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In elections employing electronic voting machines, we have observed that poor procedures, equipment failures, and honest mistakes pose a real threat to the accuracy of the final tally. The event logs kept by these machines can give auditors clues as to the causes of anomalies and inconsistencies; however, each voting machine is trusted to keep its own audit and ballot data, making the record unreliable. If a machine is damaged, accidentally erased, or otherwise compromised during the election, we have no way to detect tampering or loss of auditing records and cast votes. We see a need for voting systems in which event logs can serve as robust forensic documents, describing a provable timeline of events leading up to and transpiring on election day. To this end, we propose an auditing infrastructure that draws on ideas from distributed systems and secure logging to provide a verifiable, global picture of critical election-day events, one which can survive individual machine malfunction or malice. Our system, the Auditorium, joins the voting machines in a polling place together in a private broadcast network in which all election events are logged redundantly by every machine. Each event is irrevocably tied to the originating machine by a digital signature, and to earlier events from other machines via hash chaining. In this paper we describe in detail how to conduct an election in the Auditorium. We demonstrate our system's robustness to benign failures and malicious attacks, resulting in a believable audit trail and vote count, with acceptable overhead for a network the size of a polling place.