American Institute of Mathematical Sciences

Advanced
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

[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

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

[1]

Zhengshan Dong, Jianli Chen, Wenxing Zhu. Homotopy method for matrix rank minimization based on the matrix hard thresholding method. Numerical Algebra, Control & Optimization, 2019, 9 (2) : 211-224. doi: 10.3934/naco.2019015
[2]

Sho Matsumoto, Jonathan Novak. A moment method for invariant ensembles. Electronic Research Announcements, 2018, 25: 60-71. doi: 10.3934/era.2018.25.007
[3]

Gholam Hassan Shirdel, Somayeh Ramezani-Tarkhorani. A new method for ranking decision making units using common set of weights: A developed criterion. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-19. doi: 10.3934/jimo.2018171
[4]

Yuan Shen, Xin Liu. An alternating minimization method for matrix completion problems. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 0-0. doi: 10.3934/dcdss.2020103
[5]

Tao Wu, Yu Lei, Jiao Shi, Maoguo Gong. An evolutionary multiobjective method for low-rank and sparse matrix decomposition. Big Data & Information Analytics, 2017, 2 (1) : 23-37. doi: 10.3934/bdia.2017006
[6]

El-Sayed M.E. Mostafa. A nonlinear conjugate gradient method for a special class of matrix optimization problems. Journal of Industrial & Management Optimization, 2014, 10 (3) : 883-903. doi: 10.3934/jimo.2014.10.883
[7]

Liu Liu. Uniform spectral convergence of the stochastic Galerkin method for the linear semiconductor Boltzmann equation with random inputs and diffusive scaling. Kinetic & Related Models, 2018, 11 (5) : 1139-1156. doi: 10.3934/krm.2018044
[8]

R. Baier, M. Dellnitz, M. Hessel-von Molo, S. Sertl, I. G. Kevrekidis. The computation of convex invariant sets via Newton's method. Journal of Computational Dynamics, 2014, 1 (1) : 39-69. doi: 10.3934/jcd.2014.1.39
[9]

Klas Modin. Geometry of matrix decompositions seen through optimal transport and information geometry. Journal of Geometric Mechanics, 2017, 9 (3) : 335-390. doi: 10.3934/jgm.2017014
[10]

Marie-Françoise Bidaut-Véron, Marta Garcia-Huidobro, Laurent Véron. Radial solutions of scaling invariant nonlinear elliptic equations with mixed reaction terms. Discrete & Continuous Dynamical Systems - A, 2020, 40 (2) : 933-982. doi: 10.3934/dcds.2020067
[11]

Aldana M. González Montoro, Ricardo Cao, Christel Faes, Geert Molenberghs, Nelson Espinosa, Javier Cudeiro, Jorge Mariño. Cross nearest-spike interval based method to measure synchrony dynamics. Mathematical Biosciences & Engineering, 2014, 11 (1) : 27-48. doi: 10.3934/mbe.2014.11.27
[12]

Luca Dieci, Cinzia Elia. Smooth to discontinuous systems: A geometric and numerical method for slow-fast dynamics. Discrete & Continuous Dynamical Systems - B, 2018, 23 (7) : 2935-2950. doi: 10.3934/dcdsb.2018112
[13]

Alessandro Corbetta, Adrian Muntean, Kiamars Vafayi. Parameter estimation of social forces in pedestrian dynamics models via a probabilistic method. Mathematical Biosciences & Engineering, 2015, 12 (2) : 337-356. doi: 10.3934/mbe.2015.12.337
[14]

Kolade M. Owolabi, Kailash C. Patidar, Albert Shikongo. Efficient numerical method for a model arising in biological stoichiometry of tumour dynamics. Discrete & Continuous Dynamical Systems - S, 2019, 12 (3) : 591-613. doi: 10.3934/dcdss.2019038
[15]

Manfred Einsiedler, Elon Lindenstrauss. On measures invariant under diagonalizable actions: the Rank-One case and the general Low-Entropy method. Journal of Modern Dynamics, 2008, 2 (1) : 83-128. doi: 10.3934/jmd.2008.2.83
[16]

Mikhail B. Sevryuk. Invariant tori in quasi-periodic non-autonomous dynamical systems via Herman's method. Discrete & Continuous Dynamical Systems - A, 2007, 18 (2&3) : 569-595. doi: 10.3934/dcds.2007.18.569
[17]

Àlex Haro, Rafael de la Llave. A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: Numerical algorithms. Discrete & Continuous Dynamical Systems - B, 2006, 6 (6) : 1261-1300. doi: 10.3934/dcdsb.2006.6.1261
[18]

Inmaculada Baldomá, Ernest Fontich, Rafael de la Llave, Pau Martín. The parameterization method for one- dimensional invariant manifolds of higher dimensional parabolic fixed points. Discrete & Continuous Dynamical Systems - A, 2007, 17 (4) : 835-865. doi: 10.3934/dcds.2007.17.835
[19]

Sharif E. Guseynov, Sergey M. Yunusov. New regularizing approach to determining the influence coefficient matrix for gas-turbine engines. Conference Publications, 2011, 2011 (Special) : 614-623. doi: 10.3934/proc.2011.2011.614
[20]

Andreas Widder, Christian Kuehn. Heterogeneous population dynamics and scaling laws near epidemic outbreaks. Mathematical Biosciences & Engineering, 2016, 13 (5) : 1093-1118. doi: 10.3934/mbe.2016032

 Impact Factor: 

Tools

Metrics

  • PDF downloads (14)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences