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

- 546 Downloads
- 1 Citations

## 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.

## Keywords

Webometrics Condorcet jury theorem Linking Independence Ranking PageRank## Notes

### Acknowledgments

The research for this article was funded by the Swedish Research Council through the framework grant *Knowledge in a Digital World: Trust, Credibility and Relevance on the Web* (Olsson, PI).

## References

- Almind, T. C., & Ingwersen, P. (1997). Informetric analyses on the World Wide Web: Methodological approaches to ‘webometrics’.
*Journal of Documentation,**53*(4), 404–426.CrossRefGoogle Scholar - 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 - Bar-Ilan, J. (2004). A microscopic link analysis of academic institutions within a country: The case of Israel.
*Scientometrics,**59*(3), 391–403.CrossRefGoogle Scholar - Berg, S. (1993). Condorcet’s jury theorem: Dependency among voters.
*Social Choice and Welfare,**10*, 87–95.CrossRefMathSciNetMATHGoogle Scholar - Björneborn, L., & Ingwersen, P. (2001). Perspectives of webometrics.
*Scientometrics,**50*(1), 65–82.CrossRefGoogle 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 - Boland, P. J., Proschan, F., & Tong, Y. (1989). Modelling dependence in simple and indirect majority systems.
*Journal of Applied Probability,**26*, 81–88.CrossRefMathSciNetMATHGoogle 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 - Diedrich, F., & Spiekermann, K. (2013). Epistemic democracy with defensible premises.
*Economics and Philosophy,**29*, 87–120.CrossRefGoogle Scholar - Dietrich, F. (2008). The premises of Condorcet’s jury theorem are not simultaneously justified.
*Episteme,**58*, 56–73.CrossRefGoogle Scholar - Dietrich, F., & List, C. (2004). A model of jury decisions where all jurors have the same evidence.
*Synthese,**142*, 175–202.CrossRefMathSciNetMATHGoogle Scholar - Estlund, D. M. (1994). Opinion leaders, independence, and Condorcet’s jury theorem.
*Theory and Decision,**36*, 131–162.CrossRefMATHGoogle Scholar - Estlund, D. M. (2008).
*Democratic authority: A philosophical framework*. Princeton, NJ: Princeton University Press.Google Scholar - Estlund, D., Waldron, J., Grofman, B., & Feld, S. L. (1989). Democratic theory and the public interest: Condorcet and Rousseau revisited.
*American Political Science Review,**83*, 1317–1340.CrossRefGoogle 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 - Franceschet, M. (2011). PageRank: Standing on the shoulders of giants.
*Communications of the ACM,**54*(6), 92–101.CrossRefGoogle Scholar - Gaus, G. (1997). Does democracy reveal the voice of the people? Four takes on Rousseau.
*Australasian Journal of Philosophy,**75*, 141–162.CrossRefGoogle Scholar - Goodin, R. E. (2003).
*Reflective democracy*. Oxford: Oxford University Press.CrossRefGoogle Scholar - Grofman, B., & Feld, S. L. (1988). Rousseau’s general will: A Condorcetian perspective.
*American Political Science Review,**82*, 567–576.CrossRefGoogle 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. - Ingwersen, P. (1998). The calculation of web impact factors.
*Journal of Documentation,**54*(2), 236–243.CrossRefGoogle Scholar - Kaniovski, S. (2010). Aggregation of correlated votes and Condorcet’s jury theorem.
*Theory and Decision,**69*, 453–468.CrossRefMathSciNetMATHGoogle Scholar - Kendall, M. (1938). A new measure of rank correlation.
*Biometrika,**30*, 81–89.CrossRefMathSciNetMATHGoogle Scholar - Kleinberg, J. M. (1999). Authoritative sources in a hyperlinked environment.
*Journal of the ACM,**46*(5), 604–632.CrossRefMathSciNetMATHGoogle Scholar - Ladha, K. K. (1992). The Condorcet’s jury theorem, free speech, and correlated votes.
*American Journal of Political Science,**36*, 617–634.CrossRefGoogle Scholar - Ladha, K. K. (1993). Condorcet’s jury theorem in light of de Finetti’s theorem.
*Social Choice and Welfare,**10*, 69–85.CrossRefMathSciNetMATHGoogle Scholar - Ladha, K. K. (1995). Information pooling through majority-rule voting: Condorcet’s jury theorem with correlated votes.
*Journal of Economic Behavior & Organization,**26*, 353–372.CrossRefGoogle Scholar - List, C., & Goodin, R. E. (2001). Epistemic democracy: Generalizing the Condorcet jury theorem.
*Journal of Political Philosophy,**9*(3), 277–306.CrossRefGoogle Scholar - Lorentzen, D. G. (2014). Webometrics benefitting from web mining? An investigation of methods and applications of two research fields.
*Scientometrics,**99*, 409–445.CrossRefGoogle Scholar - XXXXGoogle Scholar
- McLean, I., & Hewitt, F. (1994).
*Condorcet: Foundations of social choice and political theory*. Northampton, MA: Edward Elgar Publishing Limited.Google Scholar - Nitzan, S., & Paroush, J. (1984). The significance of independent decisions in uncertain dichotomous choice situations.
*Theory and Decision,**17*, 47–60.CrossRefMathSciNetMATHGoogle Scholar - Owen, G., Grofman, B., & Feld, S. L. (1989). Proving a distribution-free generalization of the Condorcet jury theorem.
*Mathematical Social Sciences,**17*, 1–16.CrossRefMathSciNetMATHGoogle 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 - Romeijn, J., & Atkinson, D. (2011). A Condorcet jury theorem for unknown juror competence.
*Politics, Philosophy, and Economics,**10*, 237–262.CrossRefGoogle Scholar - Schweinberger, M., & Handcock, M. S. (2015). Local dependence in random graph models: Characterization, properties and statistical inference.
*Journal of the Royal Statistical Society: Series B (Statistical Methodology),**77*(3), 647–676.CrossRefMathSciNetGoogle Scholar - Shapley, L., & Grofman, B. (1984). Optimizing group judgmental accuracy in the presence of interdependencies.
*Public Choice,**43*, 329–343.CrossRefGoogle Scholar - Spiekermann, K. R., & Goodin, R. E. (2012). Courts of many minds.
*British Journal of Political Science,**12*, 555–571.CrossRefGoogle 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 - Thelwall, M. (2006). Interpreting social science link analysis research: A theoretical framework.
*Journal of the American Society for Information Science and Technology archive,**57*(1), 60–68.CrossRefGoogle Scholar - Vaughan, L., & Thelwall, M. (2003). Scholarly use of the web: What are the key inducers of links to journal web sites?
*Journal of the American Society for Information Science and Technology,**54*(1), 29–38.CrossRefGoogle 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 - Wills, R. S. (2006). Google’s PageRAnk: The maths behind the search engine.
*The Mathematical Intelligencer,**28*(4), 6–11.CrossRefMathSciNetGoogle Scholar