American Institute of Mathematical Sciences

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January  2014, 1(1): 17-43. doi: 10.3934/jdg.2014.1.17

Collective attention and ranking methods

Gabrielle Demange 1,

1. 

PSE-EHESS, 48 bd Jourdan, Paris, 75014, France

Received  May 2012 Revised  February 2013 Published  June 2013

In a world with a tremendous amount of choices, ranking systems are becoming increasingly important in helping individuals to find information relevant to them. As such, rankings play a crucial role of influencing the attention that is devoted to the various alternatives. This role generates a feedback when the ranking is based on citations, as is the case for PageRank used by Google. The attention bias due to published rankings affects new stated opinions (citations), which will, in turn, affect the next ranking. The purpose of this paper is to investigate this feedback by studying some simple but reasonable dynamics. We show that the long run behavior of the process much depends on the preferences, in particular on their diversity, and on the used ranking method. Two main families of methods are investigated, one based on the notion of handicaps, the other one on the notion of peers' rankings.
Keywords: scoring, attention, Ranking, invariant method, peers' method, scaling matrix, dynamics through influence., handicap.
Mathematics Subject Classification: Primary: 91C05, 91B1.
Citation: Gabrielle Demange. Collective attention and ranking methods. Journal of Dynamics & Games, 2014, 1 (1) : 17-43. doi: 10.3934/jdg.2014.1.17
References:
[1]

A. Altman and M. Tennenholtz, On the axiomatic foundations of ranking systems,, Proc. 19th International Joint Conference on Artificial Intelligence, (2005), 917. Google Scholar

[2]

R. Amir, Impact-adjusted citations as a measure of journal quality,, CORE DP 74, (2002). Google Scholar

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A.-L. Barabási, R. Albert and H. Jeong, Mean-field theory for scale-free random networks,, Physica A: Statistical Mechanics and its Applications, 272 (1999), 173. doi: 10.1016/S0378-4371(99)00291-5. Google Scholar

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M. Bacharach, Estimating nonnegative matrices from marginal data,, Int. Econ. Rev., 6 (1965), 294. doi: 10.2307/2525582. Google Scholar

[5]

P. Bonacich, Power and centrality: A family of measures,, Amer. J. Sociology, 92 (1987), 1170. doi: 10.1086/228631. Google Scholar

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S. Brin and L. Page, The anatomy of large-scale hypertextual web search engine,, Computer Networks and ISDN Systems, 30 (1998), 107. doi: 10.1016/S0169-7552(98)00110-X. Google Scholar

[7]

J. Cho, S. Roy and R. Adams, Page quality: In search of an unbiased web ranking,, in, (2005), 551. doi: 10.1145/1066157.1066220. Google Scholar

[8]

G. de Clippel, H. Moulin and N. Tideman, Impartial division of a dollar,, J. Econ. Theory, 139 (2008), 176. doi: 10.1016/j.jet.2007.06.005. Google Scholar

[9]

M. H. DeGroot, Reaching a consensus,, J. Am. Stat. Assoc., 69 (1974), 118. Google Scholar

[10]

G. Demange, On the influence of a ranking system,, Soc. Choice Welfare, 39 (2012), 431. doi: 10.1007/s00355-011-0631-5. Google Scholar

[11]

G. Demange, A ranking method based on handicaps,, PSE DP 16 (2012). Available from: \url{http://halshs.archives-ouvertes.fr/halshs-00687180}., (2012). Google Scholar

[12]

P. M. DeMarzo, D. Vayanos and J. Zwiebel, Persuasion bias, social influence, and unidimensional opinions,, Q. J. Econ., 118 (2003), 909. doi: 10.1162/00335530360698469. Google Scholar

[13]

B. Golub and M. Jackson, Naïve learning in social networks and the wisdom of crowds,, Am. Econ. J.: Microeconomics, 2 (2010), 112. Google Scholar

[14]

S. Goyal, Learning in networks,, in, (2005), 122. Google Scholar

[15]

L. Katz, A new status index derived from sociometric analysis,, Psychometrika, 18 (1953), 39. doi: 10.1007/BF02289026. Google Scholar

[16]

J. Kleinberg, Authoritative sources in a hyperlinked environment,, J. ACM, 46 (1999), 604. doi: 10.1145/324133.324140. Google Scholar

[17]

S. J. Liebowitz and J. C. Palmer, Assessing the relative impacts of economics journals,, J. Econ. Lit., 22 (1984), 77. Google Scholar

[18]

I. Palacios-Huerta and O. Volij, The measurement of intellectual influence,, Econometrica, 72 (2004), 963. Google Scholar

[19]

S. Pandey, S. Roy, C. Olston, J. Cho and S. Chakrabarti, Shuffling a stacked deck: The case for partially randomized ranking of search engine results,, VLDP Conference, (2005), 781. Google Scholar

[20]

G. Pinski and F. Narin, Citation influence for journal aggregates of scientific publications: Theory, with application to the literature of physics,, Information Processing and Management, 12 (1976), 297. doi: 10.1016/0306-4573(76)90048-0. Google Scholar

[21]

G. Slutzki and O. Volij, Scoring of web pages and tournaments-axiomatizations,, Soc. Choice Welfare, 26 (2006), 75. doi: 10.1007/s00355-005-0033-7. Google Scholar

show all references

References:
[1]

A. Altman and M. Tennenholtz, On the axiomatic foundations of ranking systems,, Proc. 19th International Joint Conference on Artificial Intelligence, (2005), 917. Google Scholar

[2]

R. Amir, Impact-adjusted citations as a measure of journal quality,, CORE DP 74, (2002). Google Scholar

[3]

A.-L. Barabási, R. Albert and H. Jeong, Mean-field theory for scale-free random networks,, Physica A: Statistical Mechanics and its Applications, 272 (1999), 173. doi: 10.1016/S0378-4371(99)00291-5. Google Scholar

[4]

M. Bacharach, Estimating nonnegative matrices from marginal data,, Int. Econ. Rev., 6 (1965), 294. doi: 10.2307/2525582. Google Scholar

[5]

P. Bonacich, Power and centrality: A family of measures,, Amer. J. Sociology, 92 (1987), 1170. doi: 10.1086/228631. Google Scholar

[6]

S. Brin and L. Page, The anatomy of large-scale hypertextual web search engine,, Computer Networks and ISDN Systems, 30 (1998), 107. doi: 10.1016/S0169-7552(98)00110-X. Google Scholar

[7]

J. Cho, S. Roy and R. Adams, Page quality: In search of an unbiased web ranking,, in, (2005), 551. doi: 10.1145/1066157.1066220. Google Scholar

[8]

G. de Clippel, H. Moulin and N. Tideman, Impartial division of a dollar,, J. Econ. Theory, 139 (2008), 176. doi: 10.1016/j.jet.2007.06.005. Google Scholar

[9]

M. H. DeGroot, Reaching a consensus,, J. Am. Stat. Assoc., 69 (1974), 118. Google Scholar

[10]

G. Demange, On the influence of a ranking system,, Soc. Choice Welfare, 39 (2012), 431. doi: 10.1007/s00355-011-0631-5. Google Scholar

[11]

G. Demange, A ranking method based on handicaps,, PSE DP 16 (2012). Available from: \url{http://halshs.archives-ouvertes.fr/halshs-00687180}., (2012). Google Scholar

[12]

P. M. DeMarzo, D. Vayanos and J. Zwiebel, Persuasion bias, social influence, and unidimensional opinions,, Q. J. Econ., 118 (2003), 909. doi: 10.1162/00335530360698469. Google Scholar

[13]

B. Golub and M. Jackson, Naïve learning in social networks and the wisdom of crowds,, Am. Econ. J.: Microeconomics, 2 (2010), 112. Google Scholar

[14]

S. Goyal, Learning in networks,, in, (2005), 122. Google Scholar

[15]

L. Katz, A new status index derived from sociometric analysis,, Psychometrika, 18 (1953), 39. doi: 10.1007/BF02289026. Google Scholar

[16]

J. Kleinberg, Authoritative sources in a hyperlinked environment,, J. ACM, 46 (1999), 604. doi: 10.1145/324133.324140. Google Scholar

[17]

S. J. Liebowitz and J. C. Palmer, Assessing the relative impacts of economics journals,, J. Econ. Lit., 22 (1984), 77. Google Scholar

[18]

I. Palacios-Huerta and O. Volij, The measurement of intellectual influence,, Econometrica, 72 (2004), 963. Google Scholar

[19]

S. Pandey, S. Roy, C. Olston, J. Cho and S. Chakrabarti, Shuffling a stacked deck: The case for partially randomized ranking of search engine results,, VLDP Conference, (2005), 781. Google Scholar

[20]

G. Pinski and F. Narin, Citation influence for journal aggregates of scientific publications: Theory, with application to the literature of physics,, Information Processing and Management, 12 (1976), 297. doi: 10.1016/0306-4573(76)90048-0. Google Scholar

[21]

G. Slutzki and O. Volij, Scoring of web pages and tournaments-axiomatizations,, Soc. Choice Welfare, 26 (2006), 75. doi: 10.1007/s00355-005-0033-7. Google Scholar

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