For reasons that are obscure to us, the State of Iowa holds the first presidential primary in the nation every four years. (Shouldn’t the first presidential primary vote be allocated at random to a different State every four years?) This year, the Iowa Caucus took place on 1 February 2016. Aside from the outcome of the caucuses, it is also being reported (see here, for example) that a total of six “county delegates” were allocated to Hillary Clinton by six separate coin tosses and that Secretary Clinton won all six coin tosses! Although such an outcome appears highly improbable, since there is only a 1-in-64 (or a 1.56%) chance of all six coin flips going Clinton’s way, scientist Ethan Siegel explains in this informative essay that the true probability of one candidate winning all six coin tosses is in reality 3.12%:
Sure, there might have only been a 1.56% chance that Clinton would win all six, but those odds aren’t all that long, especially when you consider that there’s also a 1.56% chance that Sanders could’ve won all six, for a total chance of 3.12% that someone would have won all six. Three percent may not be a lot, but it’s not that small either: if you had a three percent chance of getting run over the next time you crossed the street, you just might think twice before doing so.
More importantly, while we’re on the subject of randomness, the voters in Iowa have a pretty bad track record at predicting the eventual nominee (sorry, Senator Cruz). According to Wikipedia (emphasis added), “Since 1972, the Iowa caucuses have had a 43% success rate at predicting which Democratic candidate … and a 50% success rate at predicting which Republican candidate … will go on to win the nomination of their political party [for president] …” In other words, with respect to the Republican candidates, the results of the Iowa caucuses are historically no better than random, like a coin toss! And with respect to the Democratic candidates, in a two-man race you’d have a better chance of predicting the eventual nominee by flipping a coin.
prior probability 