Linking as voting: how the Condorcet jury theorem in political science is relevant to webometrics
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.
KeywordsWebometrics Condorcet jury theorem Linking Independence Ranking PageRank
- Auletta, K. (2010). Googled: The end of the world as we know it. London: The Penguin Press.Google Scholar
- Barabási, A. L. (2002). Linked: The new science of networks. Cambridge, Massachusetts: Perseus Publishing.Google Scholar
- Boland, P. J. (1989). “Majority systems and the Condorcet jury theorem. Journal of the Royal Statistical Society, Series D (The Statistician), 38, 181–189.Google Scholar
- Brin, S., & Page, L. (1998). The anatomy of a large-scale hypertextual web search engine”, WWW 1998. In Seventh international world-wide web conference. Brisbane, Australia.Google Scholar
- Brin, S., Page, L., Motwami, R., & Winograd, T. (1998). The PageRank citation ranking: Bringing order to the web. Stanford University Technical Report.Google Scholar
- Davenport, E., & Cronin, B. (2000). The citation network as a prototype for representing trust in virtual environments. In B. Cronin & H. B. Atkins (Eds.), The web of knowledge: A Festschrift in Honor of Eugene Garfield. ASIS Monograph Series (pp. 517–534). Metford, NJ: Information Today Inc.Google Scholar
- de Condorcet, N. (1785). Essai sur l’application de l’analyse à la probabilité des decisions rendues à la pluralité des voix (Essay on the application of analysis to the probability of majority decisions). Paris: L'Impremerie Royale [facsimile edition New York: Chelsea, 1972].Google Scholar
- Estlund, D. M. (2008). Democratic authority: A philosophical framework. Princeton, NJ: Princeton University Press.Google Scholar
- Fortunato, S., Boguñá, M., Flammini, A., & Menczer, F. (2008). Approximating PageRank from In-Degree. In W. Aiello, A. Broder, J. Janssen & E. Milios (Eds.), Algorithms and models for the web-graph (pp. 59–71). Berlin/Heidelberg: Springer-Verlag.Google Scholar
- Hernández-Borges, A. A., Macías-Cervi, P., Gaspar-Guardado, M. A., Torres-Álvarez de Arcaya, M. L., Ruiz-Rabaza, A., & Jiménez-Sosa, A. (1999). Can examination of WWW usage statistics and other indirect quality indicators distinguish the relative quality of medical Web sites? Journal of Medical Internet Research, 1(1). http://www.jmir.org/1999/1991/e1991/index.htm.
- XXXXGoogle Scholar
- McLean, I., & Hewitt, F. (1994). Condorcet: Foundations of social choice and political theory. Northampton, MA: Edward Elgar Publishing Limited.Google Scholar
- Palmer, J. W., Bailey, J. P., & Faraj, S. (2000). The role of intermediaries in the development of trust on the WWW: The use and prominence of trusted third parties and privacy statements. Journal of Computer-Mediated Communication, 5(3). doi:10.1111/j.1083-6101.2000.tb00342.x.
- Pearl, J. (2000). Causality: Models, reasoning and inference. Cambridge: Cambridge University Press.Google Scholar
- Rheingold, H. (2002). Smart mobs: The next social revolution. Cambridge, MA: Perseus Publishing.Google Scholar
- Surowiecki, J. (2004). The wisdom of crowds: Why the many are smarter than the few and how collective wisdom shapes business, economies, societies, and nations. London: Little Brown.Google Scholar
- Vreeland, R. C. (2000). Law libraries in hyperspace: A citation analysis of World Wide Web sites. Law Library Journal, 92(1), 9–25.Google Scholar