Learning the Value of Value Learning

TL;DR

This work extends decision theory by formalizing axiological refinement within the Jeffrey-Bolker framework and proves a value-of-value-refinement theorem for a single agent. It then shows that refinement dissolves value dilemmas and converts zero-sum conflicts into positive-sum opportunities in two-player games, and expands Nash bargaining to yield Pareto improvements in expectation. The results rely on a Refinement Reflection Principle and a probabilistic model of refinement outcomes, unifying epistemic and axiological uncertainty. Together, the approach offers normative guidance on when and why reflecting on one’s values can improve both individual and collective decision-making across single-agent and strategic contexts.

Abstract

Standard decision frameworks addresses uncertainty about facts but assumes fixed values. We extend the Jeffrey-Bolker framework to model refinements in values and prove a value-of-information theorem for axiological refinement. In multi-agent settings, we establish that mutual refinement will characteristically transform zero-sum games into positive-sum interactions and yields Pareto-improving Nash bargains. These results show that a framework of rational choice can be extended to model value refinement and its associated benefits. By unifying epistemic and axiological refinement under a single formalism, we broaden the conceptual foundations of rational choice and illuminate the normative status of ethical deliberation.

Figures (6)

• Figure 1: Visualization of the realization of distinct values $V_1$ and $V_2$ by two acts: $a$ and $b$. The left vertical axis denotes the degree of realization of the first value $V_1$. The right vertical axis denotes the degree of realization of the second value $V_2$. The horizontal axis denotes the potential relative weight $p$ of each value, and $p^*$ denotes a particular commensuration of the two values into a single measure where $V_2$ composes a greater per-unit weight in the agent's utility.
• Figure 2: A binary refinement of act $A\in\mathbb{A}_0$. The initial act partition $\mathbb{A}_0$ consists of acts $A$ and $\neg A$. Refinement produces $\mathbb{A}_1$ by splitting $A$ into the more fine-grained acts $A \land B_1$ and $A \land B_2$.
• Figure 3: Refinement transforms commitment to an average of a coarse-grained bundle into the ability to select the best component among it fine-grained elements. Under RRP and refinement uncertainty, $\mathbb{E}_{\mu_A}[\max\{u_1,u_2\}] > \mathbb{E}_{\mu_A}[p u_1+(1-p)u_2]$. The expected maximum of a non-uniform bundle exceeds its expected mean.
• Figure 4: Visualization of how refinement can dissolve a value conflict with two value dimensions, $V_1$, $V_2$, and two acts, $A$, and $\neg A$. The left vertical axis denotes the degree of realization of the first value $V_1$; the right vertical axis denotes the degree of realization of the second $V_2$. Figure \ref{['fig:base']} shows the dilemmas: $A$ is favored by $V_1$ and $\neg A$ is favored by $V_2$. Figures \ref{['fig:variant1']} and \ref{['fig:variant2']} show two possible results of refining act $A$: In \ref{['fig:variant1']} the dilemma remains, while in \ref{['fig:variant2']} a dominating action $A \land B$ is revealed making commensuration unnecessary.
• Figure 5: Transformation of a 2×2 zero-sum game into a 2×3 game through refinement. The original action profile $(A^1, A^2)$ with payoffs $(v, -v)$ expands into a 2×2 subgame (upper-left quadrant of refined game) where payoffs are perturbed by independent noise terms $\epsilon^i_{ij}$.

Theorems & Definitions (24)

• Definition 5: Binary Refinement
• Definition 6: $k$-Ary Refinement
• Definition 7: Expansion via Catch-All
• Definition 8: Refinement Reflection Principle - General Form
• Definition 9: Refinement Reflection Principle - Binary Case
• Definition 10: Refinement Uncertainty
• Theorem 11: Value of Value Refinement
• Corollary 12: Monotonicity of Refinement Value
• Definition 13: Vanishing Returns
• Theorem 14: Optimal Refinement with Fixed Costs