Probabilistic causality

Abstract

Necessity and Sufficiency are two of the most important concepts in science. Indeed, they are the basis for establishing causal relationships between factors, variables, etc.In contradistinction to most treatments of causality, we show how to compute the probability that Necessity and Sufficiency obtain. We thus treat probabilistic causality, which is key to Technological Forecasting since we are never dealing with complete knowledge or perfect certainty.This paper shows how decision makers can obtain direct estimates of the probabilities of the Necessity and the Sufficiency of various proposed courses of action and thereby make better decisions with regard to their efficacy.The paper goes beyond typical chi-square analyses that show whether there are significant statistical relationships between two or more variables. Instead, whatever the level of statistical significance, it shows how one can determine the amount or degree of Sufficiency and Necessity that exists between two or more variables. In fact, we show how statistical significance and Sufficiency and Necessity are related. In particular, we show how the correlation coefficient between two variables is a direct function of Sufficiency and Necessity.To do this, we adapt a framework from epidemiology: Predictive Value Theory. Although Predictive Value Theory was originally developed to help physicians make critical decisions, e.g., whether to administer or not to administer a treatment, or to screen or not to screen for say cancer, it is so general that with little modification it applies equally well to decision making in general.By combining probability theory and elementary logic, we show how one can measure directly the Sufficiency and the Necessity of a test from the data that are gathered in a typical application of Predictive Value Theory.The result is not only a better understanding of Predictive Value Theory, but its extended application to decision making in general.Finally, the paper goes beyond traditional Bayesian ways of computing the probability of implication and hence Sufficiency and Necessity.