Social laws – sets of constraints imposed on the behaviour of agents within a multi-agent system with the goal of some desirable overall behaviour resulting – are an important mechanism for coordinating multi-agent behaviour. When considering social laws in human environments, the inspiration for social laws in multiagent systems, we argue that a key design principle is least change. That is, social laws are more likely to be accepted and adopted, and hence successful, if they are conservative, in the sense that they represent the smallest change possible from the pre-existing status quo that is required to effect the desired objective. Our aim in the present paper is to introduce, formalise, and investigate the notion of a conservative social law for multi-agent systems. To make the idea of a conservative social law precise, we formalise the notion of a distance metric for social laws, and discuss a range of possible properties for such metrics. We then formulate the conservative social law problem, (i.e., the problem of constructing an effective social law that requires the least change according to this metric), discuss some possible interpretations of distance in this context, and discuss some issues surrounding conservative social laws.
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