The Conjunction Rule and First-Order Stochastic Dominance are two of the simplest and basic rules of probability. Abiding by these rules is therefore a basic tenet of any theory of rational choice in the face of risk and uncertainty. Moreover, unlike other principles of choice, the simplicity of these rules makes it compelling, particularly in situations in which its applicability is transparent. In this lecture I report results of two separate studies by Charness, Karni and Levin* that examine the robustness of such violations observed in experimental studies across environments and particularly when subjects can also deliberate in pairs and trios. The main finding is that although such deliberations rarely eliminate violations entirely they reduce it to a small fraction of those reported originally.