Who Will Watch the Watchmen? Information Aggregation in the Four-Eyes Principle

We study how rational decision makers would approach the Four-Eyes Procedure (based on the Four- Eyes Principle, also referred to as 4EP), a voting algorithm widely used in industry where two auditors have to unanimously agree with a proposal for it to be accepted, whereas if at least one of them disagrees with it the proposal is rejected. We compare this setup with an immediate analogous, the setup with a single auditor whose approval is necessary and sufficient for green-lighting. We start by discussing the current state of research on voting algorithms and information aggregation, taking as initial point the very prolific debate regarding the Condorcet Jury Theorem. We furthermore argue that there are already suggestions in both empirical and theoretical literature that the 4EP is in fact not an improvement on simpler auditing procedures. In the main section of the paper, we represent the decision-making process as a model of auditing, first with one auditor and then with two; we include an additional strategic layer in the figure of the proposer, who chooses costly quality of her proposal, with higher quality being modeled as a higher probability that the proposal is good (and hence yields desirable payoffs for both the auditors and the proposer when approved). We find, in line with comparable literature, an equivalence result between the 4EP and its single-auditor analogous, where in particular it can be shown that the former doesn't lead to strictly better expected payoffs or probabilities of error, so it would be suboptimal for a principal (the auditors' employer) to implement such a procedure. The final section discusses results, casting some light on possible interpretations of specific assumptions and suggesting implications for applied implementation; suggestions for extensions and insightful directions for future research are included