Combining and Abstracting Causal Models
Abstract
Consider a policymaker who is trying to decide which interventions should be implemented in order to bring about a desired outcome, such as preventing violent behavior in prisons or reducing famine mortality in some country. The policymaker has access to various experts who can advise her on which interventions to consider. Some experts may be (in the policymakerÕs view) more reliable than others; they may also have different areas of expertise; or may have perceived alternative factors in their analysis. The policymaker must somehow combine these expertsÕ advice to reach her decision. It is assumed the experts use structural causal models to express their judgments. These models describe the effect of one variable on another, and can capture the effect of interventions. The qualitative information in a causal model can be described using a causal network, which makes it particularly easy to present causal information to decision makers. But even if an expert can present his view of the world using a causal model, how should the causal models of experts be combined? There has been a great deal of work on combining expertsÕ probabilistic judgments. But a causal model contains much more than probabilistic information; it also has causal information. In general, the expertsÕ models may involve different variables (since the experts may be focusing on different aspects of the problem). Moreover, even if two models both include variables C1 and C2, they may disagree on the relationships between them. For example, one expert may believe that C2 is independent of C1 while another may believe that C1 causally depends on C2. Yet somehow the expertsÕ judgments must be combined. There is surprisingly little work on combining expertsÕ causal judgments in the literature. Indeed, Bradley, Dietrich, and List prove an impossibility result. Specifically, they describe certain arguably reasonable desiderata, and show that there is no way of combining causal models so as to satisfy all their desiderata. This project will attempt to provide conditions under which two causal models M1 and M2 are compatible, and so can be combined to produce a model M1 À M2 that incorporates information from both. The general approach to combining expertsÕ judgments would then be to combine the expertsÕ models when they are compatible, and if not, just place a probability on each model being the right model. Intuitively, if the expertsÕ models are not compatible, then the experts are disagreeing, so we should not try to combine their models; rather, we should just assign a likelihood to each model being right. On the other hand, if the models are compatible, then we should consider a model that takes into account both experts information. This approach should provide a useful formal framework that can be applied to the determination of appropriate interventions in real-world scenarios involving complex sociological phenomena. Combining judgments is only one operation on causal models. Another that will be considered is abstraction. Suppose that an expert provides a detailed causal model, involving many variables. Such a detailed model may be far too complicated for a policymaker to understand and work with. What the policymaker wants is a high-level ÒmacroÓ model of the situationÉ
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Sep 11, 2018
- Source ID
- W911NF1710592
Entities
People
- Joseph Halpern
Organizations
- Army Contracting Command
- Cornell University
- United States Army