The Growth of Incarceration in the United States: Leaving Proportionality Behind

The unprecedented growth of incarceration in the U.S has been driven by changes in criminal justice policy. These changes cannot be justified according to a theory of proportionality that reconciles consequentialist and deontological requirements. Punishment should be as proportional to its crime-reducing effects as possible without being disproportional to the crime itself. Not only have the changes in criminal justice policy made the system of punishment less proportional to its crime-reducing effects, but they have also created a system of punishment that is, in many cases, disproportional to the crime.


Introduction
The United States of America (U.S) has the highest prison population in the world (Obama, 2015). With 2.2 million, or one in every thirty-one, adults currently in prison, the U.S incarcerates more people than the top thirty-five European countries combined (Obama, 2015). Despite accounting for just five percent of the world's population, the U.S is home to twenty-five percent of the world's prisoners (Roeder et al. 2015, p. 2). Over the past forty years, the general population has increased by less than forty percent, yet the number of people in prison has increased by more than five hundred percent (Obama, 2015). If the U.S general population had increased as quickly as the incarceration rate, the U.S would now have the same population as China (Worldometers, 2014). Punishment is not a natural fact, but an institution created and deliberately used by society (Stanford Encyclopedia of Philosophy, 2015). The decision to deprive an individual of their freedom is an immense exercise of power that must be justified. This is because the deprivation of freedom without justification is the kind of "arbitrary control" that the Founding Fathers were so fearful of (Madison, 2001, p. 252). For this reason, I will answer the following question: Is the growth of incarceration in the U.S justified?
The changes in criminal justice policy responsible for incarceration growth in the U.S cannot be justified. My first task is to identify the changes in criminal justice policy that are responsible for U.S incarceration growth. I must then define the standard by which these changes should be evaluated. Therefore, I will provide a theory of proportionality; punishment should be as proportional to its crime-reducing effects as possible without being disproportional to the crime itself. I will then argue that changes in criminal justice policy have made punishment less proportional to its crime-reducing effects and, in some cases, disproportional to the crime itself. Therefore, I will have shown that the changes in criminal justice policy responsible for the growth of U.S incarceration cannot be justified.

The Causes Of Incarceration Growth In The United States
The United States, land of the incarcerated Travis and Western establish that the incarceration rate has two main determinants; the level of crime in society and the policy responses to crime (2014, p. 44). Firstly, if the crime rate increases when all else is unchanged, then the prison population will increase (Travis and Western, 2014, p. 47). This is simply because there are more people to arrest, each with a fixed probability of apprehension (Travis and Western, 2014). Secondly, while the crime rate determines the number of people who might be arrested, criminal justice policy determines how likely it is and for how long those arrested will be incarcerated (Travis and Western, 2014, p. 44). Figure 1 illustrates that while the crime rate has fallen, the incarceration rate has continued to rise (Travis and Western, 2014). This means that U.S incarceration growth cannot simply be attributed to changes in the crime rate. However, what Figure 1 does not show is that the most rapid growth of incarceration was preceded by large increases in crime for roughly a decade (Travis and Western, 2014, p. 3). Therefore, as Travis and Western argue, rising incarceration can best be explained by ' an increasingly punitive political climate surrounding criminal justice policy formed in a period of rising crime ' (2014, p. 4).
Raphael and Stoll support this claim, contending that criminal justice policy was 'the chief factor that drove up U.S incarceration rates ' (2014, p. 17). They argue that several mechanisms began to limit the discretionary power of judges and parole boards whilst enhancing the bargaining power of prosecutors in the criminal justice system (Raphael and Stoll, 2014, p. 16). For example, "truth-in-sentencing" laws required certain offenders to serve a minimum portion of their nominal sentences (Raphael and Stoll, 2014, p. 15). By 2008, twenty-eight states mandated that violent offenders serve eighty-five percent of their sentence (Raphael and Stoll, 2014, p. 14). Furthermore, between 1975 and2002, every state along with the federal government adopted mandatory minimum sentences for a multitude of non-violent and violent crimes (Raphael and Stoll, 2014). In particular, drug offences were targeted by three quarters of states along with the federal government (Raphael and Stoll, 2014). By the end of the 1990s, roughly half of the states had joined the federal government by employing a particular kind of mandatory minimum sentencing: 'three strike laws' (Raphael and Stoll, 2014, p. 16). These laws demanded a twenty-five-year minimum sentence without the possibility of parole for ' offenders with three or more convictions for serious violent or drug trafficking crimes' (United States Department of Justice, 1994). I will now outline two key trends that have emerged from this increasingly punitive approach.

The amount of time served for violent crime has increased
There has been a substantial increase in the amount of time served for violent offences (Raphael and Stoll, 2014, p. 8). For example, Figure 2 shows that the estimated time served has increased most rapidly for murder (Travis and Western, 2014, p. 53). 1 The vertical red line marks where incarceration growth began to decelerate. I must emphasise that the increases in time served are yet to be fully felt and thus will be underestimated by the graph. Therefore, these figures should be interpreted as lower bound estimates (Travis and Western, 2014, pp. 52-53). For example, Gelb et al. report much longer sentences than displayed in Figure 2. They find that murderers released in 2009 have served on average fourteen years, yet the expected Figure 1: Less Crime, More Criminals (Roeder et al. 2015, p.16). time served for those convicted of murder in 2009 is thirty-eight years, almost three times as long (Gelb et al. 2012, pp. 21-22).

Prison has been used increasingly for less serious offences
There has been a substantial growth in incarceration for less serious crimes. By "less serious" offences, I refer to those crimes that are non-violent, such as theft, receiving stolen property, vandalism and other misdemeanours, forgery and, in particular, drug offences (Raphael and Stoll, 2014, p. 13;California Department of Corrections and Rehabilitations, 2013, pp. 2-11). While this distinction is often blurred, I mitigate this ambiguity by focusing primarily on said drug offences. Although it is widely supported that offences such as murder and rape are more serious than drug offences, I provide a further, explicit and necessary justification for this claim in section five (Raphael and Stoll, 2014;California Department of Corrections and Rehabilitations, 2013). In regards to my research in section four, however, the impact of an increasingly punitive approach to drug offences remains relevant and valid regardless of whether these drugs offences can be labelled as "less serious." Figure 3 shows the combined state incarceration rate by crime, illustrating that drug offences represent the largest increase in the amount of people incarcerated. This was in response to the proclaimed "crack cocaine epidemic" in the late 1980s (King et al. 2005, p. 4). In 1980, the state incarceration rate for drug offences was fifteen per onehundred thousand people (Travis and Western, 2014, p. 153). In 2010, the rate was one hundred and forty per one-hundred thousand people (Travis and Western, 2014). The Sentencing Project notice a similarly alarming trend when they combine state and federal prison population figures. In 1980, there were forty-thousand people incarcerated for drug offences (The Sentencing Project, 2015, p. 3). In 2014, there were nearly five-hundred thousand (The Sentencing Project, 2015).

A Theory Of Proportionality
I have established that incarceration growth has been driven by changes in criminal justice policy. I must now define the standard by which these changes should be evaluated. In order to do this, I must define the circumstances in which punishment is justified. I want to pay attention to both consequentialist and deontological requirements. Therefore, I will appeal to a principle that lies at the core of both; proportionality.

Two theories of proportionality
Consequentialism is forward-looking and justifies practices according to their effects (Stanford Encycopedia of Philosophy, 2015). As Hanna argues, punishment necessarily and intentionally causes harm and suffering (Hanna, 2009, p. 329). This suffering is only justified if it prevents greater suffering to others. More specifically, the purpose of punishment for consequentialists is to provide public safety and reduce crime, namely through deterrence and incapacitation (Hanna, 2009, pp. 336-338). Thus, punishment is only justified if the harm caused is outweighed by these crime-reducing effects. As a result, consequentialists affirm that punishment should be proportional to its crime-reducing effects (Travis and Western, 2014, p. 87). What this means is that punishment should be no more severe than is necessary to achieve its crime-fighting purpose.
By contrast, deontology is backward-looking. Deontology does not appeal to the consequences of practices, but rather to their intrinsic moral value (Stanford Encyclopedia of Philosophy, 2014). An act is justified if it is good in itself. Retributivism provides a deontological theory of punishment. Retributivists do not consider how punishment affects the future of the offender's conduct, or anyone else's conduct for that matter. Rather, as Hart explains, the justification for punishment is that 'the return of suffering for moral evil voluntarily done, is itself just or morally good' (Hart, 2008, p. 231). Crucially, punishment is morally good if it is morally deserved (Frase, 2008, p. 42). It is this requirement means, for deontologists, punishment must be proportional to the crime (Hart, 2008, p. 237). By this, punishment must be proportional to 1) the seriousness of the harm caused or risked and 2) the offender's culpability (Frase, 2008, p. 41). Both requirements ensure that punishment is 'relative to the offender's just deserts' (Frase, 2008, p. 42). This is because the violation of criminal laws makes one eligible for punishment. Offenders deserve to be punished for the wrong they have committed. As a result, if someone receives an excessively lenient punishment, they are not being punished for the wrong they have committed. If someone receives an excessively harsh punishment, they are being punished for a wrong they have not committed (Hyman, 1979, p. 436). For this reason, as Fry argues, the "moral root of the whole doctrine of punishment" is to make the relationship between sin and suffering as "actual and as exact in proportion" as possible (Fry, [undated], cited in Bittner and Platt, 1966, p. 90). I will return to the more complicated relationship between deontological proportionality and recidivism in section five.
I want to assess the changes in criminal justice policy in a way that appeals to both the consequentialist and deontological requirements of proportionality. However, there is one fundamental problem; consequentialist and deontological requirements are often incompatible. This is because punishment that is proportional to its crimereducing effects is not always proportional to the crime itself.
For example, Berman depicts two scenarios in which Hitler is alive after committing his crimes against humanity (Berman, 2013, p. 85). In scenario A, Hitler lives happily (Berman, 2013). In scenario B, Hitler suffers pain as punishment for his offences (Berman, 2013). However, in neither scenario does Hitler go on to commit further crimes (Berman, 2013). No one is deterred from committing the same acts in scenario B nor heartened to bring about justice for the happiness Hitler experiences in scenario A (Berman, 2013). In this hypothetical situation, any punishment would be disproportional to its crime-reducing effects, given that it would necessarily cause harm without producing any benefit. Therefore, consequentialists would not be able to justify the punishment of Hitler in this hypothetical scenario (Berman, 2013). This non-punishment is excessively lenient from a deontological point of view. Clearly, Hitler deserves to be punished (Berman, 2013).
I must consider a brief objection. Frase argues that there is no such incompatibility, because consequentialists also require punishment to be proportional to the crime (2008, pp. 43-45). Frase twice appeals to Bentham to corroborate this claim. Firstly, the greater the offence, 'the greater reason there is to hazard a severe punishment for the chance of preventing it' (Bentham, 1871, p. 326). This means that the severity of the punishment must be proportional to the amount of harm you are trying to prevent (Frase, 2008, p. 44). Secondly, Bentham argues that punishments proportional to the crime give offenders ' a motive to stop at the lesser' crime (1871, p. 326). Conversely, punishment that is disproportional to the crime produces destructive incentives (Bentham, 1871). If less serious offences are punished as harshly as more serious crimes, then there is a decreased incentive to stop at the lesser crime (Frase, 2008, p. 45).
However, this does not accurately represent consequentialism. This is because Frase places a flawed emphasis on the harm that punishment is trying to prevent, yet consequentialists are only concerned with the amount of harm actually prevented. This means that consequentialists endorse the punishment that has the best overall consequences. Yet consequentialists cannot prevent this punishment being excessively lenient or excessively harsh from a deontological point of view. Ultimately, Frase constructs a theory of consequentialism based on his own assumptions about the crime-reducing effects of punishment. Yet this is the very task of consequentialism itself. If longer sentences had a greater deterrent effect, then consequentialists would endorse a longer sentence. However, if longer sentences did not have a greater deterrent effect, then consequentialists would not endorse longer sentences. This is because it would cause unnecessary harm. Consequentialists simply endorse the sentence that is most proportional to its crime-reducing effects.
I am not claiming that a punishment that is proportional to its crime-reducing effects cannot also be proportional to the crime itself. Simply, punishment that is as proportional to its crime-reducing effects as possible is not necessarily proportional to the crime itself. Consequentialist and deontological requirements of proportionality are not always compatible.

Reconciling consequentialism and deontology
This conflict undermines existing research contending that punishment in the U.S is disproportional from both a consequentialist and deontological point of view. For example, Travis and Western contend that punishment in the U.S is not proportional to its crime-reducing effects, because the crime-fighting benefits of incarceration diminish the more it is used (2014, pp. 94-102, 130-156). They also contend that criminal justice policies have violated deontological requirements of proportionality (Travis and Western, 2014, pp. 94-102). Both of these findings are instrumental to the conclusions I will make in this essay. However, the approach Travis and Western adopt is unsatisfactory. This is because the argument that punishment is disproportional to both the effects and the crime itself has no weight unless Travis and Western firstly justify why punishment should be proportional to both its crimereducing effects and the crime itself. However, as I have demonstrated, punishment cannot always be proportional to both. As a result, it is unconvincing to assume that punishment should be proportional to both its crimereducing effects and to the crime without an attempt to reconcile the two theories first. Herein lies the central contribution I wish to make to research condemning the current level of mass incarceration in the U.S. My aim is to apply the problem of U.S mass incarceration to a theory of proportionality that reconciles consequentialist and deontological goals.
First and foremost, punishment must be proportional to the crime. By giving deontology priority, we avoid those sentences that are intuitively wrong, namely the possibility of Hitler going free (Berman, 2013, p. 85). However, simply because deontology takes priority does not mean that there is no room for consequentialist requirements. Rather, there is a fundamental weakness of deontology that means it cannot represent a theory of proportionality by itself. This presents an opportunity for the reconciliation of consequentialism and deontology.
The principal weakness of the deontological theory of proportionality is that we cannot achieve Fry's aforementioned goal of producing an exact relationship between sin and suffering (Bittner and Platt, 1966, p. 90). For example, how many years does someone convicted of robbery, or rape, deserve? Bedau contends that the answers to these questions inevitably yield either absurd or arbitrary results (1978, p. 611). For example, if we interpret proportionality strictly, we might punish a rapist by raping him (Bedau, 1978). This is plainly wrong (Bedau, 1978). If we do not interpret proportionality strictly, then we arrive at a sentence that is ultimately arbitrary. This is because, as Travis and Western argue that 'no one can make a compelling case for why any particular crime deserves to be punished to a uniquely appropriate degree ' (2014, p. 324).
In order to cope with this problem, Travis and Western propose a purely ordinal system, where ' comparably serious crimes are punished in comparable ways' (Travis and Western, 2014). For example, murder should be punished more severely than theft. Travis and Western contend that deontology provides guidance in setting relative, not absolute, levels of punishment (Travis and Western, 2014). This avoids the difficulties in applying proportionality to a uniquely appropriate degree, which is inherently arbitrary. However, a purely ordinal approach would still produce disproportional punishment. An ordinal approach could endorse a range of punishments from a £10 to a £100 fine, but could also range from a twenty-year to sixty-year prison sentences, as long as serious crimes were punished more severely than minor crimes (Stanford Encyclopedia of Philosophy, 2014). Accordingly, murder could be punished with a £100 fine in the first range, or petty theft could be punished with twenty years in the second (Stanford Encyclopedia of Philosophy, 2014). These sentences are excessively lenient and harsh respectively.
Thus, a more convincing way to deal with the problem is to create an ordinal approach anchored in a broad band of acceptable cardinal boundaries. This is endorsed by Morris, who proposes a theory of 'limiting retributivism' (Morris, 1974, pp. 60, 73-77). Morris agrees that deontology cannot convincingly specify a sentence that is precisely proportional to the crime (Morris, 1974, 60). Instead, therefore, deontology should define broad limits to ensure sentences are not intuitively too severe or lenient (Morris, 1974, pp. 60, 73-77;Morris, 1977, pp. 158-159). Morris argues that, within broad upper and lower limits, there exists a range of 'not undeserved' punishments (Morris, 1982, p. 151). By this, there will be A, B and C sentences that are situated within upper and lower boundaries and can all be reasonably considered proportional to the crime. In some circumstances, each band of cardinal values may overlap (Morris, 1982). For example, the lower bound for assault may overlap with the higher bound for petty theft. What Morris does not acknowledge is that this also presents an important role for the ordinal values discussed. In cases where the cardinal values for different crimes overlap, ordinal requirements should ensure that more serious crimes are punished more severely than less serious crimes.

A space to fill
Deontology should thereby serve two roles. Firstly, deontology must ensure that more serious crimes are punished more severely than less serious crimes. Secondly, deontology must define broad upper and lower limits. Within these limits lie multiple punishments that can reasonably be considered proportional to the crime. This presents a vital role for consequentialism.
As long as the punishment can reasonably be considered proportional to the crime, it should be as proportional to its crime-reducing effects as possible. This account of proportionality, firstly, gives consequentialism an important role without producing sentences that are disproportional to the crime. Secondly, this account ensures that the punishment is no more severe than is necessary to achieve this purpose, once we can ensure it gives an offender what they deserve. Thirdly, this account avoids generating the kind of precise but arbitrary sentences produced by a purely deontological approach. This is because consequentialism can provide a sufficiently precise sentence for a reason that we can attempt to measure quantitatively.
I must consider an objection; my anchored ordinal account of proportionality seems just as arbitrary as the purely cardinal account that I have rejected. Defining cardinal boundaries is a task no less arbitrary than defining the precise sentence that is deemed proportional to the crime. However, while the lower and upper cardinal limits are inevitably arbitrary, these limits must exist in order to prevent excessively lenient or harsh sentences (Berman, 2013, p. 85). At the same time, this arbitrariness is precisely what I have attempted to mitigate by allowing room for consequentialist considerations. There is no such room in an approach that attempts to produce an exact sentence by appealing purely to deontology.

Implications for U.S criminal justice policy
I have demonstrated that as long as punishment can reasonably be considered proportional to the crime, it should be as proportional to its crime-reducing effects as possible. I can now determine whether the changes in criminal justice policy meet these requirements. I must concede, however, that to require U.S criminal justice policy to be as proportional to its crime-reducing effects as possible is excessively demanding. Rather, my aim is to see if the changes in criminal justice policy are moving in the right direction, consistent with the theory of proportionality presented. Therefore, I will determine whether the changes in criminal justice policy have made punishment in the U.S more proportional or less proportional to its crime-reducing effects. According to the consequential-ist requirements delineated, punishment becomes more proportional to its crime reducing effects if these crimereducing effects increase relative to the amount of harm caused. Punishment becomes less proportional to its crime-reducing effects if any increase in the amount of harm caused does not co-exist with increased reductions in crime.
By contrast, I will answer the deontological question in absolute terms. This is because the theory of proportionality I have presented requires that I do so. As I have emphasised, any sentence within broad cardinal boundaries can reasonably be considered proportional to the crime (Bedau, 1978, p. 611). This means a sentence is proportional to the crime when it lies within these boundaries, or disproportional when it lies outside these boundaries (Morris, 1977, pp. 158-9). However, a sentence near the upper boundary is neither more nor less proportional to the crime than a sentence near the lower boundary.
Therefore, if changes in criminal justice policy are to be justified, they must make punishment more proportional to its crime-reducing effects, unless by doing so this makes punishment disproportional to the crime. By contrast, any changes that make punishment less proportional to its crime-reducing effects are only justified if this is necessary to ensure that punishment, previously disproportional to the crime, can now reasonably be considered proportional to the crime. My first task, then, is to find out whether the changes have made punishment more, or less proportional to its crime-reducing effects.

More Harm, Less Reward
Changes in criminal justice policy have made punishment in the U.S less proportional to its crime-reducing effects. This is because these changes have produced more harm for less reward.

More punishment, less reward; a case of diminishing returns
Given that punishment itself necessarily constitutes a harm, one more person that is incarcerated constitutes one more unit of harm caused (Hanna, 2009, p. 329). Therefore, as the number of people incarcerated has increased from approximately 300,000 in 1975 to 2.2 million today, the amount of harm caused has necessarily increased (King et al. 2005, p. 1). Not only does punishment necessarily cause harm, there are also further associated harms. For example, a year in prison can cost more than a year at Harvard University (Stiglitz, 2015, p. 1). This means that the U.S spends $80 billion on incarceration a year (Chettiar, 2015, p. 3). For that price, the U.S could eliminate tuition at every university, or double the salary of every high school teacher, or provide universal preschool for every three and four-year old (Obama, 2015).
There are also costs that cannot be measured financially. Most notably, from 1980 to 2000, the number of children with fathers in prison rose from 350,000 to 2.1 million (Travis and Western, 2014, p. 6). However, a meaningful explication of the indirect costs of withdrawing individuals from society requires a much deeper empirical investigation than I have room for (Travis and Western, 2014, p. 21). For this reason, what is most important to emphasise is that the amount of harm caused has increased with rising incarceration. Therefore, if this increase in harm does not co-exist with increases in crime-reducing benefits, then punishment has become less proportional to its crime-reducing effects.
There are two approaches to understanding the relationship between incarceration and crime that I want to dismiss. The first approach assumes that more incarceration equals less crime (Wray, 2005, p. 1). The second approach discredits the existence of any relationship at all (Gainsborough and Mauer, 2010, p. 10).
The first approach emerges in response to the paradox I presented in the second section: the crime rate has reduced, yet the incarceration rate has increased. If the crime rate is decreasing, why is the U.S imprisoning more people? One response is to deny the existence of any paradox at all. Wray affirms that "tough sentencing means less crime…by ensuring that criminal sentences take violent offenders off the streets, impose just punishments and deter others from committing crime" (2005, p. 1). For Wray, the U.S is not putting more people behind bars in spite of the fact that the crime rate is reducing. Rather, the crime rate is reducing because the incarceration rate is increasing.
Gainsborough and Mauer debunk this claim. Between 1998 and 2003, twelve states reduced their incarceration rate (Gainsborough and Mauer, 2010, p. 10). However, crime fell on average by 12%, which is the same as in the thirty-eight states in which rates of incarceration increased (Gainsborough and Mauer, 2010). If incarceration had a linear negative effect on the crime rate, then those states with greatest incarceration growth would also have the greatest reduction in crime (Gainsborough and Mauer, 2010). However, there is a danger of interpreting this data as evidence for the absence of any relationship between incarceration and crime at all. Like Wray's assertion, this would also greatly oversimplify the relationship.
Rather, what Gainsborough and Mauer's data shows is that the causal relationship between incarceration and crime is inconsistent and complex. As King et al. contend, the inconsistent trends between states "do not necessarily suggest that incarceration has no impact on crime," but that "incarceration does not always have a uniformly positive impact on reducing crime" (King et al. 2005, p. 3). I will now demonstrate that as the U.S' incarceration rate increases, the crime-reducing effects diminish. This is not the same as contending that as the incarceration rate increases, crime itself increases. This just means that the amount of crime being reduced is getting smaller as the amount of harm caused is getting larger. This means punishment is becoming less proportional to its crime-reducing effects.
As the U.S' incarceration rate increases, the crime-fighting benefits decrease. This is because the effectiveness of incarceration is subject to ' diminishing returns' (Raphael and Stoll, 2014, p. 9). By this, the crime-reducing effects of incarceration decrease the more it is used (Raphael and Stoll, 2014). When the incarceration rate is low, there is a greater effect of incarceration on crime (Raphael and Stoll, 2014). By contrast, when the incarceration rate is high, there is a smaller effect of incarceration on crime (Raphael and Stoll, 2014). Roeder et al. show that the effectiveness of incarceration diminishes between 1980 and 2013 (2015, p. 23). In Figure 4, the effectiveness of incarceration is represented by the expected decrease in crime resulting from a 1% increase in state imprisonment (Roeder et al. 2015). The most important thing to note is that a 1% increase in incarceration today reduces less crime than it did in 1980. Figure 5 shows that incarceration for motor vehicle theft had the most rapidly diminishing crime-reducing effect. By contrast, the effect of incarceration on the robbery rate initially increased until 1998 (Roeder et al. 2015). I will return to the unusual homicide trend in response to a possible objection to my argument. Overall though, between 1980 and 2013, incarceration has become less effective. It is crucial to emphasise something I have repeatedly stressed; the incarceration rate has increased over the same period (Roeder et al. 2015, p. 16). This means that incarceration in the U.S has become less effective the more it is used. Furthermore, Figure 4 demonstrates that as of 2013, the effectiveness of incarceration has started to increase, albeit very gradually. This shows that when prison is used less frequently, incarceration has a larger crime-reducing effect. This is because as of 2013, the U.S prison population began to gradually decline (Goode, 2013). Ultimately, the amount of harm caused has necessarily increased since 1980, but the crime-fighting benefits have diminished. Therefore, punishment has become less proportional to its crime-reducing effects. Incarceration still prevents crime I must consider a possible objection. Roeder et al. neglect the fact that a 1% increase in incarceration, while producing fewer crime-reducing benefits now than it did in 1980, still produces some crime-reducing benefit. For example, as Figure 4 shows, a 1% increase in state imprisonment in 2013 still produces approximately a 0.02% reduction in crime (Roeder et al. 2015, p. 23). This suggests that it is not meaningful to emphasise a diminishing crime-reducing effect, when ultimately incarceration still serves a crimereducing purpose. This objection fails for two reasons. Firstly, it misunderstands my aim. I do not claim that punishment is either proportional or disproportional to its crime-reducing effects. If this was my aim, I would have to ascertain whether a 0.02% reduction of crime outweighs the cost of a 1% increase in incarceration. Instead, my aim is to show that punishment has become less proportional to its crime-reducing effects. The fact that incarceration still produces some benefit is irrelevant to this aim.
What is relevant is that this benefit is getting smaller. This is important in itself for the reason that, as I established earlier in this section, the amount of harm caused has necessarily increased between 1980 and 2013 (Roeder et al. 2015, p. 16). When the incarceration rate was low in 1980, it had a larger effect on crime reduction than in 2013 when the incarceration rate was high (Roeder et al. 2015, p. 23). While harm has increased, the reward has decreased. This means that punishment has become less proportional to its crime-reducing effects.
Secondly, the emphasis on the fact that incarceration still fights crime loses weight in light of the fact that incarceration today hardly has any effect on the crime rate at all (Roeder et al. 2015). Figure 1 shows that, as of 1999, the effect of a 1% increase in incarceration on crime-reduction approaches a figure close to zero. Consider the trend for homicide in Figure 5, which initially undermines the existence of diminishing returns given that the effect of incarceration on crime-reduction has increased slightly. However, the effect of incarceration has improved from a situation in which it was previously increasing the homicide crime rate to the current situation in which incarceration has almost no effect on the homicide rate at all. More generally, Roeder et al. contend that increased incarceration did not have any observable effect at all on the violent crime rate in the 1990s or 2000s (2015). In these circumstances, rising incarceration is causing almost unnecessary harm, given that it hardly has any crime-fighting benefit at all (Roeder et al. 2015).
As the U.S' incarceration rate has risen, the harm caused has necessarily increased but the crime-reducing effects have diminished. Therefore, punishment has become less proportional to its crime-reducing effects. I will now argue that this correlation can be attributed to the changes in criminal justice policy.

Causal explanations and the mechanisms of incarceration
I have already discerned that 1) the amount of time served has increased for violent crime and 2) prison has been used increasingly for less serious offences, namely drug offences. In order to attribute the diminishing effects of incarceration to these changes, I must firstly present the mechanisms through which incarceration is supposed to reduce crime. I will focus on deterrence and incapacitation theory. I do not want to discredit the validity of these theoretical mechanisms altogether. Rather, changes in criminal justice policy have made certain assumptions about the way in which these mechanisms work. It is these assumptions that I will discredit.

Deterrence
Deterrence theory contends that the experience or threat of punishment discourages individuals from offending (Drago et al. 2009, p. 258). Underpinning deterrence theory is a rationalistic view of crime, where an individual weighs the benefit of crime against the cost of punishment (Drago et al. 2009). Accordingly, punishment provides a cost that is sufficiently high to outweigh the benefit of committing a crime. Deterrence can be general or specific. General deterrence refers to the threat of punishment, where the "visible use of prison" discourages citizens from breaking the law (McGuire, 1995, p. 10). Specific deterrence refers to the experience of incarceration, which discourages those who have already committed a crime from re-offending (Smith and Gartin, 1989, p. 94).

Incapacitation
Incapacitation theory contends that by incarcerating an individual, we prevent them from committing any crime for the duration of their imprisonment (Travis and Western, 2014, p. 18). While deterrence theory rests on the likelihood of individuals changing their behaviour in response to the stimulus of punishment, incapacitation is simply the product of the "mechanical removal of criminals from society" (Drago et al. 2009, p. 258). Incarceration reduces the amount of crime committed by the individual had they not been apprehended (Travis and Western, 2014, p. 18). I will now demonstrate that changes in criminal justice policy have reduced the effectiveness of both deterrence and incapacitation.

As prison is used increasingly for drug offences, the incapacitation effect diminishes
Incapacitation theory initially suggests that the more people we incarcerate, the more harm we prevent by removing them from society (Drago et al. 2009, p. 258). However, this ignores the vital question of who we are incarcerating, which affects how much harm we are preventing. Using prison increasingly for less serious offences, namely drug offences, means that the incapacitative benefit to public safety decreases with the scale of incarceration (Roeder et al. 2015, p. 25). For example in 1980, non-violent drug offenders accounted for less than 10% of all those imprisoned (Schmitt et al. 2010, p. 8). In 2010, non-violent drug offenders accounted for roughly 25% (Schmitt et al. 2010). For every increase in cost, you are getting less in return for your investment.
A strong objection to this is that while rising incarceration prevents less serious harms, these are still harms nonetheless. More incarceration therefore prevents more harm via incapacitation, even if these harms represent a Durose: The Growth of Incarceration in the United States Art. 1, page 9 of 17 less serious risk to public safety. However, there are three reasons why this objection fails. Firstly, Canela-Cacho et al. make an important distinction between low and high rate offenders. Expanding the prison population leads to the imprisonment of those individuals who commit less crime (Canela-Cacho et al. 1997, pp. 133, 153). This is because most of the high-rate offenders are already incarcerated and so there are fewer of them to apprehend (Travis and Western, 2014, pp. 142-143). Thus, not only does rising incarceration prevent less serious harm, but it also prevents a smaller amount of crime itself (Petersilia, 2003, p. 53).
Secondly, using prison increasingly for less serious crimes, namely misdemeanours and drug offences, might even have the effect of increasing crime (Petersilia, 2003). This is because, as Petersila contends, the incapacitation effect is negated by a criminogenic effect, whereby the experience of prison increases the probability of offending when they are released (2003). This effect is largest among those with few past offences with little experience of the criminal justice system, who become criminalised by their contact with serious offenders (Lerman, 2009, p. 164). As Mueller-Smith finds, in Harris County, Texas, from 1980-2009, every additional year that a prisoner was incarcerated increased the probability that he would re-offend by 5.6% per quarter (2015, p. 9). Fundamentally, Mueller-Smith finds that post-release criminal behaviour displays increases in violent offences, even though the original incapacitation was primarily imprisoning those who committed misdemeanours (2015).
Thirdly and more specifically, using prison for drug offences prevents less harm via incapacitation because of the "drug replacement effect" (Travis and Western, 2014, p. 146). By this, most of those sent to prison are swiftly replaced by others in the criminal network (Travis and Western, 2014). As Smith and Dickey contend, arrests are "easy to prosecute," but "the drug market [continues] to thrive at the intersection" (Smith and Dickey, 1999, p. 8). This explains why, despite huge increases in incarceration for drug offences, the availability of drugs has increased (The Pew Charitable Trusts, 2015). This is corroborated by the fact that the price of cocaine, heroin and methamphetamine have all decreased from 1981 to 2012 (The Pew Charitable Trusts, 2015).
Using prison increasingly for less serious offences, namely drug offences, has made the system of punishment less proportional to its crime-reducing effects. This is because as harm increases, the crime-fighting benefits diminish.

Increasing the amount of time served for violent crime has a weak deterrent effect
It is self-evident that increasing the amount of time served necessarily increases the amount of harm caused to the offender. Furthermore, Gelb et al. estimate that the total state cost of the additional time served of offenders released in 2009 relative to 1990 was $10.4 billion (Gelb et al. 2012, p. 12). Increasing the time served does not increase the amount of crime-reduction. My main focus is on the enhancement of sentences that are already long. Recall Gelb et al.'s upper bound estimates that murderers released in 2009 have served on average fourteen years, yet the expected time served for those convicted of murder in 2009 is thirty-eight years (2012, p. 21). This trend is particularly important, because I want to show that increasing already long sentences has a diminishing crime-reducing benefit. Figure 6 represents two ways to look at the relationship between sentence length and deterrence. Line A depicts a linear negative relationship between sentence length and crime rate. The longer the sentence either experienced or threatened, the higher the cost of punishment. The higher the cost of punishment, the higher the disincentive to commit crime. Thus, according to Line A, the longer the sentence, the lower the crime rate.
Line B similarly depicts a negative relationship between sentence length and crime rate. Crucially however, the relationship is not linear. Rather, Line B represents the "heterogeneity in the deterrence response to the threat of imprisonment" (Nagin, 2013, p. 39). The longer the sentence length, the less the crime rate reduces. This is because increasing the amount of time served has a diminishing deterrent effect to the extent that, at S1, it has no deterrent effect at all. Thus, if the deterrent effect of increasing already long sentences resembles Line B more closely than Line A, then the changes in criminal justice policy have made punishment less proportional to its crime-reducing effects. I will argue that increasing already long sentences resembles Line B.
I will now consider four pieces of evidence in light of this claim. The first piece of evidence can initially be interpreted to prove the existence of Line A, undermining my argument. I will show that this would be a misrepresentation in light of the second, third and fourth pieces of evidence.
Firstly, Drago et al. find that a marginal increase in sentence length reduces the specific deterrent effect (Drago, 2009, p. 259). They were afforded the opportunity to investigate the effect of increased sentence length by the Italian Collective Clemency Bill in July 2006 (Drago, 2009, p. 262). This bill provided those incarcerated before May 2006 with an immediate three-year sentence reduction (Drago, 2009, p. 265). However, the condition was that if those released committed another crime within five years of their release, they must serve the remainder of sentence that was previously cut short on top of their new sentence (Drago, 2009, p. 266). An additional month in the residual sentence reduced the possibility of recidivism by 1.3% (Drago, 2009, p. 272). The longer the threatened sentence, the greater the deterrent effect (Drago, 2009, p. 266). Increased sentence length increased the deterrent effect.
It is easy to misinterpret this data to claim the existence of Line A and undermine my argument. For example, Drago et al. contend that this data represents the effectiveness of sentencing as a disincentive of criminal activity (2009, p. 259). Crucially however, the majority of the sample in Drago et al.'s data "were convicted for crimes against property or offenses related to the drug law" (2009, p. 269). This means that they cannot substantiate the existence of either Line A or B. This is because Drago et al.'s data only examines the effect of short increases (ranging from one to thirty-six months) on short sentences (2009, p. 258). Drago et al.'s findings do not test the effect of increasing already long sentences. Therefore, they cannot determine whether increasing sentence length will continue to have a deterrent effect past a certain point, represented by S1 in Figure 6.
The specific deterrent effect is undermined, in a way that represents Line B, by the following evidence. In 1980, the recidivism rate for federal inmates, and therefore including those with longer sentences, was 38% (Gaes et al. 1986). However, the recidivism rate for federal offenders released in 2005 was 49% (Hunt and Dumville, 2016, p. 5). I have established that the amount of time served has increased over this period. Therefore, despite longer sentencing over this period, federal offenders were not being deterred from re-committing in 2005 any more than they were in 1980. In fact, they were being deterred even less. This corroborates the claim that longer sentencing does not increase the deterrent effect. In particular, this casts doubt on the effectiveness on policies that aim to send a clear warning to criminals who may re-offend, such as the aforementioned "three strikes" policy.
The third piece of evidence illustrates that increasing already long sentences also diminishes the general deterrent effect, resembling Line B (Nagin, 2013, p. 3). Nagin points to six studies that substantiate this claim (2013, pp. 35-8). One of these is conducted by Raphael and Ludwig (Raphael and Ludwig, 2003, pp. 251-86). Those convicted of gun crimes in Richmond, Virginia, with a prior felony record, were subject to federal incarceration (Raphael and Ludwig, 2003, p. 251). This produced a more severe punishment than that generated by Virginia state law (Raphael and Ludwig, 2003). By comparing the gun homicide rate between Richmond and other cities, controlling for confounding variables, they found that the threat of an enhanced sentence that is already long has no deterrent effect (Raphael and Ludwig, 2003, p. 252). Increasing already long sentences has a weak deterrent effect, as represented by Line B in Figure 4.
The fourth piece of evidence returns to the incapacitation effect. Ulmer and Boutwell contend that offending declines noticeably with age after adolescence (Figure 7) (Raphael and Ludwig, 2003). Therefore, by keeping people in prison for longer, we are reducing the likelihood that incarceration is having any incapacitative effect (Raphael and Ludwig, 2003). This is because it is less likely that these individuals would be causing harm anyway if they were not incarcerated. Increasing the amount of time served for violent crime has made the punishment less proportional to its crime-reducing effects.
I have established that increases in harm have not coexisted with increases in crime-reducing benefits. I then provided causal explanations for this correlation. By doing so, I have established that increasing the use of prison for less serious offences and the amount of time served for violent crime has made the punishment, in both cases, less proportional to its crime-reducing effects. However, I cannot assert that these changes are unjustified until I have considered the possibility that they were necessary to ensure that the punishment, in both cases, could reasonably be considered proportional to the crime itself.

Deontology: An Unconvincing Excuse
I have established that changes in U.S criminal justice policy have made punishment less proportional to its crimereducing effects. Changes in criminal justice policy that make punishment less proportional to its crime-reducing effects are only justified if this is necessary to ensure that punishment is proportional to the crime itself.

Violent offenders were already getting what they deserved
I will firstly focus on the increase in the amount of time served for violent crime. I have established that the clearest example of increases in sentences for violent crime was for murder. Recall that, according to upper bound estimates, murderers released in 2009 have served, on average, fourteen years, yet the expected time served for those convicted of murder in 2009 is thirty-eight years (Gelb et al. 2012, p. 21). I established that this has made the punishment less proportional to its crime-reducing effects. This change in criminal justice policy can only be justified if it was necessary to ensure that the punishment can now reasonably be considered proportional to the crime. However, I will now demonstrate that increasing the amount of time served for violent crime was not necessary to ensure the punishment was proportional to the crime. Therefore, this change is criminal justice policy cannot be justified.
Before I validate this claim, I must consider an initial limitation. I want to show that increasing the amount of time served for violent crime was not necessary to ensure that the punishment was proportional to the crime. However, I am focusing on the time served for murder. This is problematic, because other violent crimes will have their own cardinal boundaries for what punishment can be reasonably considered proportional to the crime. However, recall that murder represents the most substantial increases in time served for violent crime. If I can show that the most substantial increases in time served have not changed whether the punishment is proportional to the crime, then we can assume that less substantial increases in time served for violent crime have similarly made no meaningful difference.
The best way to validate the claim that increasing the amount of time served for violent crime was not necessary to ensure the punishment was proportional to the crime is to consider the opposing view. The opposing view contends that fourteen years is excessively lenient and therefore increasing the amount of time served was necessary to ensure the punishment was proportional to the crime. Importantly, this view only has weight if it can be convincingly established that thirty-eight years is proportional to the crime. Otherwise, the changes did not make the punishment proportional to the crime. Yet as I emphasised in section three, there is no convincing justification for why any particular crime deserves a particular punishment (Gelb et al. 2012, p. 324). Accordingly, there is no convincing justification for why an individual deserves to serve thirty-eight years.
Therefore, the only way to justify the claim that thirtyeight years is proportional to the crime is to appeal to the need for broad cardinal boundaries (Morris, 1977, pp. 158-9). As I have stressed, cardinal boundaries must be broad enough to avoid attempts at specifying sentences that are precisely proportional to the crime, which will ultimately yield either absurd or arbitrary results (Bedau, 1978, p. 611). Therefore, a sentence can be reasonably considered proportional to the crime if it lies within these accepted cardinal boundaries (Morris, 1974, pp. 73-7). As Morris argues, cardinal boundaries are there to prevent "undeserved" penalties widely seen as excessively harsh or lenient (Morris, 1982, pp. 158-9).
In light of the fact that 61% of the American public are in favour of the death penalty for murder, it would be difficult to argue that thirty-eight years is widely seen as excessively harsh (Dugan, 2015). For this reason, I do not claim that thirty-eight years is undeserved. Ultimately, though, there is no convincing way to justify the claim that thirty-eight years is not undeserved without conceding that fourteen years is also not undeserved. This claim is substantiated if we look at the average time served in other countries for those with a life sentence, which includes those convicted of murder. In 2010, the average time served was twenty-eight years in Canada and seventeen years in Ireland (Office of the Correctional Investigator, 2013; Irish Penal Reform Trust, 2012, p. 7). In 2011, the average time served was eleven years in Australia (Australia Bureau of Statistics, 2011). In 2014, the average time served was seventeen and a half years in the UK, and sixteen years in Denmark (Prison Reform Trust, 2014, p. 2;Hanson, 2014).
Therefore, thirty-eight years can only be considered proportional to the crime if the cardinal boundaries are sufficiently extended beyond these sentences. Crucially, if the boundaries are broad enough to include thirty-eight years, then the boundaries are necessarily broad enough to include fourteen years as well. Accordingly, I do not claim that increasing already long sentences has made the punishment disproportional to the crime. Rather, increasing already long sentences has simply not changed the fact that the punishment can reasonably be considered proportional to the crime. Therefore, both punishments before and after the changes in criminal justice policy can reasonably be considered proportional to the crime. As I have stressed, as long as punishment can reasonably be considered proportional to the crime, punishment should be as proportional to its crime-reducing effects as possible. Crucially, in the previous section, I established that the changes have made the punishment less proportional to its crimereducing effects. Therefore, increasing the amount of time served for violent crime cannot be justified.

Drugs and disproportionality
Having discussed the increase in the amount of time served for violent crime, I now move to the increasing use of prison for less serious offences, namely drug offences. In the previous section, I established that using prison increasingly for less serious offences has made the punishment less proportional to its crime-reducing effects. Again, this can only be justified if, before the changes, less serious crimes were punished with excessive lenience from a deontological viewpoint. This would mean that the changes were necessary to ensure that the punishment, previously disproportional to the crime, can now reasonably be considered proportional to the crime. However, I will now argue that the increasing use of prison for less serious offences has created a system of punishment that is disproportional to the crime. Therefore, using prison increasingly for less serious offences cannot be justified. This is because any appeal to the need for deontological proportionality is unconvincing if the change in criminal justice policy cannot itself meet this very requirement.
As I have previously established, deontological proportionality requires that comparably serious crimes are punished in comparable ways. I will argue that the increasing use of prison for less serious crimes has violated this ordinal requirement. In order to validate this claim, I will firstly argue that the use of mandatory minimum sentences has punished less serious crimes more harshly than more serious crimes. Secondly, I will consider an objection, which attempts to endorse circumstances in which this is acceptable. However, I will contend that this objection simply highlights that the punishment often fits the offender's character, not the crime. Thirdly, I will contend that differential punishments for similar drug offences have produced racial disproportionality.
The use of mandatory minimum sentences violates ordinal requirements by punishing less severe crimes as harshly, if not more harshly, than more severe crimes. The average time served, as of 2012 in California, for receiving stolen property was higher than assault with a deadly weapon (California Department of Corrections and Rehabilitations, 2013, p. 4). Many street-level drug traffickers in the U.S receive mandatory minimum sentences of five, ten, twenty or more years (California Department of Corrections and Rehabilitations, 2013, p. 88). Possessing one gram of LSD with an intent to distribute, without any resultant death or serious bodily injury, mandates a minimum five-year sentence (Families Against Mandatory Minimums, 2012). If this is your second offence, the minimum sentence is ten years (Families Against Mandatory Minimums, 2012). Ten grams of LSD triggers a ten-year sentence, or twenty-years if it is your second offence (Families Against Mandatory Minimums, 2012). The most harsh sentences for less serious crimes have been generated by a specific kind of mandatory minimum sentencing law that I have previously mentioned; the "three strikes" policy. Until recent reform, California triggered the three strike law for third offences that included petty theft (Raphael and Stoll, 2014, p. 17). To give one example, in 1998 a 55-year old man named Dale Curtis Gaines was given 25 years in prison for receiving stolen property (Staples, 2012). His first two strikes were unarmed burglaries of empty houses (Staples, 2012).
The implication of these mandatory minimum sentences, and in particular the three-strike laws, is that some property and drug offences have received lengthier sentences than many violent offences, including robberies, rapes and aggravated assaults (Travis and Wester, 2014, p. 88). As Obama proclaims, 'the punishment simply does not fit the crime. If you are a low-level drug dealer, you owe some debt to society…But you don't owe twenty years, you don't owe a life sentence. That's disproportionate' (Obama, 2015). This is not because twenty years is intrinsically unjust by itself. Rather, these sentences violate the ordinal requirement that comparably serious crimes are punished in comparably serious ways (Travis and Western, 2014, p. 324).
This rests on the assumption that street-level drug dealers deserve less severe penalties than violent offenders. Travis and Western appeal to the general public, who 'typically views robberies, rapes, and aggravated assaults as more serious than most drug sales' (Travis and Western, 2014, p. 88). This is corroborated if we use the criteria for deontological proportionality. Recall that punishment should be proportional to 1) the seriousness of the harm caused or risked and 2) the offender's culpability.
Firstly, street-level drug crime is less serious than violent crime simply because of the non-violent nature of the crime in itself. For example, nine out of ten federal drug offenders sentenced in 2002 had no weapon involvement (King et al. 2005, p. 6). Furthermore, the examples of sentences I gave were for offences that did not result in death or serious injury. Secondly, street-level offenders are less culpable for any harm caused than those who have committed violent crime. This is simply because the drug trafficker provides the means for harm, whereas the violent offender inflicts the harm themselves. According to deontological requirements of proportionality, streetlevel drug offenders deserve less severe punishment than those convicted of violent crime. Therefore, the use of mandatory minimums for less serious crimes has violated ordinal requirements of proportionality. This means that using prison increasingly for less serious offences has created a system of punishment that is, in many cases, disproportional to the crime.

The recidivist premium
I will now consider an objection to the claim that the use of the three strikes policy in particular has produced punishments that are disproportional to the crime. This objection contends that, in cases of re-offending, it is irrelevant that comparably serious crimes are not punished in com-parably severe ways. This is because of the "recidivist premium," whereby prior offences justify lengthier sentences (Roberts, 1997). Roberts considers two justifications for the recidivist premium. The first is consequentialist; recidivists have a higher risk of reoffending and thus need greater disincentives (Roberts, 1997, p. 303). However, I have already illustrated that longer sentences do not necessarily produce greater crime-reducing effects. Instead therefore, the focus of this section is deontological and whether recidivists deserve harsher punishments.
Herein lies the second justification that Roberts considers. Roberts re-emphasises the two components of retributive proportionality: the seriousness of the harm caused and the offender's culpability. The recidivist premium makes use of the second component. According to the U.S Sentencing Commission, "a defendant with a record of prior criminal behaviour is more culpable than a first offender and thus deserving of greater punishment" (1992, p. 267). This is built on Lee's theory of "recidivism as omission" (Lee, 2009). This represents "the offender's failure, after his conviction, to arrange his life in a way that ensures a life free of further criminality" (Lee, 2009, p. 571). Reoffenders are culpable, not only for the offence, but for their failure to fulfil this obligation to "steer clear of criminality" (Lee, 2009, p. 613). However, it remains unclear why first-time offenders are not equally culpable of failing to steer clear of criminality.
The reason why is provided by Wasik and von Hirsch. They argue that first-time offenders, who "lapse into criminality after a lifetime of law-abiding" should be treated with a certain degree of lenience (Wasik and von Hirsch, 1994, p. 410). This is because, "after being confronted with censure or blame," they have the capacity to reflect on the morality of their actions (Wasik and von Hirsch, 1994). This lenience, however, should diminish with every reoffence (Wasik and von Hirsch, 1994). This is because lenience is contingent on the assumption that the individual is capable of moral reflection. Reoffending is evidence in itself that the offender does not have such capacity. While first-time offenders are given the opportunity for moral reflection, they have not yet dishonoured this obligation (Lee, 2009, pp. 611-12). By contrast, re-offenders are culpable for dishonouring this very obligation (Lee, 2009, pp. 612). Accordingly, it is irrelevant that comparably serious crimes are not punished in comparably severe ways if the offender has a criminal record.
However, this objection simply reinforces the claim that the use of the three strike policy has created a system of punishment that is disproportional to the crime. This is because the recidivist premium does not punish the individual for the wrong they have committed. Rather, the individual is punished for a crime for which he has already received his just deserts. As Fletcher argues, individuals are punished, and deemed culpable, a second time for the same criminal conduct (Fletcher, 1978, p. 466). As a result, when an individual is punished more severely in light of prior offences, the punishment fits the offender's character, not the crime (Roberts, 2008, p. 474).
Thus, using prison increasingly for less serious crimes has created a system of punishment that is disproportional to the crime. This is because mandatory minimums, including three strike laws, violate the ordinal requirement that comparably serious crimes are punished in comparable ways. Any attempt to defend the use of three strike laws by appealing to the "recidivist premium" simply highlights that the punishment fits the character, not the crime.

Justice for all?
Using prison increasingly for less serious crimes has also generated racial disproportionality. In order to validate this claim, I will firstly outline the level of racial imbalance that exists in the U.S criminal justice system. After doing this, I will argue that the increasing use of prison for drug offences has contributed to this racial imbalance. I will then argue that it has done so by producing differential punishments for similar offences. I will show that this violates ordinal requirements of proportionality, which means the increasing use of prison for less serious offences has created a system of punishment that is disproportional to the crime.
Despite the fact that Blacks and Latinos represent 30% of the total population, they represent 60% of the prison population (Obama, 2015). Black men are six times as likely to be incarcerated as white men (The Sentencing Project, 2015, p. 5). There are more black men in U.S' prisons that the total prison populations of India, Argentina, Canada, Lebanon, Japan, Germany, Finland, Israel and England combined (Walmsley, 2016, pp. 1-6). If current trends continue, one in three black males and one in six Latino males born today will be incarcerated at some point during their life, compared to one in every seventeen white males (Knafo, 2013).
The increasing use of prison for drug offences has contributed greatly to this racial imbalance. Between 1980 and 2000, the national drug arrest rate among Whites increased from 350 to 463 per 100,000 (Beckett et al. 2005, p. 419). By contrast, the rate among Blacks increased from 650 to 2,907 per 100,000 (Beckett et al. 2005). This imbalance is supported by Figure 8, which shows drug arrests among Blacks grew most rapidly between 1980 and 1990. The graph shows that, in the 1970s, Blacks were twice as likely to be arrested than Whites for a drug offence (Western, 2014, p. 46). By 1989, Blacks were four times as likely to be arrested (Travis and Western, 2014, p. 94).
I must now demonstrate that this racial imbalance is evidence of a system of disproportional punishment. This is because, by itself, the existence of racial imbalance is insufficient. As Travis and Western postulate, this racial imbalance might simply be a result of 'group differences in criminality' (2014, p. 94). Crucially though, Travis and Western contend that the "numbers of arrests of black people for drug crimes bear little relationship to levels of black Americans' drug use or involvement in drug trafficking (Travis and Western, 2014, p. 97). If this is true, then racial imbalance in incarceration is evidence of disproportional punishment.
On one hand, there is no definitive crime data on drug use to confidently corroborate this statement (Travis and Western, 2014). However, Figure 9 shows that white high school students report more drug use and make three times more drug-related emergency visits than black students during the 1990s. For adults, the National Survey on Drug Abuse found that drug use does not significantly differ between Blacks and Whites (Travis and Western, 2014, p. 50). Therefore, the racial disparity in drug incarceration cannot be explained by racial disparities in crime. Instead, the increasing use of prison for drug crimes has created racial imbalance by generating different punishments for similar offences (Travis and Western, 2014, p. 97).
The use of mandatory minimum sentencing for crack and powder cocaine provides the strongest evidence for this claim, creating racial imbalance by violating ordinal requirements. Before the Fair Sentencing Act 2010, it took one hundred times as much power cocaine to receive the same mandatory minimum sentence given to crack cocaine offences (Travis and Western, 2014, p. 47). Although the Fair Sentencing Act reduced the severity ratio reduced from 100:1 to 18:1, this ratio still produces huge racial imbalance (Travis and Western, 2014). This is because Blacks are more likely to be arrested for  : White students use drugs more than black students (Western, 2014, p.47).
Durose: The Growth of Incarceration in the United States Art. 1, page 15 of 17 crack cocaine and Whites are more likely to be arrested for powder cocaine (Beckett et al. 2005, p. 428). For example, Beckett et al. took a sample from Seattle and found that 63.1% of crack cocaine arrestees were black and 26.3% were white (Beckett et al. 2005). By contrast, 52.1% of powder cocaine arrestees were white, and only 22.6% were black (Beckett et al. 2005). Racial imbalance is generated by the fact that Blacks are more likely to be arrested for those offences that carry longer sentences.
Fundamentally, powder and crack cocaine are different forms of the same drug (Raphael and Stoll, 2014, p. 25). Thus, the use of differential mandatory minimum sentencing has created racial imbalance in a way that violates ordinal requirements of proportionality. This is because similar offences are punished with varying severity, which contradicts the requirement that comparably serious crimes are punished in comparably serious ways. The increasing use of prison for less serious offences has created a system of punishment that simply does not fit the crime.
Neither increasing the amount of time served for violent crime, nor using prison increasingly for less serious offences, can be justified by appealing to the deontological requirement of proportionality. This is because, firstly, increasing the amount of time served for violent crime was not necessary to ensure that the punishment was proportional to the crime. Secondly, using prison increasingly for less serious offences has generated punishment that is disproportional to the crime. Thus, it is indefensible that both changes have made the punishment less proportional to its crime-reducing effects. Any appeal to the need for deontological proportionality is unconvincing if the change in criminal justice policy cannot itself meet this very requirement.

Conclusion
The changes in criminal justice policy responsible for the growth of incarceration in the U.S cannot be justified. I firstly presented a theory of proportionality that reconciles consequentialist and deontological goals; as long as the punishment can reasonably be considered proportional to the crime, it should be as proportional to its crime-reducing effects as possible. I then established that both A) increasing the amount of time served for violent crime and B) using prison increasingly for less serious offences have made the punishment less proportional to its crime-reducing effects. Therefore, these changes can only be justified if they are necessary to ensure that punishment is proportional to the crime itself. However, I then demonstrated that, firstly, increasing the amount of time served for violent crime was not necessary to ensure that the punishment is proportional to the crime and, secondly, using prison increasingly for less serious offences has created a system of punishment that is disproportional to the crime. For this reason, the changes in criminal justice policy responsible for the growth of incarceration cannot be justified. Donald Trump has proclaimed that "we have to get a lot tougher" for violent immigration, and low-level drug offences (Trump, 2015). He has also hinted at an executive action to re-apply solitary confinement for juveniles, as well as advocating the death penalty and greater investment in private prisons (Massey, 2016). Therefore, what is most alarming is not the tragic consequences nor deep injustice of mass incarceration, but that for some, the era of mass incarceration has only just begun. If punishment is being used without justification from either, the infliction of suffering that is necessarily caused is merely the arbitrary use of power. For this reason, the U.S must restore the fundamental role of proportionality in its system of punishment or reconsider its status as the land of the free.

Notes
1 Note that time served is not the same thing as sentence length. 2 Roeder et al. divided the percentage change in crime by the percent change in incarceration in each decade. This "elasticity estimate" was multiplied by the percentage change in incarceration. This tells us the estimated percentage change in crime. Roeder et al. then divided the estimated percentage change in crime by the real percentage change in crime. This tells us how much of the percentage change in crime is attributable to incarceration.