In a 2010 article for Psychology Today, Satoshi Kanazawa gives a suggestion as to why low IQs and criminality seem to go hand in hand:
From the perspective of the Hypothesis, there are two important points to note. First, much of what we call interpersonal crime today, such as murder, assault, robbery, and theft, were probably routine means of intrasexual male competition in the ancestral environment. This is how men likely competed for resources and mating opportunities for much of human evolutionary history. They beat up and killed each other, and they stole from each other if they could get away with it.
We may infer this from the fact that behavior that would be classified as criminal if engaged in by humans, like murder, rape, assault, and theft, are quite common among other species. The criminologist Lee Ellis documented many instances of these “criminal behavior” among different species with photographs in 1998. The primatologist Frans de Waal and his colleagues have documented brutal murders, assaults, and other interpersonal violence among chimpanzees, bonobos, and capuchin monkeys.
Second, the technologies and institutions that control, detect, and punish criminal behavior in society today – CCTV cameras, DNA fingerprinting, the police, the courts, the prisons – are all evolutionarily novel. There was very little formal third-party enforcement of norms in the ancestral environment, only second-party enforcement (retaliation from vigilance by victims and their kin and allies) or informal third-party enforcement (ostracism).
It therefore makes sense from the perspective of the Hypothesis that men with low intelligence may be more likely to resort to evolutionarily familiar means of competition for resources (theft rather than full-time employment) and mating opportunities (rape rather than computer dating), and not to comprehend fully the consequences of criminal behavior imposed by evolutionarily novel entities of law enforcement.
Men with lower intelligence are less likely truly to comprehend evolutionarily novel entities. Some of these evolutionarily novel entities are alternative means to resource acquisition and accumulation they could pursue instead of evolutionarily familiar means which are now classified as criminal in civilized societies. Other evolutionarily novel entities they are less likely truly to comprehend are means that law enforcement agencies employ to detect and capture criminals. The Hypothesis therefore offers one possible explanation for the negative association between intelligence and criminality.
At the same time, the Hypothesis also offers a novel hypothesis with regard to intelligence and criminality. As I mention above, while formal third-party enforcement of norms is evolutionarily novel, second-party enforcement and informal third-party enforcement are evolutionarily familiar. Thus the Hypothesis would predict that the difference in intelligence between criminals and noncriminals will disappear in situations where formal third-party enforcement of norms is weak or absent, and criminal behavior is controlled largely via second-party enforcement, such as situations of prolonged anarchy and statelessness, in fact, any situation that resembles the ancestral environment. Paradoxically, the Hypothesis would predict that less intelligent men will commit fewer crimes if the police disappeared, although more intelligent men may commit more crimes then.”