Basic properties of both percentile rank scores and the I3 indicator

We introduce the notions of congruous indicator of relative performance and congruous indicator of absolute performance. These notions are very similar to the notions of independence and consistency, yet slightly different. It is shown that percentile rank scores, as recently introduced by Leydesdorff, Bornmann, Mutz, and Opthof ( 2011 ), are strictly congruous indicators of relative performance, and similarly, that the Integrated Impact Indicator (I3), introduced by Leydesdorff and Bornmann ( 2011 ), is a strictly congruous indicator of absolute performance. Our analysis highlights the challenge of finding adequate axioms for ranking and for research evaluation.