Determining models of influence

• Autorzy: Grabisch M. , Rusinowska A.

Identyfikatory

DOI

10.5277/ord160205

• Języki publikacji: EN

Abstrakty

EN

We consider a model of opinion formation based on aggregation functions. Each player modifies his opinion by arbitrarily aggregating the current opinion of all players. A player is influential on another player if the opinion of the first one matters to the latter. Generalization of an influential player to a coalition whose opinion matters to a player is called an influential coalition. Influential players (coalitions) can be graphically represented by the graph (hypergraph) of influence, and convergence analysis is based on properties of the hypergraphs of influence. In the paper, we focus on the practical issues of applicability of the model w.r.t. a standard framework for opinion formation driven by Markov chain theory. For a qualitative analysis of convergence, knowing the aggregation functions of the players is not required, one only needs to know the set of influential coalitions for each player. We propose simple algorithms that permit us to fully determine the influential coalitions. We distinguish three cases: a symmetric decomposable model, an anonymous model, and a general model.

Słowa kluczowe

EN

social network; opinion formation; aggregation function; influential coalition; algorithm

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Operations Research and Decisions
• Rocznik: 2016
• Tom: Vol. 26, No. 2
• Strony: 69--85
• Opis fizyczny: Bibliogr. 40 poz., rys.

Twórcy

autor

Grabisch M.

• Paris School of Economics – CNRS, Université Paris I Panthéon-Sorbonne, Centre d’Economie de la Sorbonne, 106-112 Bd de l’Hôpital, 75647 Paris, France

autor

Rusinowska A.

• Paris School of Economics – CNRS, Université Paris I Panthéon-Sorbonne, Centre d’Economie de la Sorbonne, 106-112 Bd de l’Hôpital, 75647 Paris, France

Bibliografia

• [1] ACEMOGLU D., OZDAGLAR A., Opinion dynamics and learning in social networks, Dynamic Games and Applications, 2011, 1, 3.
• [2] ASAVATHIRATHAM C., Influence model: a tractable representation of networked Markov chains, PhD thesis, Massachusetts Institute of Technology, Cambridge, MA, 2000.
• [3] ASAVATHIRATHAM C., ROY S., LESIEUTRE B., VERGHESE G., The influence model, IEEE Control Systems Magazine, 2001, 21, 52.
• [4] BALA V., GOYAL S., Learning from neighbours, The Review of Economic Studies, 1998, 65 (3), 595.
• [5] BALA V., GOYAL S., Conformism and diversity under social learning, Economic Theory, 2001, 17, 101.
• [6] BANERJEE A.V., A simple model of herd behavior, Quarterly Journal of Economics, 1992, 107 (3), 797.
• [7] BANERJEE A.V., FUDENBERG D., Word-of-mouth learning, Games and Economic Behavior, 2004, 46, 1.
• [8] BERGE C., Graphs and hypergraphs, North-Holland, 2nd Ed., Amsterdam 1976.
• [9] BERGER R.L., A necessary and sufficient condition for reaching a consensus using DeGroots method, Journal of the American Statistical Association, 1981, 76, 415.
• [10] BONACICH P.B., Power and centrality. A family of measures, American Journal of Sociology, 1987, 92, 1170.
• [11] BONACICH P.B., LLOYD P., Eigenvector-like measures of centrality for asymmetric relations, Social Networks, 2001, 23 (3), 191.
• [12] CELEN B., KARIV S., Distinguishing informational cascades from herd behavior in the laboratory, American Economic Review, 2004, 94 (3), 484.
• [13] CONLISK J., Interactive Markov chains, Journal of Mathematical Sociology, 1976, 4, 157.
• [14] CONLISK J., A stability theorem for an interactive Markov chain, Journal of Mathematical Sociology, 1978, 6, 163.
• [15] CONLISK J., Stability and monotonicity for interactive Markov chains, Journal of Mathematical Sociology, 1992, 17, 127.
• [16] DEGROOT M.H., Reaching a consensus, Journal of the American Statistical Association, 1974, 69, 118.
• [17] DEMARZO P., VAYANOS D., ZWIEBEL J., Persuasion bias, social influence, and unidimensional opinions, Quarterly Journal of Economics, 2003, 118, 909.
• [18] ELLISON G., Learning, local interaction, and coordination, Econometrica, 1993, 61, 1047.
• [19] ELLISON G., FUDENBERG D., Rules of thumb for social learning, Journal of Political Economy, 1993, 101 (4), 612.
• [20] ELLISON G., FUDENBERG D., Word-of-mouth communication and social learning, Journal of Political Economy, 1995, 111 (1), 93.
• [21] FOERSTER M., GRABISCH M., RUSINOWSKA A., Anonymous social influence, Games and Economic Behavior, 2013, 82, 621.
• [22] FRENCH J., A formal theory of social power, Psychological Review, 1956, 63 (3), 181.
• [23] FRIEDKIN N.E., JOHNSEN E.C., Social influence and opinions, Journal of Mathematical Sociology, 1990, 15, 193.
• [24] FRIEDKIN N.E., JOHNSEN E.C., Social positions in influence networks, Social Networks, 1997, 19, 209.
• [25] GALE D., KARIV S., Bayesian learning in social networks, Games and Economic Behavior, 2003, 45 (2), 329.
• [26] GOLUB B.JACKSON M.O., Naïve learning in social networks and the wisdom of crowds, American Economic Journal: Microeconomics, 2010, 2 (1), 112.
• [27] GRABISCH M., RUSINOWSKA A., A model of influence based on aggregation functions, Mathematical Social Sciences, 2013, 66, 316.
• [28] GRANOVETTER M., Threshold models of collective behavior, American Journal of Sociology, 1978, 83, 1420.
• [29] HARARY F., Status and contrastatus, Sociometry, 1959, 22, 23.
• [30] HU X., SHAPLEY L.S., On authority distributions in organizations: equilibrium, Games and Economic Behavior, 2003, 45, 132.
• [31] HU X., SHAPLEY L.S., On authority distributions in organizations: controls, Games and Economic Behavior, 2003, 45, 153.
• [32] JACKSON M.O., Social and economic networks, Princeton University Press, 2008.
• [33] KATZ L., A new status index derived from sociometric analysis, Psychometrika, 1953, 18, 39.
• [34] KRACKHARDT D., Cognitive social structures, Social Networks, 1987, 9, 109.
• [35] KRAUSE U., A discrete nonlinear and nonautonomous model of consensus formation, [in:] S. Elaydi, G. Ladas, J. Popenda, J. Rakowski (Eds.), Communications in Difference Equations, Gordon and Breach, Amsterdam 2000.
• [36] LEHOCZKY J.P., Approximations for interactive Markov chains in discrete and continuous time, Journal of Mathematical Sociology, 1980, 7, 139.
• [37] LORENZ J., A stabilization theorem for dynamics of continuous opinions, Physica A, 2005, 355, 217.
• [38] SHAPLEY L.S., A Boolean model of organization authority based on the theory of simple games, Mimeo, 1994.
• [39] WASSERMAN S., FAUST K., Social network analysis.Methods and applications, Cambridge University Press, Cambridge 1994.
• [40] YAGER R., An ordered weighted averaging aggregation operators in multicriteria decision making, IEEE Transactions on Systems, Man and Cybernetics, 1988, 18 (1), 183

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.