Polar predictions and hierarchical models

I was recently asked to predict how many of the states which will implemented the Medicaid expansion by 2016 and 2020. The question led to a reflection about the nature of predictions in which the extremes are more likely than the middle. The probability of many states having signed up in 2016 is high given the level of federal subsities offered to the states (100% for the first three years, then 90%). On the other hand, there may be political costs (seemingly accepting the ACA may have a political cost) and worries about the credibility of the promised federal funding. In addition, however, the presidential election in 2016 may drastically alter the system. So, I find myself believing that in 2020 there is a high probability that very many or very few (none!) of the states will be enrolled in the expansion. Exacly how would I derive the probabilities?

The answer is that a hierarchy of distriution and beliefs must be aggregated. We have beliefs about a democratic vs. republican vicory in 2016. We also have beliefs about the extent to which the Republicans will change different aspects of ACA. Then there is the risk of a financial crisis and renegotiation of the terms. Taken together this may lead to a polar prediction distribution - with fat end points and little in between.

So what? Well, it may be obviuous, but still one ofte thinks about probabilities as monotonically increasing. If 36 is most likely, then 35 is quite likely and 0 is very unlikely. The example reminds me that this intuition is wrong. It is perfectly possible that the extremes have high probabilities.