The Analytical Hierarchy Process (AHP) is increasingly used as decision support method in concurrent innovation projects with multiple stakeholders. AHP is welcomed for supporting procedural justice, which regards transparency and fairness of decisions. This is useful for policy settings, with diverse stakeholder interests, for prioritization questions with diverse criteria or for allocation of scarce resources. However, AHP's promises for procedural justice are partly grounded in its supposed numerical accuracy. We show that the numerical basis of AHP is not as unambiguous as current 'AHP standard practice' suggests. By contrast, AHP can contribute to the other criteria for procedural justice (efficiency and participation), which may explain AHP's continuing and growing popularity. We conclude that the research and practitioner community should on the one hand continue to develop AHP's procedures for full participation of all types of stakeholders, while on the other hand finding solutions to the accuracy problems.