Summary:

This post outlines how a view we call subjective naturalism^[1] poses challenges to classical Savage-style decision theory. Subjective naturalism requires (i) richness (the ability to represent all propositions the agent can entertain, including self-referential ones) and (ii) austerity (excluding events the agent deems impossible). It is one way of making precise certain requirements of embedded agency. We then present the Jeffrey–Bolker (JB) framework, which better accommodates an agent’s self-model and avoids forcing her to consider things she takes to be impossible.^[2]

1. Subjective Naturalism: Richness & Austerity

A naturalistic perspective treats an agent as part of the physical world—just another system subject to the same laws. Among other constraints, we think this means:

Richness: The model must include all the propositions the agent can meaningfully consider, including those about herself. If the agent can form a proposition “I will do X”, then that belongs in the space of propositions over which she has beliefs and (where appropriate) desirabilities.
Austerity: The model should only include events the agent thinks are genuinely possible. If she is certain something cannot happen, the theory shouldn’t force her to rank or measure preferences for that scenario. (Formally, we can regard zero-probability events as excluded from the relevant algebra.)

A decision-theoretic framework that meets both conditions is subjectively naturalist: it reflects the agent’s own worldview fully (richness) but doesn’t outstrip that worldview (austerity).

1.1. Framework vs. Action-Guiding Rule

In the literature, “decision theory” can refer to (at least) two different kinds of things:

A conceptual or mathematical framework for representing an agent’s beliefs, desires, and preferences. These frameworks show how one might encode uncertainty, evaluate outcomes, or measure utility—but they don’t necessarily dictate a unique rule for which choice to make in any given scenario.
A decision rule or algorithmic procedure for taking an action—e.g., “choose the act that maximizes expected utility according to these probabilities,” or “choose so as to maximize causal expected utility.”

When people say “vNM decision theory”, “Savage’s decision theory”, or “Jeffrey–Bolker,” they sometimes shift back and forth between framework-level discussion (how to model an agent’s preferenc...

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