Interest has grown worldwide in risk adjustment and risk sharing due to their potential to contain costs, improve fairness, and reduce selection problems in health care markets. Significant steps have been made in the empirical development of risk adjustment models, and in the theoretical foundations of risk adjustment and risk sharing. This literature has often modeled the effects of risk adjustment without highlighting the institutional setting, regulations, and diverse selection problems that risk adjustment is intended to fix. Perhaps because of this, the existing literature and their recommendations for optimal risk adjustment or optimal payment systems are sometimes confusing. In this paper, we present a unified way of thinking about the organizational structure of health care systems, which enables us to focus on two key dimensions of markets that have received less attention: what choices are available that may lead to selection problems, and what financial or regulatory tools other than risk adjustment are used to influence these choices. We specifically examine the health care systems, choices, and problems in four countries: the US, Canada, Chile, and Colombia, and examine the relationship between selection-related efficiency and fairness problems and the choices that are allowed in each country, and discuss recent regulatory reforms that affect choices and selection problems. In this sample, countries and insurance programs with more choices have more selection problems.