Just as a side note, Harsanyi’s result is not directly applicable to a formal setup involving subjective uncertainty, such as Savage’s or the Jeffrey-Bolker framework underlying evidential and causal decision theory. Though there are results for the Savage setup too, e.g., https://www.jstor.org/stable/10.1086/421173, and Caspar Oesterheld and I are working on a similar result for the Jeffrey Bolker framework. In this setup, to get useful results, the indifference Axiom can only be applied to a restricted class of propositions where everyone agrees on beliefs.
Just as a side note, Harsanyi’s result is not directly applicable to a formal setup involving subjective uncertainty, such as Savage’s or the Jeffrey-Bolker framework underlying evidential and causal decision theory. Though there are results for the Savage setup too, e.g., https://www.jstor.org/stable/10.1086/421173, and Caspar Oesterheld and I are working on a similar result for the Jeffrey Bolker framework. In this setup, to get useful results, the indifference Axiom can only be applied to a restricted class of propositions where everyone agrees on beliefs.