On the Information Contents of Indirect Citations

Citation indices, originally designed to measure influence, in practice are often repurposed by administrators and funding agencies as proxies for quality. Suppose there are more researchers in the mainstream than in the fringe, and it takes a higher quality to have the same influence across groups than within groups. Then, controlling for quality, a mainstream researcher may receive more citations than a fringe researcher. To correct for this mainstream bias, a citation index may need to be increasing in direct citations but decreasing in indirect citations.