Accountability mechanisms, which rely on after-the-fact verification, are an attractive means to enforce authorization policies. In this paper, we describe an operational model of accountability-based distributed systems. We describe analyses which support both the design of accountability systems and the validation of auditors for finitary accountability systems. Our study provides formal foundations to explore the tradeoffs underlying the design of accountability systems including: the power of the auditor, the efficiency of the audit protocol, the requirements placed on the agents, and the requirements placed on the communication infrastructure.