Bentham mainly uses it to think about the design of legal and political institutions, rather than the actions of individuals. The principle requires lawgivers to design institutions so that they produce the most happiness. Bentham and Beccaria believed that the main way that the criminal justice system—a central part of the law—contributes to the happiness of the members of society is by reducing the amount of crime. Criminal acts, they believed, tend to cause harm and thus reduce the amount of happiness in society. Therefore, if punishments reduce the amount of crime they increase the amount of happiness.

It must be added, though, that this understanding of the significance of crime reduction only makes sense against a background of good ‘substantive’ criminal laws. In other words, a utilitarian lawgiver first needs to set up a system of criminal laws that only prohibit acts that really do cause harm to society in some way. (The term that Bentham often uses for harm is ‘mischief’.) Bentham might have said that good substantive criminal laws prohibit acts that are morally wrong in utilitarian terms; that is, acts that do not produce the most happiness. In fact, he might have said that good substantive criminal laws prohibit acts that are seriously wrong in utilitarian terms; that is, acts that are not only wrong, but that produce great losses in happiness for society. As we will see, there are large costs involved in operating the criminal justice system; this means that it is a set of institutions that should only be used to reduce the incidence of acts of serious wrongdoing. If a society has criminal laws that prohibit actions that are not seriously wrong—witchcraft, say, or assisting fugitive slaves or drinking alcoholic beverages—then reducing the number of these actions may not increase the amount of happiness in society. Indeed, punishing these activities is likely to decrease the amount of happiness in society. This is because punishing ‘witches’, for example, will cause pain to people who are not harming anyone. So the pain of their punishment is ‘wasted’, since it has no tendency to reduce further harms, and it causes suffering to the alleged witch. Bentham discusses the problem of designing reasonable substantive criminal laws elsewhere in his book. These laws define the legal ‘offenses’, that is, the acts that are prohibited by law. Once we have such a system of laws in place, we need to decide what sorts of punishment will be attached to the various offenses.

Punishment can reduce crime in various ways. Beccaria and Bentham focus almost entirely on the deterrence of potential criminals. Bentham recognizes other ways that punishment can affect the crime rate, but he follows Beccaria in focusing on deterrence. Roughly speaking, deterrence is achieved when ‘crime doesn’t pay’ and people choose to refrain from committing offenses because they fear the punishments they will undergo if they do commit them. The perspective adopted here in effect looks at the punitive part of the criminal law as an announced system of threats that the state makes to the entire populace. If the threats are successful people who would have chosen to commit offenses choose instead to obey the law.

How else can punishment decrease the crime rate? Here are two that are commonly mentioned by philosophers:

  1. Incapacitation. The common punishment of imprisonment does not deter people from committing crimes while they are confined there. It simply prevents them from doing so. (More exactly: it generally prevents them from committing crimes that victimize people not in the prison itself. Someone in prison can harm other inmates or the guards.) Other sorts of punishment also have incapacitating effects: death, banishment, cutting off of hands, castration (it is sometimes believed). Incapacitating punishments can work even on criminals who are not rational. Deterrence, in contrast, operates by affecting a person’s decision-making. Beccaria and Bentham believed that rational decision-making involves weighing risks and rewards. So they believed, as we will see, that deterrence is achieved via basically rational decision-making on the part of potential criminals.

  1. Reform. Some types of punishments may change criminals’ characters by causing them to reform morally. Other types may induce criminals to pursue education or vocational training. (This in effect increases the rewards to them of obeying the law.) Still other punishments may induce criminals to improve their impulse control or kick their drug habits. These effects may reduce the amount of crime, and thus increase happiness, but not simply by inducing fear in convicts of undergoing punishment again. A person who chooses to obey the law because she believes that it is right to do so is not being deterred by the threat of punishment.

Bentham recognized the importance of incapacitation and reform. A criminal justice system that only aimed to deter potential criminals might well be more brutal and less beneficial to society than one that also attempted to reform criminals, for example. And, on the other hand, some fanatical criminals may not be deterrable, so that the best way to protect society from them might be simply to incapacitate them by imprisoning them for life. So a complete and sophisticated presentation of the utilitarian approach to punishment would need to take these other sorts of processes into account. But it remains true that deterrence is always understood—by utilitarians and their critics— to be a central goal of punishment in utilitarian theory.

The rest of this document discusses utilitarianism and deterrence. Section I examines the psychological theory that Bentham accepted. This theory, which is called ‘psychological hedonism’, I will call the psychological part. Section II mentions one difficulty that the theory faces. Sections III and IV examine ‘economical deterrence’. This is the strictly moral part of the discussion, and it draws on utilitarianism to analyze the problems of establishing a morally defensible system of punishments.

The Psychology of Deterrence: Bentham’s Psychological Hedonism

I said that deterrence is achieved when people refrain from committing crimes because they fear the punishments they will undergo if they do commit them. In understanding how to deter potential criminals the problem is fundamentally psychological. That is, the basic question is this: when will the threats that the legal system makes succeed in deterring potential criminals? Answering this question requires us to understand how potential criminals make their decisions, and that is a question of psychology.

A more precise statement about deterrence might be this: deterrence is achieved when people who are considering committing crimes believe that it is too risky for them to commit them, given the possibility of being punished, and they therefore choose not to do so. This is more precise because, after all, not every potential criminal who commits a crime is actually caught and punished, as everyone knows; so the issue is how potential criminals weigh the risks of undergoing punishment in their decision-making. Beccaria and Bentham both thought about deterrence by using their understanding of how all people make decisions. They thought that the decision to commit a crime is often largely rational; hence, the decision-making of criminals and potential criminals works in much the same way as does that of non-criminals. So this part of their thinking is based on some very general claims about how the psychology of human decision-making operates.

Rational decision-making involves weighing, as we say, the risks and rewards of various alternative actions or options. Bentham believed that everyone’s decision-making about risks and rewards is conceived of in terms of the pleasures and pains they will or might experience. He does not think that all people calculate precisely the pleasure and pains that their possible actions might bring about. But he does think that rational agents always have some intuitive ‘sense’ or feeling for how pleasant and painful their various options might be. The theory of human decision-making that Bentham accepted was called by later philosophers ‘psychological hedonism’. Let us now examine it.

Bentham’s Psychological Hedonism: the Basics. Bentham does not present his psychological theory in a separate section of his book, An Introduction to the Principles of Morals and Legislation. Parts of it are presented explicitly; others are implicit in his discussion of the design of punishments. This presentation is therefore more complete than Bentham’s own.

The basic principle operating in all rational decision-making, according to Bentham, can be roughly stated this way: every person seeks to maximize her pleasure, and minimize her pain. That is, he thinks (again, roughly) that this statement is true:

Simple Psychological Hedonism (SPH): Every person chooses the action that she believes will maximize the net amount of her pleasure.
It can be seen that Bentham believed that every human action is self-interested, that is, it is intended to bring about, and only intended to bring about, a benefit to the person who is acting. Self-interest (or a person’s ‘well-being’) can be thought of as having two basic elements, benefit and loss, and Bentham conceived of these in terms of pleasure and pain. Improvements in a person’s well-being or self-interest consist in pleasurable experiences, and losses to a person’s well-being, or set-backs to her self-interest, consist in painful experiences. Death is a special kind of loss which I won’t discuss. Also, as we will see, benefit and loss need to take account of probability.

To illustrate the ideas contained in SPH: suppose that a person has two options: do A or do B. And suppose that if she does A, she believes that she will experience 20 units of pleasure and 10 units of pain “when all is said and done”; if she does B, she believes that she will experience 40 units of pleasure and 35 units of pain “when all is said and done”. The expression “when all is said and done” is meant to convey the idea that the numbers represent all of the effects that the person believes she will experience by choosing a certain option. They do not represent only the short-term effects. Something that is pleasant in the short run, like getting drunk, can produce pain in the long run. Decision-making will often take account of these long-term effects. (However, see the remarks on ‘proximity’ below.) We can represent the person’s options in the following way.


Pleasure (for me) 20 40

Pain (for me) -10 -35

Net (for me) 10 5

In this case, Bentham thinks that this person will choose to do A. This maximizes the ‘net’ amount of pleasure she believes can experience over the long run. The amount of pain expected for each option is subtracted from the amount of pleasure in that option to yield a net amount of pleasure, and the agent will choose the option that yields the greatest net amount. Notice that there is a sense in which act B is believed to produce more pleasure for the agent, but Bentham would say that the person would choose to do A. Act A is believed to produce more pleasure net.

Bentham himself believed that in theory pleasure and pain could be measured, as this example assumed. This does not mean that he believed that people ordinarily assess the psychological risks and rewards of acting in numerical terms, as we just supposed. They ordinarily think about what will be enjoyable or exciting or rewarding or painful or risky, and so on. But these ‘qualitative’ ways of assessing psychological risks and rewards could, if Bentham is correct, be converted into numerical measures. Bentham not only assumed that each person could in theory measure her own pleasure and pain, but that one person could measure everyone’s pleasure and pain. He sometimes speaks of the ‘felicific calculus’, which would require such measurements of everyone’s pleasure and pain. Philosophers in the utilitarian tradition sometimes call the imaginary units of such a calculus ‘hedons’. Obviously there is no way yet to measure pleasure and pain with this kind of exactitude. Psychologists and economists are working on this problem, and some related ones—like measuring the strength of desires. You might ask yourself how we could measure the pleasure that a person receives from something.

I assumed in the example, as is commonly done, that pain can be represented by negative numbers, so that -10 represents 10 hedons or units of pain. If we think of pleasures and pain as measurable in this way then we can say that 11 units of pain is ‘more painful than 10 hedons is pleasant’. In other words, there is a greater amount of pain in 11 units of it than there is pleasure in 10 units of pleasure. In mathematical terms, we could therefore say that the absolute value of that amount of pain is greater than that amount of pleasure. In other words, the absolute value of -11 is 11, and 11 is greater than 10.

It is important to understand that the numbers in the table are supposed to represent the amounts of pleasure and pain that the agent will or would experience in the future if she chooses to do A or B. In fact, numbers can more correctly be said to represent the amounts of pleasure and pain that an agent believes she will or would experience in the future if she chooses to do A or B. In making a choice about whether to do A or B an agent has to make some sort of estimate of the effects on her in the future of doing one or the other. This means that it may turn out to be true that B would actually produce more net pleasure for her than A would: she may have estimated incorrectly the psychological risks and rewards of her two options. Psychological hedonism is a theory that attempts to explain how people make decisions. The theory could be true even if people make mistakes—as, of course, they often do—in judging how their actions will turn out for themselves.

I have begun to put Bentham’s thinking into a sort of mathematical form. Both Beccaria and Bentham started to do this, and they are, in fact, two of the founders of modern psychology and economics (and also criminology). They hoped that the various measurements and calculations would eventually be carried out with great precision and accuracy. Neither of them, as far as I know, put their thinking into as much explicit mathematical terms as I just did. I will make some further, very simple mathematical assumptions in this document as we proceed. I think the mathematics helps us to understand what Beccaria and Bentham are trying to say. However, we should not draw the conclusion that their thinking is useless if we cannot now measure pleasure and pain exactly, or represent a potential criminal’s thinking numerically. I believe Beccaria and Bentham would both say that where we cannot measure the relevant factors precisely we will have to estimate their magnitudes as best we can. We will have to estimate them because the factors we are considering are real elements in human psychology, and they really do affect the decision-making of potential criminals (and everyone else). Utilitarian legislators will need to take account of them somehow or other, if they want to reduce the number of crimes. In a famous passage, Bentham insists that even the dullest criminal calculates to some extent how ‘profitable’ it is to act, and is influenced by his sense of the risks involved in acting (end of Chapter XIV). Another way to put his thinking is this: most potential criminals are somewhat rational, and wise legislation can influence their decision-making so as to cut down on the incidence of crime.

I said that Simple Psychological Hedonism is roughly correct as a statement of Bentham’s view. I said ‘roughly’ because it neglects two factors that he believed really operate in decision-making. I will now explain these two other factors.

Probability. The second factor affecting the attractiveness of any action is the probability of success. This is obviously important: a low probability of success significantly reduces how attractive a person would consider an action to be. A high probability of success would make it more attractive.

How can we represent the significance of probability in decision-making? For various reasons, probability is always represented in mathematical treatments of it by numbers between 0 and 1, inclusive. Something with a 0 probability is impossible; something with a probability of 1 is certain; something with a probability of .5—like heads coming up on the flip of a coin—is just as likely to occur as not. (Of course, we could also use fractions like ½ to represent the same idea.)

The simplest way to represent the significance of probability would be to multiply the expected gain or loss of an action by a number representing its probability. The basic idea here is that probability considerations increase or reduce the psychological rewards and risks of possible actions. For example, an action might give a person a .5 chance of experiencing 100 hedons. (The action might be betting $10 on the flip of a coin.) In this case, we could say that the ‘probable gain’ of performing it is 100 times .5, or 50 hedons. Bentham conveys the same idea by speaking of the ‘value’ of an action; the value in this case is 50 hedons. In contemporary economics a related idea is conveyed by the concept of ‘expected utility’.

The probability that is being represented here has to be understood as what philosophers call ‘subjective probability’. This is the probability that a person believes an event has, whether she is correct or incorrect about that. (The correct probability measure of an event is called its ‘objective probability’.) People’s decision-making is governed by their beliefs about probabilities, just as it is governed, in Bentham’s view, by their beliefs about the amounts of pleasure and pain that will ensue. If someone believes that she has a good chance of winning a lottery, for example, she may buy tickets, even though, in fact, her estimate of the chances is way off. Of course, over time people may change their beliefs, as they learn more. It is said that people ‘update’ their probability beliefs as they have greater experience. Similarly, they update their beliefs about how much pain or pleasure will come about from an action as they have greater experience of its consequences. Experienced criminals surely do such updating about the severity of the punishments they undergo and their probability of undergoing them.

Proximity. The third factor affecting the attractiveness of an action is what Bentham calls ‘proximity’, meaning the ‘proximity in time of the pleasure or pain it will bring’. (He might better have called it ‘promptness’, but I will use his word.) If an action is believed to bring pleasure soon—say, today—that reward has more proximity than one that will occur in a year. Bentham seems to think that proximity has an independent role in affecting decision-making. That is, even when a person has a belief about the magnitude of a future pleasure or pain, and a belief about its probability, she may have a different attitude towards the possible experience of undergoing it depending on how soon the pleasure or pain will occur. This could be true even when everything else about her situation after the different choices is exactly the same. For example, suppose that Jones believes that it is certain that if she does A then she will receive 100 hedons tomorrow, and if she does B it is certain that she will receive 100 hedons in a year, and nothing else will be different between the circumstances or consequences of the two acts. (For example, she won’t experience some bad after-effect in one case and not the other.) Jones might prefer to do A. If so, proximity has affected her decision-making.

Once again, this factor must be understood in terms of an agent’s beliefs, and the attitudes she has in virtue of them. An agent may believe that a pleasure or pain will come tomorrow even if, in fact, it will come much later, or not at all. It is an agent’s beliefs about the facts—not the objective facts themselves—that affect her attitudes and these attitudes will affect her decision-making. Again, agents will usually update their beliefs about proximity as they learn more about how the world works; their attitudes may also change as a result.

Economists speak of the psychological tendency to devalue possible events in this fashion as ‘discounting the future’. Philosophers have also discussed this phenomenon, and a number of them have regarded it as irrational. We do not need to decide if this claim about rationality is true. Even if an agent who takes proximity into account is irrational, the fact is that some people, and not only potential criminals, tend to do this. In other words, even if it is irrational it really occurs. This means that it affects how some potential criminals make decisions, and that is what we are trying to understand.

How can we represent numerically the significance of proximity in decision-making? What we are trying to capture is how much a person cares about what happens to her, or might happen to her, in the future, independently of the two factors of the magnitude of a pleasure or pain and its probability. The simplest way to do this, I think, is again to use fractions. If someone does no discounting of an event that will happen soon then we multiply the amount of the probable pain or pleasure she expects by 1. In contrast, if she discounts another event far in the future a lot, then we would multiply the probable pleasure or pain she expects by, say, .2. This means that this event matters much less to her. Presumably the discounting fraction gets greater the farther in the future an event is.

A More Complicated Model. Let us try to summarize all of the points covered. Bentham could be said to believe this: the psychological profit or reward of any action whatsoever can be represented as the product of three factors, whose numerical representation we have discussed.
Psychological Reward of an Action = Pleasure x Probability x Proximity
‘Pleasure’ stands for the amount of pleasure that an agent believes she will experience as a result of performing the action. ‘Probability’ stands for the numerical representation of her belief about its probability of occurring. ‘Proximity’ stands for the numerical representation of her discounting, if any, with regard to a pleasure, given her beliefs about its probability, and about its distance from the time of an action. For some people a possible pleasure may be discounted twice, both for its probability and for its distance in time. Other people may only discount for its probability.

Obviously probability and proximity affect the losses that actions may produce as well as their gains. The pain that an action brings about may be uncertain or lie far in the future. So these two factors need to be reckoned into the calculation that represents decision-making. Let us then say this, where ‘pain’ is pain that the agent expects to receive from an action.

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