| Title:
|
The irrelevant information principle for collective probabilistic reasoning (English) |
| Author:
|
Adamčík, Martin |
| Author:
|
Wilmers, George |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
50 |
| Issue:
|
2 |
| Year:
|
2014 |
| Pages:
|
175-188 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Within the framework of discrete probabilistic uncertain reasoning a large literature exists justifying the maximum entropy inference process, $\operatorname{\mathbf{ME}}$, 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 $\operatorname{\mathbf{ME}}$ 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 $\operatorname{\mathbf{ME}}$ called the social entropy process, $\operatorname{\mathbf{SEP}}$. However, while $\operatorname{\mathbf{SEP}}$ 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 $\operatorname{\mathbf{ME}}$ whose immediate generalisations to the multi-agent case are not satisfied by $\operatorname{\mathbf{SEP}}$. 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 $\operatorname{\mathbf{SEP}}$ can satisfy an interesting modified generalisation of this principle. (English) |
| Keyword:
|
uncertain reasoning |
| Keyword:
|
discrete probability function |
| Keyword:
|
social inference process |
| Keyword:
|
maximum entropy |
| Keyword:
|
Kullback–Leibler |
| Keyword:
|
irrelevant information principle |
| MSC:
|
03B42 |
| MSC:
|
03B48 |
| MSC:
|
60A99 |
| MSC:
|
68T37 |
| MSC:
|
94A17 |
| idZBL:
|
Zbl 1297.68221 |
| idMR:
|
MR3216989 |
| DOI:
|
10.14736/kyb-2014-2-0175 |
| . |
| Date available:
|
2014-06-06T14:37:48Z |
| Last updated:
|
2016-01-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143788 |
| . |
| Reference:
|
[1] Adamčík, M., Wilmers, G. M.: Probabilistic merging operators..Logique et Analyse (2013), to appear. |
| Reference:
|
[2] Carnap, R.: On the application of inductive logic..Philosophy and Phenomenological Research 8 (1947), 133-148. MR 0023216, 10.2307/2102920 |
| Reference:
|
[3] French, S.: Group consensus probability distributions: A critical survey..In: Bayesian Statistics (J. M. Bernardo, M. H. De Groot, D. V. Lindley, and A. F. M. Smith, eds.), Elsevier, North Holland 1985, pp. 183-201. Zbl 0671.62010, MR 0862490 |
| Reference:
|
[4] Hardy, G. H., Littlewood, J. E., Pólya, G.: Inequalities..Cambridge University Press, 1934. Zbl 0634.26008 |
| Reference:
|
[5] Hawes, P.: An Investigation of Properties of Some Inference Processes..Ph.D. Thesis, The University of Manchester, Manchester 2007. |
| Reference:
|
[6] Jaynes, E. T.: Where do we stand on maximum entropy?.In: The Maximum Entropy Formalism (R. D. Levine and M. Tribus, eds.), M.I.T. Press, Cambridge 1979. MR 0521743 |
| Reference:
|
[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, 10.1002/int.20027 |
| Reference:
|
[8] Kracík, J.: Cooperation Methods in Bayesian Decision Making with Multiple Participants..Ph.D. Thesis, Czech Technical University, Prague 2009. |
| Reference:
|
[9] Matúš, F.: On Iterated Averages of $I$-projections..Universität Bielefeld, Germany 2007. |
| Reference:
|
[10] Osherson, D., Vardi, M.: Aggregating disparate estimates of chance..Games and Economic Behavior 56 (2006), 1, 148-173. Zbl 1127.62129, MR 2235941, 10.1016/j.geb.2006.04.001 |
| Reference:
|
[11] Paris, J. B.: The Uncertain Reasoner's Companion..Cambridge University Press, Cambridge 1994. Zbl 0838.68104, MR 1314199 |
| Reference:
|
[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, MR 0975613, 10.1016/0888-613X(89)90012-1 |
| Reference:
|
[13] Paris, J. B., Vencovská, A.: A note on the inevitability of maximum entropy..Internat. J. of Approximate Reasoning 4 (1990), 183-224. MR 1051032, 10.1016/0888-613X(90)90020-3 |
| Reference:
|
[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. 10.1287/deca.1080.0119 |
| Reference:
|
[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, MR 0560389, 10.1109/TIT.1980.1056144 |
| Reference:
|
[16] Vomlel, J.: Methods of Probabilistic Knowledge Integration..Ph.D. Thesis, Czech Technical University, Prague 1999. |
| Reference:
|
[17] Wilmers, G. M.: The social entropy process: Axiomatising the aggregation of probabilistic beliefs..In: Probability, Uncertainty and Rationality (H. Hosni and F. Montagna, eds.), 10 CRM series, Scuola Normale Superiore, Pisa 2010, pp. 87-104. Zbl 1206.03025, MR 2731977 |
| Reference:
|
[18] Wilmers, G. M.: Generalising the Maximum Entropy Inference Process to the Aggregation of Probabilistic Beliefs..available from http://manchester.academia.edu/GeorgeWilmers/Papers |
| . |
