Search Efficiency in Reference Production

@cite{giles-etal-2026}

The search efficiency view of overinformativeness: speakers produce redundant modifiers when the modifier facilitates the listener's perceptual search for the referent. An expression is search-efficient when its production cost (to the speaker) is outweighed by its search benefit (to the listener).

Three Factors

Search efficiency depends on three perceptual properties of the display:

1. Discriminability: How easy is it to tell the target's attribute value apart from distractors' values? High discriminability → easy search along that attribute. Operationalised via psychophysical staircases in @cite{giles-etal-2026}.

2. Contextual distinctiveness: What fraction of items in the display share the target's attribute value? When the target is unique on an attribute (high distinctiveness), mentioning that attribute enables immediate filtering.

3. Display density: How many items are in the display? More items → slower serial search, increasing the benefit of any filtering cue.

Connection to RSA

In the cs-RSA framework (@cite{degen-etal-2020}), search efficiency enters through the noise parameters. High discriminability corresponds to a large noise gap (match − mismatch), which makes the redundant modifier informative to L0 even when it doesn't change the Boolean denotation.

The search efficiency view adds a perceptual grounding for the noise parameters: they reflect the physical properties of the display, not just abstract semantic noise.

structure Core.SearchEfficiency.SearchContext : Type

A referential display characterised by its search-relevant properties. These three factors jointly determine the listener's search cost and the potential benefit of a redundant modifier.

@cite{giles-etal-2026} Exp 1 manipulates discriminability × sufficiency; Exp 2 compares attribute types (colour vs orientation) across display density and contextual distinctiveness levels.

• displaySize : ℕ

  Display density: total number of objects in the display. More objects → slower serial search.

• nDistractorsSharing : ℕ

  Contextual distinctiveness: number of objects sharing the target's value on the redundant attribute. 0 = target is unique; displaySize − 1 = all objects share the value.

• discriminability : ℚ

  Perceptual discriminability of the redundant attribute: the noise gap (match − mismatch) from RSA.Noise. Range: 0 (no discrimination) to 1 (perfect).

• domain : PropertyDomain

  The redundant attribute's property domain.

instance Core.SearchEfficiency.instReprSearchContext : Repr SearchContext

Equations

• Core.SearchEfficiency.instReprSearchContext = { reprPrec := Core.SearchEfficiency.instReprSearchContext.repr }

def Core.SearchEfficiency.instReprSearchContext.repr : SearchContext → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

inductive Core.SearchEfficiency.Sufficiency : Type

Whether an attribute is informationally sufficient to identify the target: the attribute value uniquely picks out the target among all objects in the display.

• sufficient : Sufficiency

  The attribute alone identifies the target.

• redundant : Sufficiency

  The attribute does not alone identify the target; it is redundant when paired with a sufficient attribute.

instance Core.SearchEfficiency.instReprSufficiency : Repr Sufficiency

Equations

• Core.SearchEfficiency.instReprSufficiency = { reprPrec := Core.SearchEfficiency.instReprSufficiency.repr }

def Core.SearchEfficiency.instReprSufficiency.repr : Sufficiency → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

instance Core.SearchEfficiency.instDecidableEqSufficiency : DecidableEq Sufficiency

Equations

• Core.SearchEfficiency.instDecidableEqSufficiency x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Core.SearchEfficiency.instBEqSufficiency.beq : Sufficiency → Sufficiency → Bool

Equations

• Core.SearchEfficiency.instBEqSufficiency.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Core.SearchEfficiency.instBEqSufficiency : BEq Sufficiency

Equations

• Core.SearchEfficiency.instBEqSufficiency = { beq := Core.SearchEfficiency.instBEqSufficiency.beq }

inductive Core.SearchEfficiency.DisplayType : Type

The experimental conditions from @cite{giles-etal-2026} Exp 1, defined by the sufficiency × discriminability interaction.

• sHighRLow : DisplayType

  Sufficient attribute: high discriminability, Redundant attribute: low discriminability. Search efficiency predicts LOW overinformativeness: the sufficient attribute is already search-efficient.

• sLowRHigh : DisplayType

  Sufficient attribute: low discriminability, Redundant attribute: high discriminability. Search efficiency predicts HIGH overinformativeness: the redundant attribute helps an otherwise difficult search.

• baseline : DisplayType

  Both attributes: high discriminability. Tests whether speakers mention all discriminable attributes or selectively overinform to help difficult searches.

def Core.SearchEfficiency.instReprDisplayType.repr : DisplayType → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

instance Core.SearchEfficiency.instReprDisplayType : Repr DisplayType

Equations

• Core.SearchEfficiency.instReprDisplayType = { reprPrec := Core.SearchEfficiency.instReprDisplayType.repr }

instance Core.SearchEfficiency.instDecidableEqDisplayType : DecidableEq DisplayType

Equations

• Core.SearchEfficiency.instDecidableEqDisplayType x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

instance Core.SearchEfficiency.instBEqDisplayType : BEq DisplayType

Equations

• Core.SearchEfficiency.instBEqDisplayType = { beq := Core.SearchEfficiency.instBEqDisplayType.beq }

def Core.SearchEfficiency.instBEqDisplayType.beq : DisplayType → DisplayType → Bool

Equations

• Core.SearchEfficiency.instBEqDisplayType.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

def Core.SearchEfficiency.searchEfficiencyPredicts (dt : DisplayType) : Bool

The core prediction of the search efficiency view: overinformativeness should track the interaction of sufficiency and discriminability.

When the sufficient attribute is hard to search (low discriminability) and the redundant attribute is easy (high discriminability), speakers overinform to help the listener's search. When the sufficient attribute is already search-efficient, redundancy adds no benefit.

Equations

• Core.SearchEfficiency.searchEfficiencyPredicts Core.SearchEfficiency.DisplayType.sLowRHigh = true
• Core.SearchEfficiency.searchEfficiencyPredicts Core.SearchEfficiency.DisplayType.baseline = false
• Core.SearchEfficiency.searchEfficiencyPredicts Core.SearchEfficiency.DisplayType.sHighRLow = false