An Introduction to Decision Theory

Philosophers disagree about what probability is. Somewhat roughly put, there are three camps in this debate, objectivism, subjectivism and the epistemic approach. Objectivists maintain that probability statements refer to some facts in the external world. If you claim that the probability is fifty percent that the coin I hold in my hand will land heads up when tossed, then you are – according to the objectivist – referring to a property of the external world, such as the physical propensity of the coin to land heads up about every second time it is tossed. From an intuitive point of view, this seems to be a very plausible idea. However, subjectivists disagree with this picture. Subjectivists deny that probability statements can be understood as claims about the external world. What is, for instance, the probability that your suitor will ask you to marry him? It seems rather pointless to talk about some very complex propensity of that person, or count the number of marriage proposals that other people make, because this does not tell us anything about the probability that you will be faced with a marriage proposal. If it is true that the probability is, say, 1/2 then it is true because of someone's mental state.

According to the subjective view, probability statements refer to the degree to which the speaker believes something. When you say that the probability is 1/2 that your suitor will make a marriage proposal, this merely means that you believe to a certain degree that this proposal will be made, and the strength of your belief can be represented by the number 1/2; and if you were to start thinking that it was absolutely certain that you would get the offer, your subjective degree of belief would be 1. The scope of the subjective analysis can easily be extended to all kinds of examples, because virtually any probability statement can be interpreted as a claim about the speaker's subjective degree of belief. For instance, when you say that the probability is 1/2 that the coin will land heads up next time it is tossed, you are essentially referring to your subjective degree of belief that that event will occur.