Collective attention and ranking methods

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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

Abstract
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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 and 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. 19^th International Joint Conference on Artificial Intelligence, (2005), 917-922.
[2]	R. Amir, Impact-adjusted citations as a measure of journal quality, CORE DP 74, (2002).
[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), 173-187. doi: 10.1016/S0378-4371(99)00291-5.
[4]	M. Bacharach, Estimating nonnegative matrices from marginal data, Int. Econ. Rev., 6 (1965), 294-310. doi: 10.2307/2525582.
[5]	P. Bonacich, Power and centrality: A family of measures, Amer. J. Sociology, 92 (1987), 1170-1182. doi: 10.1086/228631.
[6]	S. Brin and L. Page, The anatomy of large-scale hypertextual web search engine, Computer Networks and ISDN Systems, 30 (1998), 107-117. doi: 10.1016/S0169-7552(98)00110-X.
[7]	J. Cho, S. Roy and R. Adams, Page quality: In search of an unbiased web ranking, in "SIGMOD '05," Proceedings of the 2005 ACM SIGMOD, ACM, New York, (2005), 551-562. doi: 10.1145/1066157.1066220.
[8]	G. de Clippel, H. Moulin and N. Tideman, Impartial division of a dollar, J. Econ. Theory, 139 (2008), 176-191. doi: 10.1016/j.jet.2007.06.005.
[9]	M. H. DeGroot, Reaching a consensus, J. Am. Stat. Assoc., 69 (1974), 118-121.
[10]	G. Demange, On the influence of a ranking system, Soc. Choice Welfare, 39 (2012), 431-455. doi: 10.1007/s00355-011-0631-5.
[11]	G. Demange, A ranking method based on handicaps, PSE DP 16 (2012). Available from: http://halshs.archives-ouvertes.fr/halshs-00687180.
[12]	P. M. DeMarzo, D. Vayanos and J. Zwiebel, Persuasion bias, social influence, and unidimensional opinions, Q. J. Econ., 118 (2003), 909-968. doi: 10.1162/00335530360698469.
[13]	B. Golub and M. Jackson, Naïve learning in social networks and the wisdom of crowds, Am. Econ. J.: Microeconomics, 2 (2010), 112-149.
[14]	S. Goyal, Learning in networks, in "Group Formation in Economics: Networks, Clubs and Coalitions" (eds. G. Demange and M. Wooders), Cambridge University Press, (2005), 122-170.
[15]	L. Katz, A new status index derived from sociometric analysis, Psychometrika, 18 (1953), 39-43. doi: 10.1007/BF02289026.
[16]	J. Kleinberg, Authoritative sources in a hyperlinked environment, J. ACM, 46 (1999), 604-632. doi: 10.1145/324133.324140.
[17]	S. J. Liebowitz and J. C. Palmer, Assessing the relative impacts of economics journals, J. Econ. Lit., 22 (1984), 77-88.
[18]	I. Palacios-Huerta and O. Volij, The measurement of intellectual influence, Econometrica, 72 (2004), 963-977.
[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), 781-792.
[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), 297-312. doi: 10.1016/0306-4573(76)90048-0.
[21]	G. Slutzki and O. Volij, Scoring of web pages and tournaments-axiomatizations, Soc. Choice Welfare, 26 (2006), 75-92. doi: 10.1007/s00355-005-0033-7.

show all references

References:

[1]	A. Altman and M. Tennenholtz, On the axiomatic foundations of ranking systems, Proc. 19^th International Joint Conference on Artificial Intelligence, (2005), 917-922.
[2]	R. Amir, Impact-adjusted citations as a measure of journal quality, CORE DP 74, (2002).
[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), 173-187. doi: 10.1016/S0378-4371(99)00291-5.
[4]	M. Bacharach, Estimating nonnegative matrices from marginal data, Int. Econ. Rev., 6 (1965), 294-310. doi: 10.2307/2525582.
[5]	P. Bonacich, Power and centrality: A family of measures, Amer. J. Sociology, 92 (1987), 1170-1182. doi: 10.1086/228631.
[6]	S. Brin and L. Page, The anatomy of large-scale hypertextual web search engine, Computer Networks and ISDN Systems, 30 (1998), 107-117. doi: 10.1016/S0169-7552(98)00110-X.
[7]	J. Cho, S. Roy and R. Adams, Page quality: In search of an unbiased web ranking, in "SIGMOD '05," Proceedings of the 2005 ACM SIGMOD, ACM, New York, (2005), 551-562. doi: 10.1145/1066157.1066220.
[8]	G. de Clippel, H. Moulin and N. Tideman, Impartial division of a dollar, J. Econ. Theory, 139 (2008), 176-191. doi: 10.1016/j.jet.2007.06.005.
[9]	M. H. DeGroot, Reaching a consensus, J. Am. Stat. Assoc., 69 (1974), 118-121.
[10]	G. Demange, On the influence of a ranking system, Soc. Choice Welfare, 39 (2012), 431-455. doi: 10.1007/s00355-011-0631-5.
[11]	G. Demange, A ranking method based on handicaps, PSE DP 16 (2012). Available from: http://halshs.archives-ouvertes.fr/halshs-00687180.
[12]	P. M. DeMarzo, D. Vayanos and J. Zwiebel, Persuasion bias, social influence, and unidimensional opinions, Q. J. Econ., 118 (2003), 909-968. doi: 10.1162/00335530360698469.
[13]	B. Golub and M. Jackson, Naïve learning in social networks and the wisdom of crowds, Am. Econ. J.: Microeconomics, 2 (2010), 112-149.
[14]	S. Goyal, Learning in networks, in "Group Formation in Economics: Networks, Clubs and Coalitions" (eds. G. Demange and M. Wooders), Cambridge University Press, (2005), 122-170.
[15]	L. Katz, A new status index derived from sociometric analysis, Psychometrika, 18 (1953), 39-43. doi: 10.1007/BF02289026.
[16]	J. Kleinberg, Authoritative sources in a hyperlinked environment, J. ACM, 46 (1999), 604-632. doi: 10.1145/324133.324140.
[17]	S. J. Liebowitz and J. C. Palmer, Assessing the relative impacts of economics journals, J. Econ. Lit., 22 (1984), 77-88.
[18]	I. Palacios-Huerta and O. Volij, The measurement of intellectual influence, Econometrica, 72 (2004), 963-977.
[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), 781-792.
[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), 297-312. doi: 10.1016/0306-4573(76)90048-0.
[21]	G. Slutzki and O. Volij, Scoring of web pages and tournaments-axiomatizations, Soc. Choice Welfare, 26 (2006), 75-92. doi: 10.1007/s00355-005-0033-7.

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