Linking as voting: how the Condorcet jury theorem in political science is relevant to webometrics

Abstract

A webmaster's decision to link to a webpage can be interpreted as a "vote" for that webpage. But how far does the parallel between linking and voting extend? In this paper, we prove several "linking theorems" showing that link-based ranking tracks importance on the web in the limit as the number of webpages grows, given independence and minimal linking competence. The theorems are similar in spirit to the voting, or jury, theorem famously attributed to the 18th century mathematician Nicolas de Condorcet. We argue that the linking theorems provide a fundamental epistemological justification for link-based ranking on the web, analogous to the justification that Condorcet's theorems bestow on majority voting as a basic democratic procedure. The analogy extends to the practical limitations facing both kinds of result, in particular due to limited voting/linking independence. However, we argue, referring to the theoretical developments inspired by the jury theorem, that some of the pessimism expressed in the webometrics literature regarding the possibility of a "theory of linking" may be unjustified. The present study connects the two academic disciplines of webometrics in information science and epistemic democracy in political science by showing how they share a common structure. As such, it opens up new possibilities for theoretical cross-fertilization and interdisciplinary transference of concepts and results. In particular, we show how the relatively young field of webometrics can benefit from the extensive and sophisticated literature on the Condorcet jury theorem.