Robust normative systems and a logic of norm compliance

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. We formalise and investigate three different notions of robustness and related decision problems. We begin by considering sets of agents whose compliance is necessary and/or sufficient to guarantee the effectiveness of a normative system; we then consider quantitative approaches to robustness, where we try to identify the proportion of an agent population that must comply in order to ensure success; and finally, we consider a more general approach, where we characterise the compliance conditions required for success as a logical formula. We furthermore introduce a logic for specifying properties of norm compliance in general and norm robustness in particular.