What do probabilities mean to people? The Cost of Certainty

One of the most interesting notions in Prospect Theory, is the idea that individuals really don't understand probabilities. That is they make little distinction between similar probabilities (say the difference between 0.25 and 0.3) and treat them essentially the same. However that is not true at the extremes, we seem to have a cognitive bias in favor of zero and 1 as absolute certainties. Yet ironically, absolute certainties are never the case. Mathematically this is described as a weighting function that converts quantitative probabilities into qualitative weights - using a function like the following:

So basically we underestimate probabilities when they are slightly less than 1 and overestimate them if they are slightly more than zero. What does this mean for finance? Well, people will pay more to receive contingent cashflows which are very unlikely because they will overstate the actual probability. This is part of the attraction of lotteries - although the probability is small, there is a small probability of success and that makes all the difference. Similarly investors will heavily discount cashflows that are not absolutely certain.