@cite{degen-etal-2020} #

@cite{frank-goodman-2012} @cite{dale-reiter-1995} @cite{engelhardt-etal-2006} @cite{grice-1975} @cite{kursat-degen-2021}

When Redundancy Is Useful: A Bayesian Approach to "Overinformative" Referring Expressions. Psychological Review 127(4), 591–621.

Core Argument #

Standard RSA with Boolean semantics (φ ∈ {0,1}) predicts no preference for overmodified referring expressions — if "small" alone identifies the target, adding "blue" is literally uninformative. But speakers routinely overmodify (~31% in @cite{engelhardt-etal-2006}), with color mentioned redundantly more often than size.

cs-RSA replaces Boolean denotations with continuous semantics: φ(u, o) ∈ [0,1] via a Product of Experts (PoE) model. Each feature dimension acts as an independent noisy channel:

φ(u, o) = φ_size(u, o) · φ_color(u, o)

where φ_color = match_val if colors agree, mismatch_val otherwise (and similarly for size). The asymmetry between color and size arises from differing noise levels:

color: match = 0.99, mismatch = 0.01 → discrimination = 0.98
size:  match = 0.80, mismatch = 0.20 → discrimination = 0.60

Adding a redundant color modifier (high discrimination) sharpens the listener's posterior more than adding redundant size would → speakers overmodify with color more.

Scene (§2 demonstration) #

Three objects: {big blue pin, big red pin, small blue pin (TARGET)}.

| Object    | Size  | Color |
|-----------|-------|-------|
| bigBlue   | big   | blue  |
| bigRed    | big   | red   |
| smallBlue | small | blue  |  ← TARGET

Size-sufficient: only the target is small, so "small" uniquely identifies
Color-redundant: two objects are blue, so "blue" alone does not identify

Seven utterances: {"big", "small", "blue", "red", "big blue", "big red", "small blue"} (all followed by implicit "pin").

Architecture #

L0(o|u) ∝ φ(u, o)
S1(u|w) ∝ exp(α · log L0(w|u) − β_c · cost(u))

BDA-fitted cost β_c ≈ 0, placing the model in the No-Brevity regime. With α = 1 and β_c = 0, S1(u|w) ∝ L0(w|u).

NOTE: The paper's Table 2 uses L0(o|u) ∝ exp(φ(u,o)) (WebPPL factor convention). Our formalization uses L0 ∝ φ (matching the paper's eq. 1 directly). Both give identical S1 orderings since exp is monotone; the numerical L0 values differ but the qualitative predictions are the same.

Verified Predictions #

cs-RSA: S1 prefers overmodified "small blue" > sufficient "small"
cs-RSA: sufficient "small" > redundant "blue" (size principle)
cs-RSA: full 7-utterance S1 ordering at target
Boolean RSA: no overmodification preference (smallBlue tied with small)
Connection: cost = 0 ↔ @cite{dale-reiter-1995} No-Brevity (strength 0)
Connection: noise discrimination ordering grounds the asymmetry
Connection: explains @cite{engelhardt-etal-2006}'s ~31% over-description
Exp 2: typicality predicts color modifier production (β = −4.17, p < .0001)
Exp 3: informativeness hierarchy predicts nominal choice (β = 2.11, p < .0001)
Exp 3: typicality predicts subordinate use (β = 4.82, p < .001)
Bridge: noise (adjectives) and typicality (nouns) are parallel mechanisms

Verified Data #

Exp 1 (§3): main effect of sufficient property β = 3.54, SE = .22, p < .0001; interaction β = 2.26, SE = .74, p < .003. BDA-fitted noise parameters (Figure 10 caption): MAP x_color = .88, MAP x_size = .79, confirming color > size discrimination. Fitted β_c values near zero.

Exp 2 (§4.3): typicality β = −4.17, SE = .45, p < .0001; informativeness β = −5.56, SE = .33, p < .0001; color competitor β = 0.71, SE = .16, p < .0001.

Exp 3 (§5.2): sub necessary β = 2.11, SE = .17, p < .0001; basic vs super β = .60, SE = .15, p < .0001; typicality β = 4.82, SE = 1.35, p < .001; length β = −.95, SE = .27, p < .001; frequency β = .08, SE = .11, NS. BDA (§5.3, Figure 19): β_fixed MAP = 0.004, β_i MAP = 19.8, β_t MAP = 0.57, β_F MAP = 0.02, β_L MAP = 2.69.

Utterance	bigBlue	bigRed	smallBlue
big	sizeMatch (0.80)	sizeMatch (0.80)	sizeMismatch (0.20)
small	sizeMismatch	sizeMismatch	sizeMatch (0.80)
blue	colorMatch (0.99)	colorMismatch	colorMatch (0.99)
red	colorMismatch	colorMatch (0.99)	colorMismatch
big blue	sM·cM (0.792)	sM·cMM (0.008)	sMM·cM (0.198)
big red	sM·cMM (0.008)	sM·cM (0.792)	sMM·cMM (0.002)
small blue	sMM·cM (0.198)	sMM·cMM (0.002)	sM·cM (0.792)

Property	IA (D&R 1995)	cs-RSA
Output	deterministic	probabilistic (soft-max)
Brevity	No-Brevity	No-Brevity (β_c ≈ 0)
Overmod rate	fixed by order	varies with noise params
Color > size	from pref. order	from noise asymmetry

Phenomenon	Modifiers (Exp 1)	Nouns (Exp 3)
Sufficient	"small" (size)	"dog" (basic level)
Overinformative	"small blue" (+ color)	"dalmatian" (sub level)
Continuous φ	noise channels	typicality ratings
cs-RSA	overmod > sufficient	overspec > sufficient
Boolean	overmod = sufficient	overspec = sufficient

Cost c	Modifiers	Nouns
0	overmod > suff	overspec > basic
1/10	overmod > suff	overspec > basic
3/20	overmod > suff	basic > overspec
1/5	suff > overmod	basic > overspec
1/4	suff > overmod	basic > overspec

Utterance	dalmatian	cat	bird
sub	19/20	1/100	1/100
basic	4/5	1/20	1/20
super	7/10	7/10	7/10

Prediction	cs-RSA	Boolean
Exp 1: overmod > suff	✓	✗
Exp 3: overspec > suff	✓	✗