In this chapter from the Handbook of Probability, Kopylov provides a straightforward history of theories of subjective probabilities in decisionmaking. A number of theorists, particularly Ramsey, have thought of probability as being defined by the action an agent is willing to take concerning those probabilities. This led to de Finetti (1937) and Savage’s (1972) famous theories in which preferences over actions that occur in some states but not in others can be used to elicit the subjective probability of those states. This theory was expanded by Machina and Schmeidler (1992) to non-expected utility, Ghirardato et al (2002) and Epstein (2006) to allow agents to update their beliefs about states dynamically, and by a number of other others to handle empirical paradoxes of subjective utility theory (such as Allais and Ellsberg).
“Subjective and Other Probabilities,” I. Kopylov (2008)