Epistemic versus Aleatory Judgment Under Uncertainty

Both cases involve judgment under uncertainty, with a mixture of evidence supporting and opposing each event’s likelihood. Yet, they involve what appears to be two qualitatively distinct representations of uncertainty. In the first case, Allie’s uncertainty reflects the unpredictability inherent to a stochastic process (i.e., random draws from the pool of Bingo numbers). This type of uncertainty promotes a distributional mode of thought, with Allie perhaps thinking about how the outcome could play out in different ways upon similar occasions. In the second case, Ellie’s uncertainty reflects the confidence she places in her beliefs, based upon what she knows about the details of the crime. This type of uncertainty promotes an evaluative mode of thought, with Ellie perhaps gauging the quality of the evidence, as well as what she knows and does not know. Allie reasons under what we will call aleatory uncertainty, while Ellie reasons under epistemic uncertainty. The distinction between epistemic and aleatory uncertainty dates back to the early foundations of modern probability (Hacking, 1975). Probability theory is commonly thought to have originated in an exchange of letters between Blaise Pascal and Pierre de Fermat in 1654, over the question of how to properly divide the stakes in a game of chance were the game to be prematurely interrupted. To tackle this question, Pascal and Fermat formulated a calculus for how to think about events entailing aleatory uncertainty. Shortly thereafter Pascal posed the question of whether to believe in God as a decision-theoretic wager, with the outcome of the wager tied to the true state of nature (i.e., whether God in fact exists). In doing so, Pascal appropriated his earlier framework on the probability of chance events in order to understand a question entailing pure epistemic uncertainty. To this day probability theory is split between two dominant schools of thought, with Frequentists treating probabilities as the frequency of events repeated over multiple instantiations, and Bayesians