We investigate an application of a mathematically robust minimization method - the gradient method - to the consistencization problem of pairwise comparisons (PC) matrix. Our approach sheds new light on the notion of a priority vector and leads naturally to the definition of instant priority vectors. We describe a sample family of inconsistency indicators based on various ways of taking an average value, which extends the inconsistency indicator based on the “sup”- norm. We apply this family of inconsistency indicators both for additive and multiplicative PC matrices to show that the choice of various inconsistency indicators leads to non-equivalent consistencization procedures.