Clarification: When to Ask vs. When to Act

@cite{raiffa-schlaifer-1961}

When agents face uncertainty about an interlocutor's goals, they choose between acting under uncertainty and asking clarification questions (CQs). Both @cite{tsvilodub-etal-2026} and @cite{dong-etal-2026} find that this choice is governed by the expected value of perfect information (EVPI): agents clarify when EVPI exceeds communication cost.

EVPI captures the interaction of uncertainty and stakes — it is high when (a) uncertainty is high AND (b) acting incorrectly is costly. This interaction is the core empirical finding shared by both papers.

Connection to existing infrastructure

EVPI is the maximum possible questionUtility (@cite{van-rooy-2003}): it equals questionUtility on the identity partition, where each world is its own cell. Any specific clarification question yields at most EVPI.

def Phenomena.Clarification.bestUtilityAt {W : Type u_1} {A : Type u_2} (dp : Core.DecisionTheory.DecisionProblem W A) (actions : Finset A) (w : W) : ℚ

Maximum utility achievable at world w across actions.

With Finset actions, this is sup' over utilities at world w.

Equations

• Phenomena.Clarification.bestUtilityAt dp actions w = if h : actions.Nonempty then actions.sup' h (dp.utility w) else 0

def Phenomena.Clarification.oracleValue {W : Type u_1} {A : Type u_2} [Fintype W] (dp : Core.DecisionTheory.DecisionProblem W A) (actions : Finset A) : ℚ

Oracle value: expected utility under perfect information. Σ_w P(w) · max_a U(w, a)

Equations

• Phenomena.Clarification.oracleValue dp actions = ∑ w : W, dp.prior w * Phenomena.Clarification.bestUtilityAt dp actions w

def Phenomena.Clarification.evpi {W : Type u_1} {A : Type u_2} [Fintype W] [DecidableEq W] (dp : Core.DecisionTheory.DecisionProblem W A) (actions : Finset A) : ℚ

Expected value of perfect information (EVPI).

EVPI = oracleValue − dpValue = Σ_w P(w) · max_a U(w,a) − max_a Σ_w P(w) · U(w,a)

Equivalently, the expected regret of the current best action (@cite{tsvilodub-etal-2026}), or the upper bound on VoI for any question (@cite{dong-etal-2026}).

@cite{raiffa-schlaifer-1961}

Equations

• Phenomena.Clarification.evpi dp actions = Phenomena.Clarification.oracleValue dp actions - Core.DecisionTheory.dpValue dp actions

theorem Phenomena.Clarification.evpi_nonneg {W : Type u_1} {A : Type u_2} [Fintype W] [DecidableEq W] (dp : Core.DecisionTheory.DecisionProblem W A) (actions : Finset A) (hprior : ∀ (w : W), 0 ≤ dp.prior w) (hne : actions.Nonempty) : 0 ≤ evpi dp actions

EVPI is non-negative: acting with perfect information is at least as good as acting without.

Proof sketch: For each action a, its expected utility EU(a) equals Σ_w P(w) · U(w,a). The oracle value Σ_w P(w) · max_a' U(w,a') is pointwise ≥ Σ_w P(w) · U(w,a) since max_a' U(w,a') ≥ U(w,a). Therefore oracleValue ≥ EU(a) for every a, hence oracleValue ≥ max_a EU(a) = dpValue.