Summary: An abstract architecture for idealized multi-agent systems whose behaviour is regulated by normative systems is developed and discussed. Agent choices are determined partially by the preference ordering of possible states and partially by normative considerations: The agent chooses that act which leads to the best outcome of all permissible actions. If an action is non-permissible depends on if the result of performing that action leads to a state satisfying a condition which is forbidden, according to the norms regulating the multi-agent system. This idea is formalized by defining set-theoretic predicates characterizing multi-agent systems. The definition of the predicate uses decision theory, the Kanger-Lindahl theory of normative positions, and an algebraic representation of normative systems.