Distinguishing Two Dimensions of Uncertainty

Barack Obama made one of the most difficult decisions of his presidency: launch an attack on a compound in Pakistan that intelligence agents suspected was the home of Osama bin Laden. In an interview Obama described the raid as the longest 40 minutes of his life. He attributed that tension to two sources. First, he was not certain that bin Laden was actually residing in the compound. " As outstanding a job as our intelligence teams did, " said the President, " At the end of the day, this was still a 55/45 situation. I mean, we could not say definitively that bin Laden was there. " Second, regardless of whether bin Laden was residing in the compound, it was not certain that the operation would succeed. Asked about this concern the President cited operations by previous presidents that had failed due to chance factors, saying, " You're making your best call, your best shot, and something goes wrong – because these are tough, complicated operations. " Note that these two sources of uncertainty are qualitatively distinct. The first reflects the President's lack of confidence in his knowledge of a fact (i.e., whether or not bin Laden was residing at the compound). The second reflects variability in possible realizations of an event that is largely stochastic in nature – if the mission were to be run several times it would succeed on some occasions and fail on others due to unpredictable causes (e.g., performance of mechanical equipment, effectiveness of U.S. troops and bin Laden's defenders on a particular night). The notion that uncertainty can take multiple forms is nearly as old as probability theory itself (Hacking, 1975). Pascal and Fermat tried to address the question of how one ought to divide the stakes of a game of chance that has been prematurely interrupted (see e.g., Devlin, 2008). Their probability theory was based on an aleatory conception of uncertainty involving unknown outcomes that can differ each time one runs an experiment under similar conditions. Shortly thereafter Pascal framed the choice of whether or not to believe in God as a wager with an outcome that depends on whether or not God exists. He thus advanced an epistemic conception of uncertainty involving missing knowledge concerning a fact that either is or is not true. Disagreement concerning the nature of uncertainty persists to this day in the two dominant schools of probability theorizing, …