The views expressed in the papers are the views of the author(s) and do not necessarily reflect the views of the Centre or its sponsors. [...] The results show the public system’s allocation rule and the probability of receiving health care from the public system both significantly affect an individual’s WTP for private health insurance in the predicted direction, although the WTP values tend to be above the actual theoretical predictions. [...] In the UK, the proportion of people holding parallel private insurance has remained steady for two decades at about 11% of households, even in the presence of a subsidy in the early 1990s; in Australia the share of households with parallel private insurance fell steadily until the combination of a large premium subsidy and a regulated premium structure stabilized coverage beginning in 2000; in Sca [...] The model includes variables representing the public sector allocation rule, the probability of public sector treatment, the frame, the frustration-level for the BDM mechanism and associated control variables and interaction terms. [...] Not only is the effect of a change in public treatment probability statistically significant and large in magnitude, it is not affected by other aspects of the decision environment such as the allocation rule, the decision-making frame and the level of prices.