Efficient Committed Budget for Implementing Target Audit Probability for Many Inspectees

Strategic models of auditor-inspectee interaction have neglected implementation details in multiple-inspectee settings. With multiple inspectees, the target audit probability derived from the standard analysis can be implemented with sampling plans differing in the budgets committed to support them. Overly committed audit budgets tie up unneeded resources that could have been allocated for better uses. This paper studies the minimum committed budget required to implement a target audit probability when (i) the audit sample can be contingent on "red flags" due to signals of inspectees' private information (e.g., from self-reporting) and (ii) the number of inspectees is large. It proposes an audit rule called bounded simple random sampling (SRS), which is shown to require no more committed budget to support than two other rules naturally generalized from the one-to-one analysis. When the number of inspectees is large enough, bounded SRS is nearly as good as any efficient audit rule, which demands the lowest committed budget necessary to implement the target audit probability. The results offer insights on how audit sampling plans may be formulated to reduce inefficiency and what budget usage ratios should be expected accordingly.