We develop a model of normative systems, where roughly speaking the model is a transition-based system and a norm is the result of flagging some of the transitions as undesirable. We then use a language that is close to that of Computation Tree Logic to reason about such systems. We demonstrate how our framework facilitates to reason about the following three settings:
(1) Although normative systems, or social laws, have proved to be a highly influential approach to coordination in multi-agent systems, the issue of compliance to such normative systems remains problematic. In all real systems, it is possible that some members of an agent population will not comply with the rules of a normative system, even if it is in their interests to do so. It is therefore important to consider the extent to which a normative system is robust, i.e., the extent to which it remains effective even if some agents do not comply with it.
(2) We then show how power indices, originally developed within voting theory, can be applied to understanding the relative importance of agents when we attempt to devise a coordination mechanism using the paradigm of normative systems. Understanding how pivotal an agent is with respect to the success of a particular social law is of benefit when designing such social laws: we might typically aim to ensure that power is distributed evenly amongst the agents in a system, to avoid bottlenecks or single points of failure.
(3) We then briefly sketch how the notion of a goal can be introduced to a normative system, enabling to conceive such a system as a game where the agents make strategic decisions regarding the balance between norm compliance and the satisfaction of their goals.
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