Documentation

Linglib.Phenomena.Persuasion.Studies.BarnettEtAl2022

@cite{barnett-griffiths-hawkins-2022}: A Pragmatic Account of the Weak Evidence Effect #

@cite{barnett-griffiths-hawkins-2022}

Extends RSA with a persuasive speaker who has a goal state w* that may differ from the true world state w. The speaker's utility combines epistemic and persuasive components (Eq. 6):

U(u; w, w*) = U_epi(u; w) + β · U_pers(u; w*)

where U_epi = ln P_L0(w|u) and U_pers = ln P_L0(w*|u). The parameter β controls persuasive bias (β=0 recovers standard RSA).

Key Result: The Weak Evidence Effect #

When β > 0, weak positive evidence can backfire: a pragmatic listener who expects the speaker to show the strongest available evidence infers that the absence of strong evidence means it doesn't exist, shifting beliefs in the opposite direction.

Stick Contest Domain #

The paper's experiment uses 5 sticks from {1,...,9} (C(9,5)=126 worlds, midpoint 5). We formalize a simplified Stick Contest (3 sticks from {1,...,5}, 10 worlds, midpoint 3) that preserves the key structural properties: the prior favors ¬longer (P(longer)=0.4), and sticks have monotonically increasing L0(longer|·) values. The simplification enables verified interval arithmetic via rsa_predict.

RSAConfig Design #

The paper's Eq. 8 gives:

S(u|w, w*=longer, β) ∝ L0(longer|u)^β · 𝟙[u ∈ w]

Since the paper fixes α=1 and treats αβ as a single parameter, RSAConfig's α plays the role of β. The s1Score uses precomputed L0(longer|u) values squared (β=2), gated by stick availability.

Findings #

#	Finding	Theorem
1	L0: stick 5 is positive evidence for "longer"	`l0_s5_positive`
2	L0: stick 5 is the strongest evidence	`l0_s5_strongest`
3	L0: stick 1 is evidence against "longer"	`l0_s1_negative`
4	WEE: stick 4 backfires under L1 (β=2)	`weak_evidence_effect`
5	Strong evidence works: stick 5 favors "longer" under L1	`strong_evidence_works`
6	L0(longer	·) is monotone in stick length
7	Stick 4 has positive argStr yet backfires	`argStr_positive_but_backfires`
8	Model predicts the observed interaction effect	`model_predicts_interaction`
9	Pragmatic group shows backfire in experiment	`pragmatic_backfire`
10	RSA speaker-dependent model fits best	`rsa_speaker_dep_best_waic`

inductive Phenomena.Persuasion.Studies.BarnettEtAl2022.Stick :

Stick lengths 1–5

s1 : Stick
s2 : Stick
s3 : Stick
s4 : Stick
s5 : Stick

Instances For

instance Phenomena.Persuasion.Studies.BarnettEtAl2022.instDecidableEqStick :

DecidableEq Stick

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.instDecidableEqStick x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

instance Phenomena.Persuasion.Studies.BarnettEtAl2022.instBEqStick :

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.instBEqStick = { beq := Phenomena.Persuasion.Studies.BarnettEtAl2022.instBEqStick.beq }

def Phenomena.Persuasion.Studies.BarnettEtAl2022.instBEqStick.beq :

Stick → Stick → Bool

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.instBEqStick.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

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def Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprStick.repr :

Stick → ℕ → Std.Format

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instance Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprStick :

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprStick = { reprPrec := Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprStick.repr }

def Phenomena.Persuasion.Studies.BarnettEtAl2022.instInhabitedStick.default :

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.instInhabitedStick.default = Phenomena.Persuasion.Studies.BarnettEtAl2022.Stick.s1

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instance Phenomena.Persuasion.Studies.BarnettEtAl2022.instInhabitedStick :

Inhabited Stick

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.instInhabitedStick = { default := Phenomena.Persuasion.Studies.BarnettEtAl2022.instInhabitedStick.default }

instance Phenomena.Persuasion.Studies.BarnettEtAl2022.instFintypeStick :

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inductive Phenomena.Persuasion.Studies.BarnettEtAl2022.StickWorld :

Worlds: sets of 3 distinct sticks from {1,...,5}. C(5,3) = 10 worlds.

w123 : StickWorld
w124 : StickWorld
w125 : StickWorld
w134 : StickWorld
w135 : StickWorld
w145 : StickWorld
w234 : StickWorld
w235 : StickWorld
w245 : StickWorld
w345 : StickWorld

Instances For

instance Phenomena.Persuasion.Studies.BarnettEtAl2022.instDecidableEqStickWorld :

DecidableEq StickWorld

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.instDecidableEqStickWorld x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.Persuasion.Studies.BarnettEtAl2022.instBEqStickWorld.beq :

StickWorld → StickWorld → Bool

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.instBEqStickWorld.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

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instance Phenomena.Persuasion.Studies.BarnettEtAl2022.instBEqStickWorld :

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.instBEqStickWorld = { beq := Phenomena.Persuasion.Studies.BarnettEtAl2022.instBEqStickWorld.beq }

def Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprStickWorld.repr :

StickWorld → ℕ → Std.Format

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instance Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprStickWorld :

Repr StickWorld

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprStickWorld = { reprPrec := Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprStickWorld.repr }

instance Phenomena.Persuasion.Studies.BarnettEtAl2022.instInhabitedStickWorld :

Inhabited StickWorld

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Phenomena.Persuasion.Studies.BarnettEtAl2022.instInhabitedStickWorld = { default := Phenomena.Persuasion.Studies.BarnettEtAl2022.instInhabitedStickWorld.default }

def Phenomena.Persuasion.Studies.BarnettEtAl2022.instInhabitedStickWorld.default :

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Phenomena.Persuasion.Studies.BarnettEtAl2022.instInhabitedStickWorld.default = Phenomena.Persuasion.Studies.BarnettEtAl2022.StickWorld.w123

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instance Phenomena.Persuasion.Studies.BarnettEtAl2022.instFintypeStickWorld :

Fintype StickWorld

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def Phenomena.Persuasion.Studies.BarnettEtAl2022.worldContains :

StickWorld → Stick → Bool

Whether a stick is available in a given world.

Equations

Instances For

def Phenomena.Persuasion.Studies.BarnettEtAl2022.isLonger :

StickWorld → Bool

A world is "longer" if the average stick length exceeds the midpoint (3). Equivalently, sum > 9 for 3 sticks. 4 of 10 worlds qualify.

Equations

Instances For

def Phenomena.Persuasion.Studies.BarnettEtAl2022.l0LongerQ :

L0(longer|u) as ℚ for each stick. Each stick appears in C(4,2)=6 worlds; this gives the fraction where isLonger holds.

s1: 1/6 (only w145 is longer)
s2: 2/6 = 1/3 (w235, w245)
s3: 2/6 = 1/3 (w235, w345)
s4: 3/6 = 1/2 (w145, w245, w345)
s5: 4/6 = 2/3 (w145, w235, w245, w345)

Equations

Instances For

def Phenomena.Persuasion.Studies.BarnettEtAl2022.priorLonger :

Prior probability of "longer": 4 out of 10 worlds

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.priorLonger = 2 / 5

Instances For

def Phenomena.Persuasion.Studies.BarnettEtAl2022.s1ScoreQ (w : StickWorld) (u : Stick) :

S1 score as ℚ: L0(longer|u)^β · 𝟙[u ∈ w], at β=2. The squared L0 values are precomputed as literal fractions so that the reifier extracts concrete ℚ values from the ℚ→ℝ cast without needing to reduce function calls.

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noncomputable def Phenomena.Persuasion.Studies.BarnettEtAl2022.cfg :

RSA.RSAConfig Stick StickWorld

@cite{barnett-griffiths-hawkins-2022} RSA with persuasive speaker.

The s1Score implements Eq. 8: S(u|w, longer, β) ∝ L0(longer|u)^β · 𝟙[u ∈ w]. The score is precomputed as s1ScoreQ (ℚ) and cast to ℝ, so that rsa_predict's reifier can extract the rational value directly.

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theorem Phenomena.Persuasion.Studies.BarnettEtAl2022.l0_s5_positive :

cfg.L0_marginal () Stick.s5 isLonger > cfg.L0_marginal () Stick.s5 fun (w : StickWorld) => !isLonger w

L0(longer|s5) > L0(¬longer|s5): stick 5 is positive evidence for "longer". 4 of 6 worlds containing s5 are longer, vs 2 not-longer.

theorem Phenomena.Persuasion.Studies.BarnettEtAl2022.l0_s5_strongest :

cfg.L0_marginal () Stick.s5 isLonger > cfg.L0_marginal () Stick.s4 isLonger

L0(longer|s5) > L0(longer|s4): stick 5 provides stronger evidence than s4.

theorem Phenomena.Persuasion.Studies.BarnettEtAl2022.l0_s1_negative :

(cfg.L0_marginal () Stick.s1 fun (w : StickWorld) => !isLonger w) > cfg.L0_marginal () Stick.s1 isLonger

L0(¬longer|s1) > L0(longer|s1): stick 1 is evidence against "longer". Only 1 of 6 worlds containing s1 is longer.

L0(longer|·) is monotonically increasing in stick length. This structural property ensures the simplified domain faithfully mirrors the paper's full domain (Appendix Theorem 2).

theorem Phenomena.Persuasion.Studies.BarnettEtAl2022.weak_evidence_effect :

(cfg.L1_marginal Stick.s4 fun (w : StickWorld) => !isLonger w) > cfg.L1_marginal Stick.s4 isLonger

Weak evidence effect: at β=2, showing stick 4 (positive literal evidence) decreases the pragmatic listener's belief in "longer" below the prior.

The listener reasons: "If the true average were high, the speaker would have had stronger sticks (like 5) available and would have shown them instead. The fact that they showed a 4 implies they lacked stronger evidence."

L1 assigns more posterior mass to ¬longer than longer worlds after seeing s4.

theorem Phenomena.Persuasion.Studies.BarnettEtAl2022.strong_evidence_works :

cfg.L1_marginal Stick.s5 isLonger > cfg.L1_marginal Stick.s5 fun (w : StickWorld) => !isLonger w

Strong evidence does NOT backfire: stick 5 increases belief at β=2.

The strongest available evidence is always effective because it cannot be "explained away" by the absence of something better.

theorem Phenomena.Persuasion.Studies.BarnettEtAl2022.goalOriented_at_one (uEpi uPers : ℚ) :

RSA.CombinedUtility.goalOrientedUtility uEpi uPers 1 = RSA.CombinedUtility.combinedWeighted 1 1 uEpi uPers

At β=1, the persuasive utility equals combinedWeighted(1,1,...).

theorem Phenomena.Persuasion.Studies.BarnettEtAl2022.goalOriented_via_combined (uEpi uPers β : ℚ) (hβ : 0 ≤ β) :

RSA.CombinedUtility.goalOrientedUtility uEpi uPers β = (1 + β) * RSA.CombinedUtility.combined (RSA.CombinedUtility.betaToLam β) uEpi uPers

The paper's Eq. 6 (additive: U_epi + β·U_pers) equals (1+β) · combined(β/(1+β), U_epi, U_pers).

theorem Phenomena.Persuasion.Studies.BarnettEtAl2022.s4_positive_argStr :

RSA.ArgumentativeStrength.hasPositiveArgStr (l0LongerQ Stick.s4) priorLonger

Connection to ArgumentativeStrength: stick 4 has positive argumentative strength for the goal "longer" (L0(longer|s4) = 1/2 > 2/5 = P(longer)).

theorem Phenomena.Persuasion.Studies.BarnettEtAl2022.s3_not_positive_argStr :

¬RSA.ArgumentativeStrength.hasPositiveArgStr (l0LongerQ Stick.s3) priorLonger

Stick 3 does NOT have positive argumentative strength (L0(longer|s3) = 1/3 < 2/5 = P(longer)).

theorem Phenomena.Persuasion.Studies.BarnettEtAl2022.argStr_positive_but_backfires :

RSA.ArgumentativeStrength.hasPositiveArgStr (l0LongerQ Stick.s4) priorLonger ∧ (cfg.L1_marginal Stick.s4 fun (w : StickWorld) => !isLonger w) > cfg.L1_marginal Stick.s4 isLonger

The weak evidence effect shows that argumentatively positive evidence can still backfire under a pragmatic listener model. This is the core insight connecting @cite{barnett-griffiths-hawkins-2022} to @cite{cummins-franke-2021}'s work on argumentative strength.

Stick 4 has positive argStr at L0 (1/2 > 2/5), yet L1 assigns more mass to ¬longer than longer after seeing s4.

inductive Phenomena.Persuasion.Studies.BarnettEtAl2022.ListenerType :

Listener type inferred from speaker expectation phase

pragmatic : ListenerType
literal : ListenerType

Instances For

instance Phenomena.Persuasion.Studies.BarnettEtAl2022.instDecidableEqListenerType :

DecidableEq ListenerType

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.instDecidableEqListenerType x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

instance Phenomena.Persuasion.Studies.BarnettEtAl2022.instBEqListenerType :

BEq ListenerType

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.instBEqListenerType = { beq := Phenomena.Persuasion.Studies.BarnettEtAl2022.instBEqListenerType.beq }

def Phenomena.Persuasion.Studies.BarnettEtAl2022.instBEqListenerType.beq :

ListenerType → ListenerType → Bool

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.instBEqListenerType.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

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def Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprListenerType.repr :

ListenerType → ℕ → Std.Format

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instance Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprListenerType :

Repr ListenerType

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprListenerType = { reprPrec := Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprListenerType.repr }

inductive Phenomena.Persuasion.Studies.BarnettEtAl2022.EvidenceStrength :

Evidence strength conditions (distance from midpoint 5")

Instances For

instance Phenomena.Persuasion.Studies.BarnettEtAl2022.instDecidableEqEvidenceStrength :

DecidableEq EvidenceStrength

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.instDecidableEqEvidenceStrength x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.Persuasion.Studies.BarnettEtAl2022.instBEqEvidenceStrength.beq :

EvidenceStrength → EvidenceStrength → Bool

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.instBEqEvidenceStrength.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

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instance Phenomena.Persuasion.Studies.BarnettEtAl2022.instBEqEvidenceStrength :

BEq EvidenceStrength

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.instBEqEvidenceStrength = { beq := Phenomena.Persuasion.Studies.BarnettEtAl2022.instBEqEvidenceStrength.beq }

instance Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprEvidenceStrength :

Repr EvidenceStrength

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprEvidenceStrength = { reprPrec := Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprEvidenceStrength.repr }

def Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprEvidenceStrength.repr :

EvidenceStrength → ℕ → Std.Format

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inductive Phenomena.Persuasion.Studies.BarnettEtAl2022.FirstContestant :

Which contestant goes first

longBiased : FirstContestant
shortBiased : FirstContestant

Instances For

instance Phenomena.Persuasion.Studies.BarnettEtAl2022.instDecidableEqFirstContestant :

DecidableEq FirstContestant

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.instDecidableEqFirstContestant x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.Persuasion.Studies.BarnettEtAl2022.instBEqFirstContestant.beq :

FirstContestant → FirstContestant → Bool

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.instBEqFirstContestant.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

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instance Phenomena.Persuasion.Studies.BarnettEtAl2022.instBEqFirstContestant :

BEq FirstContestant

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.instBEqFirstContestant = { beq := Phenomena.Persuasion.Studies.BarnettEtAl2022.instBEqFirstContestant.beq }

instance Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprFirstContestant :

Repr FirstContestant

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprFirstContestant = { reprPrec := Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprFirstContestant.repr }

def Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprFirstContestant.repr :

FirstContestant → ℕ → Std.Format

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structure Phenomena.Persuasion.Studies.BarnettEtAl2022.StickContestDesign :

Stick Contest design parameters

nSticks : ℕ
minLength : ℕ
maxLength : ℕ
midpoint : ℕ
nParticipants : ℕ

Instances For

def Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprStickContestDesign.repr :

StickContestDesign → ℕ → Std.Format

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instance Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprStickContestDesign :

Repr StickContestDesign

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprStickContestDesign = { reprPrec := Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprStickContestDesign.repr }

def Phenomena.Persuasion.Studies.BarnettEtAl2022.design :

StickContestDesign

The actual experimental parameters

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.design = { nSticks := 5, minLength := 1, maxLength := 9, midpoint := 5, nParticipants := 723 }

Instances For

def Phenomena.Persuasion.Studies.BarnettEtAl2022.pragmaticProportion :

Proportion expecting strongest evidence (pragmatic listeners)

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.pragmaticProportion = 485 / 723

Instances For

def Phenomena.Persuasion.Studies.BarnettEtAl2022.literalProportion :

Proportion expecting weaker evidence (literal listeners)

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.literalProportion = 238 / 723

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theorem Phenomena.Persuasion.Studies.BarnettEtAl2022.pragmatic_is_majority :

pragmaticProportion > 1 / 2

structure Phenomena.Persuasion.Studies.BarnettEtAl2022.InteractionEffect :

Key interaction: speaker expectations × evidence strength. t(718) = 5.2, p < 0.001 (p. 175)

tStatistic : ℚ
df : ℕ
pLessThan : ℚ

Instances For

def Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprInteractionEffect.repr :

InteractionEffect → ℕ → Std.Format

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instance Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprInteractionEffect :

Repr InteractionEffect

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprInteractionEffect = { reprPrec := Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprInteractionEffect.repr }

def Phenomena.Persuasion.Studies.BarnettEtAl2022.interactionEffect :

InteractionEffect

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.interactionEffect = { tStatistic := 52 / 10, df := 718, pLessThan := 1 / 1000 }

Instances For

structure Phenomena.Persuasion.Studies.BarnettEtAl2022.GroupResult :

Behavioral result for a listener group

listenerType : ListenerType
nParticipants : ℕ
meanSlider : ℚ
ci95Lower : Option ℚ
ci95Upper : Option ℚ

Instances For

def Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprGroupResult.repr :

GroupResult → ℕ → Std.Format

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instance Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprGroupResult :

Repr GroupResult

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprGroupResult = { reprPrec := Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprGroupResult.repr }

def Phenomena.Persuasion.Studies.BarnettEtAl2022.pragmaticResult :

Pragmatic group: weak evidence backfires (mean below 50). 95% CI: [32.3, 37.3] (paper p. 175).

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def Phenomena.Persuasion.Studies.BarnettEtAl2022.literalResult :

Literal group: no weak evidence effect (mean at 50). CIs not reported in paper.

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theorem Phenomena.Persuasion.Studies.BarnettEtAl2022.pragmatic_backfire :

pragmaticResult.meanSlider < 50

Pragmatic group shows backfire: mean significantly below 50 (midpoint)

theorem Phenomena.Persuasion.Studies.BarnettEtAl2022.literal_no_backfire :

literalResult.meanSlider > 49

Literal group shows no backfire: mean at midpoint

theorem Phenomena.Persuasion.Studies.BarnettEtAl2022.groups_differ :

pragmaticResult.meanSlider < literalResult.meanSlider

The two groups differ in the predicted direction

inductive Phenomena.Persuasion.Studies.BarnettEtAl2022.ModelFamily :

Model families compared

anchorAdjust : ModelFamily
minAcceptable : ModelFamily
rsaPragmatic : ModelFamily

Instances For

instance Phenomena.Persuasion.Studies.BarnettEtAl2022.instDecidableEqModelFamily :

DecidableEq ModelFamily

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.instDecidableEqModelFamily x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.Persuasion.Studies.BarnettEtAl2022.instBEqModelFamily.beq :

ModelFamily → ModelFamily → Bool

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.instBEqModelFamily.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

Instances For

instance Phenomena.Persuasion.Studies.BarnettEtAl2022.instBEqModelFamily :

BEq ModelFamily

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.instBEqModelFamily = { beq := Phenomena.Persuasion.Studies.BarnettEtAl2022.instBEqModelFamily.beq }

def Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprModelFamily.repr :

ModelFamily → ℕ → Std.Format

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instance Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprModelFamily :

Repr ModelFamily

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprModelFamily = { reprPrec := Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprModelFamily.repr }

inductive Phenomena.Persuasion.Studies.BarnettEtAl2022.ModelVariant :

Model variant (how individual differences are handled)

homogeneous : ModelVariant
heterogeneous : ModelVariant
speakerDependent : ModelVariant

Instances For

instance Phenomena.Persuasion.Studies.BarnettEtAl2022.instDecidableEqModelVariant :

DecidableEq ModelVariant

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.instDecidableEqModelVariant x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

instance Phenomena.Persuasion.Studies.BarnettEtAl2022.instBEqModelVariant :

BEq ModelVariant

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.instBEqModelVariant = { beq := Phenomena.Persuasion.Studies.BarnettEtAl2022.instBEqModelVariant.beq }

def Phenomena.Persuasion.Studies.BarnettEtAl2022.instBEqModelVariant.beq :

ModelVariant → ModelVariant → Bool

Equations

Phenomena.Persuasion.Studies.BarnettEtAl2022.instBEqModelVariant.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

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def Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprModelVariant.repr :

ModelVariant → ℕ → Std.Format

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instance Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprModelVariant :

Repr ModelVariant

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Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprModelVariant = { reprPrec := Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprModelVariant.repr }

structure Phenomena.Persuasion.Studies.BarnettEtAl2022.ModelComparisonDatum :

Model comparison result from Table 1

family : ModelFamily
variant : ModelVariant
logLikelihood : ℚ
waic : ℚ
waicSE : ℚ
psisLoo : ℚ
psisLooSE : ℚ

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instance Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprModelComparisonDatum :

Repr ModelComparisonDatum

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Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprModelComparisonDatum = { reprPrec := Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprModelComparisonDatum.repr }

def Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprModelComparisonDatum.repr :

ModelComparisonDatum → ℕ → Std.Format

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def Phenomena.Persuasion.Studies.BarnettEtAl2022.modelComparison :

List ModelComparisonDatum

Table 1 data

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theorem Phenomena.Persuasion.Studies.BarnettEtAl2022.rsa_speaker_dep_best_likelihood :

12 > 82 / 10

The RSA speaker-dependent model has the best (highest) log-likelihood

theorem Phenomena.Persuasion.Studies.BarnettEtAl2022.rsa_speaker_dep_best_waic :

-164 / 10 < -133 / 10

The RSA speaker-dependent model has the best (lowest) WAIC

structure Phenomena.Persuasion.Studies.BarnettEtAl2022.FittedParams :

Fitted parameters for the best model (RSA speaker-dependent). β̂ = 2.26 and mixture weights from main text (p. 178); β̄ = 2.03 and ō = −0.13 from Fig 3B caption (p. 177).

betaMAP : ℚ
betaCV : ℚ
responseOffsetCV : ℚ
pragmaticMixWeight : ℚ
literalMixWeight : ℚ

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instance Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprFittedParams :

Repr FittedParams

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Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprFittedParams = { reprPrec := Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprFittedParams.repr }

def Phenomena.Persuasion.Studies.BarnettEtAl2022.instReprFittedParams.repr :

FittedParams → ℕ → Std.Format

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def Phenomena.Persuasion.Studies.BarnettEtAl2022.bestModelParams :

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theorem Phenomena.Persuasion.Studies.BarnettEtAl2022.beta_positive :

bestModelParams.betaMAP > 0

β > 0 provides strong support for non-zero persuasive bias

theorem Phenomena.Persuasion.Studies.BarnettEtAl2022.pragmatic_group_uses_j1 :

bestModelParams.pragmaticMixWeight > 9 / 10

Pragmatic group is best explained by J1 (pragmatic listener model)

theorem Phenomena.Persuasion.Studies.BarnettEtAl2022.literal_group_uses_j0 :

bestModelParams.literalMixWeight < 2 / 10

Literal group is best explained by J0 (literal listener model)

The RSA model predicts the qualitative pattern underlying the observed interaction between listener type and evidence strength (t(718) = 5.2, p < 0.001). The literal model (L0) assigns s4 positive argumentative strength, predicting no backfire. The pragmatic model (L1) shows backfire. The experiment confirms exactly this divergence: pragmatic participants' mean (34.7) falls below neutral (50), while literal participants' mean (50.1) does not.