Measuring evidential phenomena for complex reasoning patterns about a mass of evidence

Abstract Studies on the evidential foundations of probabilistic reasoning are extended using the notion of weight of evidence to measure evidential phenomena in the presence of a mass of evidence giving rise to complex reasoning patterns. The main results provided in this paper are methods to measure inferential interactions and dissonances among items of evidence. All measures are defined to ensure a versatile applicability in inferential tasks involving the combination of evidence and a mass of evidence. These measures enable a detailed examination of recurrent phenomena in evidence-based reasoning, such as convergence, contradiction, redundancy, and synergy. Most of these phenomena have—as far as the authors are aware—either not been formally described or any formal description proposed has been of limited use for evidence-based reasoning tasks. The present research addresses this deficit in the current understanding and treatment of these evidential phenomena. It is shown by way of examples that incorrect consideration of evidential phenomena can lead to substantial misrepresentations of the value of evidence.