Laboratory experiments are a promising tool for studying how competing institutional arrangements perform and what determines preferences between them. Reliance on enforcement by peers versus formal authorities is a key example. That people incur costs to punish free riders is a well-documented departure from non-behavioural game-theoretic predictions, but how robust is peer punishment to informational problems? We report experimental evidence that reluctance to personally impose punishment when choices are reported unreliably may tip the scales towards rule-based and algorithmic formal enforcement even when observation by the centre is equally prone to error. We provide new and consonant evidence from treatments in which information quality differs for authority versus peers, and confirmatory patterns in both binary decision and quasi-continuous decision variants. Since the role of formal authority is assumed by a computer in our experiment, our findings are also relevant to the question of willingness to entrust machines to make morally fraught decisions, a choice increasingly confronting humans in the age of artificial intelligence.