  We investigate an application of a mathematically robust minimization method
-- the gradient method -- to the consistencization problem of a 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 lead to non-equivalent
consistencization procedures.
