Final answer:
The question pertains to the planning function of management, which in the context of a family vacation involves each member picking a restaurant to control decision-making and maintain peace.
Step-by-step explanation:
The management function represented by allowing each family member to pick a restaurant for one night of the trip is called planning. Planning involves setting objectives and determining in advance the appropriate actions required to achieve these goals. By letting each person choose a favorite food or style, the family is trying to ensure that everyone's preferences are accounted for, which could potentially reduce conflicts and enhance the overall vacation experience. This approach also simplifies decision-making as it prevents the group from spending excessive time trying to reach a consensus, which could result in high costs, wasted effort, or ultimately, no decision being made.