The irrelevant information principle for collective probabilistic reasoning. (English) Zbl 1297.68221

Summary: Within the framework of discrete probabilistic uncertain reasoning a large literature exists justifying the maximum entropy inference process, ME, as being optimal in the context of a single agent whose subjective probabilistic knowledge base is consistent. In particular Paris and Vencovská completely characterised the ME inference process by means of an attractive set of axioms which an inference process should satisfy. More recently the second author extended the Paris-Vencovská axiomatic approach to inference processes in the context of several agents whose subjective probabilistic knowledge bases, while individually consistent, may be collectively inconsistent. In particular he defined a natural multi-agent extension of the inference process ME called the social entropy process, SEP. However, while SEP has been shown to possess many attractive properties, those which are known are almost certainly insufficient to uniquely characterise it. It is therefore of particular interest to study those Paris-Vencovská principles valid for ME whose immediate generalisations to the multi-agent case are not satisfied by SEP. One of these principles is the Irrelevant Information Principle, a powerful and appealing principle which very few inference processes satisfy even in the single agent context. In this paper we will investigate whether SEP can satisfy an interesting modified generalisation of this principle.


68T37 Reasoning under uncertainty in the context of artificial intelligence
03B48 Probability and inductive logic
94A17 Measures of information, entropy
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[1] Adamčík, M., Wilmers, G. M.: Probabilistic merging operators. Logique et Analyse (2013), to appear.
[2] Carnap, R.: On the application of inductive logic. Philosophy and Phenomenological Research 8 (1947), 133-148. · doi:10.2307/2102920
[3] French, S.: Group consensus probability distributions: A critical survey. Bayesian Statistics (J. M. Bernardo, M. H. De Groot, D. V. Lindley, and A. F. M. Smith, Elsevier, North Holland 1985, pp. 183-201. · Zbl 0671.62010
[4] Hardy, G. H., Littlewood, J. E., Pólya, G.: Inequalities. Cambridge University Press, 1934. · Zbl 0634.26008
[5] Hawes, P.: An Investigation of Properties of Some Inference Processes. Ph.D. Thesis, The University of Manchester, Manchester 2007.
[6] Jaynes, E. T.: Where do we stand on maximum entropy?. The Maximum Entropy Formalism (R. D. Levine and M. Tribus, M.I.T. Press, Cambridge 1979.
[7] Kern-Isberner, G., Rödder, W.: Belief revision and information fusion on optimum entropy. Internat. J. of Intelligent Systems 19 (2004), 837-857. · Zbl 1101.68944 · doi:10.1002/int.20027
[8] Kracík, J.: Cooperation Methods in Bayesian Decision Making with Multiple Participants. Ph.D. Thesis, Czech Technical University, Prague 2009.
[9] Matúš, F.: On Iterated Averages of \(I\)-projections. Universität Bielefeld, Germany 2007.
[10] Osherson, D., Vardi, M.: Aggregating disparate estimates of chance. Games and Economic Behavior 56 (2006), 1, 148-173. · Zbl 1127.62129 · doi:10.1016/j.geb.2006.04.001
[11] Paris, J. B.: The Uncertain Reasoner’s Companion. Cambridge University Press, Cambridge 1994. · Zbl 0838.68104 · doi:10.1017/CBO9780511526596
[12] Paris, J. B., Vencovská, A.: On the applicability of maximum entropy to inexact reasoning. Internat. J. of Approximate Reasoning 3 (1989), 1-34. · Zbl 0665.68079 · doi:10.1016/0888-613X(89)90012-1
[13] Paris, J. B., Vencovská, A.: A note on the inevitability of maximum entropy. Internat. J. of Approximate Reasoning 4 (1990), 183-224. · Zbl 0697.68089 · doi:10.1016/0888-613X(90)90020-3
[14] Predd, J. B., Osherson, D. N., Kulkarni, S. R., Poor, H. V.: Aggregating probabilistic forecasts from incoherent and abstaining experts. Decision Analysis 5 (2008), 4, 177-189. · doi:10.1287/deca.1080.0119
[15] Shore, J. E., Johnson, R. W.: Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy. IEEE Trans. Inform. Theory 26 (1980), 1, 26-37. · Zbl 0532.94004 · doi:10.1109/TIT.1983.1056747
[16] Vomlel, J.: Methods of Probabilistic Knowledge Integration. Ph.D. Thesis, Czech Technical University, Prague 1999.
[17] Wilmers, G. M.: The social entropy process: Axiomatising the aggregation of probabilistic beliefs. Probability, Uncertainty and Rationality (H. Hosni and F. Montagna, 10 CRM series, Scuola Normale Superiore, Pisa 2010, pp. 87-104. · Zbl 1206.03025
[18] Wilmers, G. M.: Generalising the Maximum Entropy Inference Process to the Aggregation of Probabilistic Beliefs. available from · Zbl 1206.03025
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