The irrelevant information principle for collective probabilistic reasoning

Adamčík, Martin, and Wilmers, George. "The irrelevant information principle for collective probabilistic reasoning." Kybernetika 50.2 (2014): 175-188. <http://eudml.org/doc/261847>.

@article{Adamčík2014,
abstract = {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.},
author = {Adamčík, Martin, Wilmers, George},
journal = {Kybernetika},
keywords = {uncertain reasoning; discrete probability function; social inference process; maximum entropy; Kullback–Leibler; irrelevant information principle; uncertain reasoning; discrete probability function; social inference process; maximum entropy; Kullback-Leibler; irrelevant information principle},
language = {eng},
number = {2},
pages = {175-188},
publisher = {Institute of Information Theory and Automation AS CR},
title = {The irrelevant information principle for collective probabilistic reasoning},
url = {http://eudml.org/doc/261847},
volume = {50},
year = {2014},
}

TY - JOUR
AU - Adamčík, Martin
AU - Wilmers, George
TI - The irrelevant information principle for collective probabilistic reasoning
JO - Kybernetika
PY - 2014
PB - Institute of Information Theory and Automation AS CR
VL - 50
IS - 2
SP - 175
EP - 188
AB - 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.
LA - eng
KW - uncertain reasoning; discrete probability function; social inference process; maximum entropy; Kullback–Leibler; irrelevant information principle; uncertain reasoning; discrete probability function; social inference process; maximum entropy; Kullback-Leibler; irrelevant information principle
UR - http://eudml.org/doc/261847
ER -