What theory posits that police organizations are shaped by their external social environment?

The correct choice is Institutional Theory, which asserts that organizations, including police agencies, are significantly influenced by the social and cultural contexts in which they operate. This theory emphasizes the importance of social norms, values, and institutions that shape the behavior and structure of organizations. In the case of policing, the expectations of the community, legal standards, and political pressures all contribute to how police organizations are structured and how they function.

Institutional Theory explains that police organizations adapt to their environment to gain legitimacy, resources, and support from the public and other stakeholders. As such, the practices, policies, and even the culture within police departments can be reflective of broader societal changes, community values, and external expectations.

The other options relate to different aspects of organizational dynamics but do not specifically focus on the impact of external social environments in the same way. Cultural Theory would concentrate on the internal cultural dimensions of an organization, while Structural Theory deals with the arrangement and hierarchy within the organization itself. Organizational Theory may look at various frameworks for understanding organizations but does not center on the influence of the social environment as a primary driver. Thus, Institutional Theory is the most fitting explanation for how police organizations are shaped by their external social environment.