Final answer:
According to Durkheim's theory, in a society without formal punishment, individuals would rely on informal social control mechanisms such as community norms and values to respond to crime. Vigilantism and personal vengeance might still occur, but they would not be the dominant means of responding to crime. Crime rates may not drastically increase without formal punishment.
Step-by-step explanation:
According to Durkheim's theory, criminal behavior exists in all societies because it serves important functions, such as reaffirming cultural values and norms. In a society without formal punishment, individuals would rely more on informal social control mechanisms to respond to crime. Community norms and values would play a more significant role in maintaining order, as people would rely on social pressure and informal sanctions to deter criminal behavior. Vigilantism and personal vengeance might still occur to some extent, but they would not be the dominant means of responding to crime. Crime rates may not necessarily drastically increase without formal punishment, as the absence of prisons and courts does not automatically lead to a breakdown of social order.