Final answer:
A top-down structure and rigid rules define a mechanistic organization, which aligns with bureaucratic characteristics such as hierarchy of authority and explicit rules but excludes coercion to join.
Step-by-step explanation:
Top-down structure and rigid rules are characteristics of a mechanistic organization. In a mechanistic organization, communication typically flows from the top down, similarly to how an authoritarian leadership style operates. This is in contrast to more organic organizations, which tend to have a flatter structure and more flexible rules.
A bureaucracy, as defined by pioneering sociologist Max Weber, includes characteristics such as hierarchy of authority, a clear division of labor, explicit rules, and impersonality. It's worth noting that coercion to join is not a characteristic of bureaucracies, which refers to being forced to participate, which isn't a feature of a formal organization like a bureaucracy.
Organizations often have to balance the efficiency of mechanistic structures with the innovation and adaptability of more organic structures to stay relevant in a changing environment.