The New York Times has a fun feature outlining a predictive model for today's Senate elections. The most entertaining part lets you run a single simulation of the outcome by spinning wheels representing all the states. This isn't just fun. It's an excellent way of presenting uncertainty and some ways of handling it. Each time you press the button, you are running one iteration of a 'Monte Carlo' model of the election.
A 'Monte Carlo' model is a way of generating a probability of an outcome by running a large number of simulations of it, and where for each simulation the uncertain variables are randomly generated anew. It's a useful approach if there are many events that interact or combine to produce an outcome. It's easier but not as satisfying as calculating a precise probability analytically, but many systems are sufficiently complex that this is not possible anyway.
Elections are relatively easy to present this way because each polity can be considered (at least to an extent) as an independent event, and there are no complicated interactions between results to consider since no result is in the information set of any voter. So the Monte Carlo component of the model is quite straightforward to visualise. (Although in this case the probabilities for each state seem to be fixed for each iteration, the underlying model probably has a far larger number of constituent variables of which these probabilities are themselves a simulated average.)
Inter alia, the use of miniature roulette wheels as a means of presenting probability allows readers to interact to an extent with an uncertain event in a way that might cement a more concrete understanding of what probabilities actually mean in terms of outcomes. The evidence for this is currently limited but the approach has been considered in a number of contexts. The science of data visualisation is relatively young though; we are a long way from consensus on the best way to visualise uncertainty to support decision-making most effectively. Analysts should take an interest in experiments like the New York Times's as the future demand for interactive visualisations is only going to increase.