<p>Obtaining a reliable priority vector from a pairwise comparison matrix (PCM) is essential in the analytic hierarchy process (AHP) for multi-criteria decision-making. This paper presents a novel method, PCAM (Principal Component Analysis based Method), which utilizes principal component analysis (PCA) to derive the priority vector. This approach leverages PCA’s capability to preserve as much of the original information as possible while reducing dimensions. We introduce a new consistency index, PCI (Principal Component Index), to assess the consistency of PCAM. Through comparative analyses with other prioritization methods using numerical examples, we demonstrate PCAM’s feasibility and efficiency. Our results indicate that PCAM can effectively retain much of the original comparison information and produce a dependable priority vector.</p> Graphical abstract <p></p>