@cite{qing-franke-2015} #

@cite{frank-goodman-2012} @cite{grice-1975} @cite{dale-reiter-1995}

"Variations on a Bayesian Theme: Comparing Bayesian Models of Referential Reasoning"

Paradigm #

Three objects varying on two dimensions (color × shape) in a reference game: {green_square, green_circle, blue_circle}. Speaker produces a single feature word; listener identifies the target object.

Utterances: {square, circle, green, blue}

The Decomposition #

The paper decomposes Bayesian reference games along 3 orthogonal dimensions, yielding a family of models that includes @cite{frank-goodman-2012} as one instance:

Speaker Belief (y ∈ {U, S}): What does L0 assume? #

Uniform (U): L0 treats all referents equally: U(t|m) = ⟦m⟧(t) / |⟦m⟧| (Eq. 1)
Salience (S): L0 weights by perceptual salience: S(t|m) = S(t) · ⟦m⟧(t) / Σ_t' S(t') · ⟦m⟧(t')

This enters the RSAConfig via meaning: uniform uses constant 1 for true worlds; salience uses S(w) for true worlds.

Speaker Goal (x ∈ {a, b}): What does the speaker optimize? #

Belief-oriented (b): maximize log-probability of correct belief σ_b(m|t) ∝ exp(λ_S · (log y(t|m) - Cost(m))) (Eq. 10)
Action-oriented (a): maximize probability of correct action σ_a(m|t) ∝ exp(λ_S · (y(t|m) - Cost(m))) (Eq. 9)

This enters via s1Score: belief-oriented uses log L0; action-oriented uses raw L0.

Listener Action: How does the listener choose? #

Belief-oriented (b): standard Bayesian update ρ_b(t|m) ∝ v(t) · σ(m|t) (Eq. 15)
Action-oriented (a): softmax over Bayesian posterior ρ_a(t|m) ∝ exp(α_L · ρ_b(t|m)) (Eq. 14)

The belief-oriented listener IS RSAConfig.L1. The action-oriented listener is a composable extension defined as softmax ∘ L1.

Speaker Models (4 variants) #

Model	Goal	Belief	S1 Score
σ_bU	belief	uniform	exp(λ · (log U(t\|m) - C(m)))
σ_aU	action	uniform	exp(λ · (U(t\|m) - C(m)))
σ_bS	belief	salience	exp(λ · (log S(t\|m) - C(m)))
σ_aS	action	salience	exp(λ · (S(t\|m) - C(m)))

σ_bU is standard RSA with utterance costs.

Key Findings #

Speaker data (Table 1, N=144 per target): σ_bU and σ_aU best explain production data (Table 3). Salience in the speaker does NOT help. Cost preference exists (c > 0).

Listener data (Table 2, N=180 per utterance): Salience-prior models dominate in model comparison (Table 4). Best overall: ρ_aS(σ_aU) with informed-correlated hyperprior.

Salience reversal: Uniform and salience priors make opposite L1 predictions for ambiguous utterances. For "circle", human data matches the salience direction (blue_circle: 117/180 = 65%). For "green", human data matches the pragmatic direction (green_circle: 115/180 = 64%), NOT salience.

Qualitative Findings #

#	Finding	Type	Config
1	`speaker_prefers_unique_shape`	S1: "square" > "green" for green_sq	σ_bU
2	`speaker_prefers_unique_color`	S1: "blue" > "circle" for blue_circ	σ_bU
3	`cost_breaks_symmetry`	S1: "circle" > "green" for green_circ	σ_bU
4	`no_cost_symmetry`	¬(S1 "circle" > "green" for green_circ)	σ_bU, no cost
5	`salience_reversal_circle`	uniform vs salience L1 flip for "circle"	σ_bU
6	`salience_reversal_green`	uniform vs salience L1 flip for "green"	σ_bU

Model	green_sq (sq > gr)	blue_circ (bl > ci)	green_circ (ci > gr)	Score
σ_bU	✓	✓	✓	3/3
σ_aU	✓	= (tie)	✓	2/3
σ_bS	✓	✗ (ci > bl)	✗ (gr > ci)	1/3
σ_aS	✓	✗ (ci > bl)	✓	2/3