Reliability updating in linear opinion pooling for multiple decision makers

Accurate information sources are vital prerequisites for good decision making. Here, we consider a multiple participant setting, where all decision makers have a collection of neighbours with whom they share their beliefs about some common relevant uncertain quantity. When determining which course of action to follow, a decision maker takes into account all the information received from her neighbours. Over time, in light of the returns observed from choices made, decision makers update their own beliefs over the uncertain event and also adjust the degree of consideration they afford to the opinions of each neighbour based on the level of reliability their information is ascertained to have. In this article, we derive and discuss a methodology, the plug-in approach, by which this can be done, and discuss some suitable justification for this. We include an illustrative risk-based example which further demonstrates the merits of the method, before concluding with a discussion on further work and potential alternatives.