Punitive justice (or 'retributive justice') is a form of justice that advocates for a proportional punishment for the offense committed. An eye for an eye. The biggest problem with punitive justice, however, is that such equivalence is never possible.
This is because there is a disproportionate amount of value or meaning in the two instances (offense on the one hand and punishment on the other). A way we can understand this asymmetry is through Freud's concept 'cathexis'. Briefly, cathexis is the process of imbuing an object with libidinal energy. We might say that it is a process of affective, emotional, significatory piety that is infused into an object. The object on the receiving end is thus known as a cathectic object.
Think of a loved one. This person becomes valuable, not just in some abstract sense, but because they are literally objects of meaning, value, and emotional connection for the lover. When such a person is lost, there is, therefore, a literal sense in which one loses oneself as well. This is a source of melancholy. Melancholy (different from depression) is the experience of loss when a cathectic object is lost or harmed.
In an instance when such a loved one is harmed, punitive justice argues that there must be an equivalent made in order to balance the scales of justice. The problem however is that the punishment is never going to equal the intensity or form of cathexis that composed the lost object. Capital punishment is incapable of actually evening the scales for precisely this reason. Similarly, a jail sentence for rape will not be able to balance the scales of violated cathexis. This is manifold: for one, oneself is also a cathectic object for oneself that is replete with an infinite amount of cathectic value; second, the person is part of a family who will also experience harm; and third, there is a larger cultural value that is harmed, as the threat of violence is both shared in the instance and also as it becomes a real potential for others as they are exposed to the reality of such threats. All this makes the cut of the initial offense something irreparable according to punitivity, as there is no quantifiable equivalent.
What is more, punitive justice requires that an external body (the State/the community/etc) decides on what a just measure of equivalence is. 10 years for rape. 1 year for theft. Etc. These are quantities in terms of time behind bars that have very little relation to the offense and that can't really recompense for the harm caused. The reason they can't is that this model presumes that an equivalent transfer of cathectic value is possible; that somehow a punishment can be equal to the crime – at least, in the eyes of the State. But who decides how such a cathectic equivalence is measured? How can the decision of the State's punishment allocation be deemed legitimate except according to its own sovereign self-legitimacy? And further, according to what logic does the State itself make such self-legitimizing decisions?
Not to beat a dead horse, but it does seem apparent that there is an embedded capitalist logic inherent in the liberal-capitalist State's intelligibility with regard to justice per se. That is, the determining logic by which the State itself thinks is capitalist.
In his lectures on "The Birth of Biopolitics," Foucault calls the market the 'site of veridiction'. What he means by this is twofold: 1) true prices are determined by market forces through the exchange mechanisms of the market; something different than when a 'just' price was determined under previous economic regimes and (more importantly I think) 2) that truth itself is completely detached from notions of 'right' or 'just' and are completely determined by the logic of marketability. This is to say that truth, under the logic of capitalism, requires market equivalence in order for there to be social exchange. And it is this logic of market equivalence that conditions of the logic of the liberal-capital State with regard to punitivity.
Of course, this does not mean that capitalism created the 'eye for an eye' logic. This is something that has existed for millennia. Communities have long sought for appropriate ways to respond to offense. This is why 'eye for an eye' was such a revolutionary concept. The difference, however, is that pre-capitalist equivalence was rooted in different systems of exchange that go beyond pure reduction to number. For example, the Levitical priesthood's enforcement of 'eye for an eye' was still tied up in the larger ceremonial law structures of ancient Israel that required a relation to the transcendent. Add the sacrificial system, jubilees, and other ways of managing social and personal debt and you have a far more complex system than a simple one-to-one equivalence. This is because there was a profound understanding of the logic of cathexis. (Also, it is important to consider the prophets who persistently condemned the sufficiency of the Levitical order itself.)
The point in bringing this up is not to suggest that humans once had it figured out and that capitalism has somehow bastardized human efforts. Rather, it is to note the complexity of dealing with justice and the lengths that communities have gone in order to deal with the infinite value of harming cathectic life. And further, it is to highlight how it is that punitivity as a form of justice, particularly under the conditions of capitalism, is sorely deficient.
Finally, perhaps the ultimate reason that punitivity is deficient is that the it is a positive action upon oneself. What I mean is that punitivity claims to seek to balance the scales of justice by dishing out an equivalent punishment for an offense. It is supposed to be cathartic. However, what it actually does is provide a measure of enjoyment or pleasure for those witnessing the punishment. The State, the community, and the individuals who witness the punishment of the victim receive a doubled-back amount of pleasure as the punishment is carried out. However, if there is no possibility for genuine equivalence (as explored above), then this doubling back is not truly cathartic, but only deepens the loss, hiding it, repressing it further (both into the personal psyche and into the larger cultural logic). The result of this is that 1) the logic of equivalence itself becomes further embedded; it becomes a more intensified promise of justice (which according to this very logic is impossible), and so 2) intensifies the person's/community's need for further acts of 'justice' but that only perpetuate the field of repressed cathectic energy.
The point being, the logic of punitivity itself is a form of self-deception and self-harm that only deepens our own personal and social anxieties and that ultimately further separates us from understanding and/or achieving justice in any meaningful sense.