Consider a 6-sided dice with equal dimensions on each side. By classical probability, you would expect to see a “1”, as likely as you would see a “6”, when you roll the dice once. With all probability as equal and perfect, the odds of receiving different outcomes would be equal. When conducting an experiment, to test the fairness of the dice, you roll the dice multiple times, and then you would find the dice will show a “2” around a sixth of the time it is rolled. This process of repeating a certain procedure to find the probability of an outcome is described as the Frequentist measure of probability. But what happens when we want to understand the probability of an outcome which isn’t equal and symmetric (as in classical probability), or the variables are not fixed or under identical conditions (as in the Frequentist’s case). Assume you are visiting a doctor while suffering from a stomach-ache. You have visited the doctor a few times before, so they store your medical history and can make an educated guess on the condition you may have. The doctor asks you a few questions regarding your issue and as you answer, the doctor updates his hypothesis and becomes more or possible less confident in it. Once he attains the degree of confidence in his guess in consideration with the new
information provided, he diagnoses you with food poisoning. The process of updating one’s beliefs with additional evidence is known as the Bayesian epistemology. After exploring the principle of conditionalization, central to Bayesian epistemology, this article presents the key supporting argument for the principle of conditionalization through the Dutch Book argument. This article then dissects Van Fraassen’s improvements to the argument. Bayesian epistemology Bayesian epistemology gathers its roots from Bayes’ formula, which introduces conditionalization of a probability onto an outcome. Conditionalization tells us how to reallocate our belief when given new evidence. In a Bayesian setting, you start with a prior degree of belief attained from an outcome. As you collect more evidence, you condition your previous belief and re-evaluate your belief based on this new information. Now, if you update your degree of belief to an extent it does not rationally match the new evidence, you are violating the Bayesian principle of probabilism. Remember, the probabilities involved in Bayesian epistemology are not as concrete as that of the Classical or Frequentist setting. Hence, it 3|Page
