  In prioritization schemes, based on pairwise comparisons, such as the
Analytical Hierarchy Process, it is important to extract a cardinal ranking
vector from a reciprocal matrix that is unlikely to be consistent. It is
natural to choose such a vector only from efficient ones. Recently a method to
generate inductively all efficient vectors for any reciprocal matrix has been
discovered. Here we focus upon the study of efficient vectors for a reciprocal
matrix that is a block perturbation of a consistent matrix in the sense that it
is obtained from a consistent matrix by modifying entries only in a proper
principal submatrix. We determine an explicit class of efficient vectors for
such matrices. Based upon this, we give a description of all the efficient
vectors in the 3-by-3 block perturbed case. In addition, we give sufficient
conditions for the right Perron eigenvector of such matrices to be efficient
and provide examples in which efficiency does not occur. Also, we consider a
certain type of constant block perturbed consistent matrices, for which we may
construct a class of efficient vectors, and demonstrate the efficiency of the
Perron eigenvector. Appropriate examples are provided throughout.
