Parameters in collective decision making models : estimation and sensitivity

Snijders, Tom A. B.; Zeggelink, Evelien P. H.; Stokman, Frans N.

Mathématiques informatique et sciences humaines, Tome 137 (1997), pp. 81-99.

Les modèles de simulation des processus de formation de décisions collectives sont fondés sur des aperçus théoriques et empiriques du processus de décision mais contiennent des paramètres dont les valeurs sont déterminées ad hoc. Certains de ces paramètres, du modèle d'accès dynamique sont discutés et il est proposé de compléter la fonction d'utilité par un terme aléatoire dont la variance serait un paramètre inconnu. Ces paramètres peuvent être estimés en confrontant aux données les prévisions du modèle qui peuvent être des décisions mais aussi des structures relationnelles générées comme un élément du processus de prise de décision. Etant donné la nature stochastique du modèle, l'estimation de ces paramètres peut être obtenue par l'algorithme de Robins Monro. Cet ajustement n'est pas absolument direct. Il faut choisir les statistiques sur lesquelles se fonde l'estimation des paramètres. Il n'est pas certain a priori que l'équation d'estimation admette une solution et que l'algorithme de Robins Monro converge. La méthode est illustrée par des données concernant la restructuration financière d'une grande société.

Simulation models for collective decision making are based on theoretical and empirical insight in the decision making process, but still contain a number of parameters of which the values are determined ad hoc. For the dynamic access model, some of such parameters are discussed, and it is proposed to extend the utility functions with a random term of which the variance also is an unknown parameter. These parameters can be estimated by fitting model predictions to data, where the predictions can refer to decision outcomes but also to network structure generated as a part of the decision making process. Given the stochastic nature of the model, this parameter estimation can be carried out with the Robbins Monro process. Such fitting is not completely straightforward: statistics must be chosen on which to base the parameter estimation, it is not certain a priori that there will be a solution to the estimating equation and that the Robbins Monro process will converge. The method is illustrated with data from the financial restructuring of a large company.

Berveling, J., Roozendaal, P. Van, (1992), "Amsterdam in hoger sferen. De invloed van organisaties op de bouwhoogte in het centrale deel van de IJ-oevers", in Jansen, W., Wittenboer, G.L.H. van den (eds.), Sociale netwerken en hun invloed, Meppel, Boom.

Berveling, J., (1994a), Het stempel op de besluitvorming. Macht, invloed en besluitvorming op twee Amsterdamse beleidsterreinen, Amsterdam, Thesis Publishers.

Berveling, J., (1994b), Over beeld- en beleidsvorming, Groningen, ICS (ICS Occasional Papers and Documents Series, nr.1).

Bishop, Y.M.M., Fienberg, S.E., and Holland, P.W., (1975), Discrete Multivariate Analysis, Cambridge, MA, MIT Press. | MR | Zbl

Bos, J.M.M. Van Den, (1991), Dutch EC Policy Making. A model-guided approach to coordination and negotiation, Utrecht, Thesis Publishers.

Bowman, K.O., and Shenton, L.R., (1985), "Method of moments", in Encyclopedia of Statistical Sciences, vol. 5, S. Kotz, N.L. Johnson, and C. B. Read (eds.), New York, Wiley, 467-473.

BUENO DE MESQUITA, B., and STOKMAN, F.N., (eds.) (1994), European Community Decision Making. Models, Comparisons, and Applications, New Haven, Yale University Press.

Coleman, James S., (1972) "Systems of social exchange", Journal of Mathematical Sociology, 2, 145-163. , | MR

Degenne, A., Forsé, M., (1994), Les Réseaux Sociaux, Paris, Armand Colin.

Duflo, M., (1990), Méthodes Récursives Aléatoires, Paris, Masson. | MR | Zbl

Laumann, E.O., Knoke, D., (1987), The Organizational State. Social choice in national policy domains, Madison, The University of Wisconsin Press.

Maddala, G.S., (1983), Limited-dependent and Qualitative Variables in Econometrics, Cambridge, Cambridge University Press. | MR | Zbl

Pflug, J.Ch., (1988), "Stepsize rules, stopping times and their implementation in stochastic quasigradient methods", in Yu. Ermoliev & J. R.-B. Wets (eds.), Numerical Techniques for Stochastic Optimization, Berlin, Springer, 353-372. | MR | Zbl

Robbins, H., and Monro, S., (1951), "A stochastic approximation method", Annals of Mathematical Statistics, 22, 400 - 407. | MR | Zbl

Ruppert, D., (1991), "Stochastic approximation", in Handbook of Sequential Analysis, eds. B.K. Gosh and P.K. Sen, New York, Marcel Dekker. | MR

Schonewille, J., (1990), Herstelfinanciering van AVEBE, Groningen, Masters's Thesis, Department of Sociology, University of Groningen.

Snijders, Tom A.B., (1981), "The degree variance: an index of graph heterogeneity ", Social Networks, 3, 163-174. | MR

Snijders, Tom A.B., (1996), "Stochastic actor-oriented models for network change." Journal of Mathematical Sociology, 21: 149-172. | Zbl

Snijders T.A.B., Stokman, F.N., & Zeggelink, E.P.H., (1996), "Parameterschatting in actor-georiënteerde besluitvormingsmodellen", in H. Ganzeboom & S. Lindenberg (eds.),Verklarende Sociologie: Opstellen voor Reinhard Wippler, Amsterdam, Thesis Publishers, 129-143.

Stokman, F.N., (1994), "Besluitvormingsmodellen binnen beleidsnetwerken ", in Huberts, L.W.J.C., & Kleinnijenhuis, J. (eds.), Methoden van Invloedsanalyse, Mepel, Boom.

Stokman, F.N., Berveling, J., "Predicting outcomes of decision making", in press.

Stokman, F.N., Bos, J.M.M. Van Den, (1992), "A two-stage model of policy making: With an empirical test in the U.S. Energy Policy Domain", in Moore, G., Whitt, J.A. (eds.), The Political Consequences of Social Networks. Volume 4 of Research and Society, Greenwich, Conn.

Stokman, F.N., Zeggelink, E., (1996), "Is politics power or policy oriented? A comparative analysis of dynamic access models in policy networks", Journal of Mathematical Sociology, 21, 77-111. | Zbl