Subjective probability

For Bayesians, there is a close link between subjective probability and preferences over uncertain prospects. According to their view, the more you are willing to pay for entering a bet in which you win some fixed amount if your belief turns out to be true, the higher is your subjective probability. So your willingness to bet serves as an indicator of how likely you think the belief is to be true. However, as argued in Chapter 2, Bayesians put the cart before the horse from the point of view of the deliberating agent. Bayesians define subjective probability (and utility) in terms of preferences over uncertain prospects; therefore, the obtained numbers cannot figure as reasons for forming new preferences over the same set of uncertain prospects. The aim of this chapter is to offer a non-Bayesian account of probability that avoids this problem, and that is coherent with the Humean belief-desire model of action.

The strategy in this chapter is to first cast some doubt on the two genuine alternatives to my position, subjective Bayesianism and objective non-Bayesianism. Thereafter I will defend the subjective non-Bayesian approach. The two alternative positions are briefly discussed in Sections 6.1 and 6.2. The subjective non-Bayesian position is presented and defended in Sections 6.3 and 6.4.