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We focus here upon the key component of deducing efficient vectors for a reciprocal matrix of pair-wise comparisons. It has been shown that the entry-wise geometric mean of all columns is efficient for any reciprocal matrix. Here, by combining some new basic observations with some known theory, we (1) give a method for inductively generating large collections of efficient vectors, and (2) show that the entry-wise geometric mean of any collection of distinct columns of a reciprocal matrix is efficient. We study numerically, using different measures, the performance of these geometric means in approximating the reciprocal matrix by a consistent matrix. We conclude that, as a general method to be chosen, independent of the data, the geometric mean of all columns performs well when compared with the geometric mean of proper subsets of columns.<\/jats:p>","DOI":"10.1007\/s10479-023-05771-y","type":"journal-article","created":{"date-parts":[[2024,1,2]],"date-time":"2024-01-02T09:02:17Z","timestamp":1704186137000},"page":"743-764","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Efficient vectors in priority setting methodology"],"prefix":"10.1007","volume":"332","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0395-5972","authenticated-orcid":false,"given":"Susana","family":"Furtado","sequence":"first","affiliation":[]},{"given":"Charles R.","family":"Johnson","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,1,2]]},"reference":[{"key":"5771_CR1","doi-asserted-by":"crossref","first-page":"279","DOI":"10.3233\/FI-2016-1335","volume":"144","author":"K \u00c1bele-Nagy","year":"2016","unstructured":"\u00c1bele-Nagy, K., & Boz\u00f3ki, S. 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