Documentation

Linglib.Phenomena.ScalarImplicatures.WeakEvidenceEffect

Weak Evidence Effect: Empirical Data #

@cite{barnett-griffiths-hawkins-2022}

Experimental data from @cite{barnett-griffiths-hawkins-2022} on how weak positive evidence can backfire when listeners expect speakers to have persuasive goals.

The Stick Contest #

Two contestants each want to convince a judge that the average of 5 hidden sticks (1"–9") is longer (or shorter) than the midpoint (5"). Each reveals one stick. Participants play both the speaker role (expectation phase) and judge role (listener judgment phase).

Key Findings #

67% of participants expected speakers to show the strongest evidence
For this group, weak evidence backfired (m = 34.7 on 0–100 scale, vs 50 midpoint)
The speaker-dependent RSA model outperforms anchor-and-adjust alternatives

inductive Phenomena.ScalarImplicatures.WeakEvidenceEffect.ListenerType :

Listener type inferred from speaker expectation phase

pragmatic : ListenerType
literal : ListenerType

Instances For

instance Phenomena.ScalarImplicatures.WeakEvidenceEffect.instDecidableEqListenerType :

DecidableEq ListenerType

Equations

Phenomena.ScalarImplicatures.WeakEvidenceEffect.instDecidableEqListenerType x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.ScalarImplicatures.WeakEvidenceEffect.instBEqListenerType.beq :

ListenerType → ListenerType → Bool

Equations

Phenomena.ScalarImplicatures.WeakEvidenceEffect.instBEqListenerType.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

Instances For

instance Phenomena.ScalarImplicatures.WeakEvidenceEffect.instBEqListenerType :

BEq ListenerType

Equations

Phenomena.ScalarImplicatures.WeakEvidenceEffect.instBEqListenerType = { beq := Phenomena.ScalarImplicatures.WeakEvidenceEffect.instBEqListenerType.beq }

instance Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprListenerType :

Repr ListenerType

Equations

Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprListenerType = { reprPrec := Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprListenerType.repr }

def Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprListenerType.repr :

ListenerType → ℕ → Std.Format

Equations

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

Instances For

inductive Phenomena.ScalarImplicatures.WeakEvidenceEffect.EvidenceStrength :

Evidence strength conditions (distance from midpoint 5")

Instances For

instance Phenomena.ScalarImplicatures.WeakEvidenceEffect.instDecidableEqEvidenceStrength :

DecidableEq EvidenceStrength

Equations

Phenomena.ScalarImplicatures.WeakEvidenceEffect.instDecidableEqEvidenceStrength x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.ScalarImplicatures.WeakEvidenceEffect.instBEqEvidenceStrength.beq :

EvidenceStrength → EvidenceStrength → Bool

Equations

Phenomena.ScalarImplicatures.WeakEvidenceEffect.instBEqEvidenceStrength.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

Instances For

instance Phenomena.ScalarImplicatures.WeakEvidenceEffect.instBEqEvidenceStrength :

BEq EvidenceStrength

Equations

Phenomena.ScalarImplicatures.WeakEvidenceEffect.instBEqEvidenceStrength = { beq := Phenomena.ScalarImplicatures.WeakEvidenceEffect.instBEqEvidenceStrength.beq }

instance Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprEvidenceStrength :

Repr EvidenceStrength

Equations

Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprEvidenceStrength = { reprPrec := Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprEvidenceStrength.repr }

def Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprEvidenceStrength.repr :

EvidenceStrength → ℕ → Std.Format

Equations

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

Instances For

inductive Phenomena.ScalarImplicatures.WeakEvidenceEffect.FirstContestant :

Which contestant goes first

longBiased : FirstContestant
shortBiased : FirstContestant

Instances For

instance Phenomena.ScalarImplicatures.WeakEvidenceEffect.instDecidableEqFirstContestant :

DecidableEq FirstContestant

Equations

Phenomena.ScalarImplicatures.WeakEvidenceEffect.instDecidableEqFirstContestant x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

instance Phenomena.ScalarImplicatures.WeakEvidenceEffect.instBEqFirstContestant :

BEq FirstContestant

Equations

Phenomena.ScalarImplicatures.WeakEvidenceEffect.instBEqFirstContestant = { beq := Phenomena.ScalarImplicatures.WeakEvidenceEffect.instBEqFirstContestant.beq }

def Phenomena.ScalarImplicatures.WeakEvidenceEffect.instBEqFirstContestant.beq :

FirstContestant → FirstContestant → Bool

Equations

Phenomena.ScalarImplicatures.WeakEvidenceEffect.instBEqFirstContestant.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

Instances For

def Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprFirstContestant.repr :

FirstContestant → ℕ → Std.Format

Equations

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

Instances For

instance Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprFirstContestant :

Repr FirstContestant

Equations

Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprFirstContestant = { reprPrec := Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprFirstContestant.repr }

structure Phenomena.ScalarImplicatures.WeakEvidenceEffect.StickContestDesign :

Stick Contest design parameters

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

Instances For

instance Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprStickContestDesign :

Repr StickContestDesign

Equations

Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprStickContestDesign = { reprPrec := Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprStickContestDesign.repr }

def Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprStickContestDesign.repr :

StickContestDesign → ℕ → Std.Format

Equations

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

Instances For

def Phenomena.ScalarImplicatures.WeakEvidenceEffect.design :

StickContestDesign

The actual experimental parameters

Equations

Phenomena.ScalarImplicatures.WeakEvidenceEffect.design = { nSticks := 5, minLength := 1, maxLength := 9, midpoint := 5, nParticipants := 723 }

Instances For

def Phenomena.ScalarImplicatures.WeakEvidenceEffect.pragmaticProportion :

Proportion expecting strongest evidence (pragmatic listeners)

Equations

Phenomena.ScalarImplicatures.WeakEvidenceEffect.pragmaticProportion = 485 / 723

Instances For

def Phenomena.ScalarImplicatures.WeakEvidenceEffect.literalProportion :

Proportion expecting weaker evidence (literal listeners)

Equations

Phenomena.ScalarImplicatures.WeakEvidenceEffect.literalProportion = 238 / 723

Instances For

theorem Phenomena.ScalarImplicatures.WeakEvidenceEffect.pragmatic_is_majority :

pragmaticProportion > 1 / 2

structure Phenomena.ScalarImplicatures.WeakEvidenceEffect.InteractionEffect :

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

tStatistic : ℚ
df : ℕ
pLessThan : ℚ

Instances For

def Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprInteractionEffect.repr :

InteractionEffect → ℕ → Std.Format

Equations

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

Instances For

instance Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprInteractionEffect :

Repr InteractionEffect

Equations

Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprInteractionEffect = { reprPrec := Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprInteractionEffect.repr }

def Phenomena.ScalarImplicatures.WeakEvidenceEffect.interactionEffect :

InteractionEffect

Equations

Phenomena.ScalarImplicatures.WeakEvidenceEffect.interactionEffect = { tStatistic := 52 / 10, df := 718, pLessThan := 1 / 1000 }

Instances For

structure Phenomena.ScalarImplicatures.WeakEvidenceEffect.GroupResult :

Behavioral result for a listener group

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

Instances For

def Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprGroupResult.repr :

GroupResult → ℕ → Std.Format

Equations

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

Instances For

instance Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprGroupResult :

Repr GroupResult

Equations

Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprGroupResult = { reprPrec := Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprGroupResult.repr }

def Phenomena.ScalarImplicatures.WeakEvidenceEffect.pragmaticResult :

Pragmatic group: weak evidence backfires (mean below 50)

Equations

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

Instances For

def Phenomena.ScalarImplicatures.WeakEvidenceEffect.literalResult :

Literal group: no weak evidence effect (mean at 50)

Equations

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

Instances For

theorem Phenomena.ScalarImplicatures.WeakEvidenceEffect.pragmatic_backfire :

pragmaticResult.meanSlider < 50

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

theorem Phenomena.ScalarImplicatures.WeakEvidenceEffect.literal_no_backfire :

literalResult.meanSlider > 49

Literal group shows no backfire: mean at midpoint

theorem Phenomena.ScalarImplicatures.WeakEvidenceEffect.groups_differ :

pragmaticResult.meanSlider < literalResult.meanSlider

The two groups differ in the predicted direction

inductive Phenomena.ScalarImplicatures.WeakEvidenceEffect.ModelFamily :

Model families compared

anchorAdjust : ModelFamily
minAcceptable : ModelFamily
rsaPragmatic : ModelFamily

Instances For

instance Phenomena.ScalarImplicatures.WeakEvidenceEffect.instDecidableEqModelFamily :

DecidableEq ModelFamily

Equations

Phenomena.ScalarImplicatures.WeakEvidenceEffect.instDecidableEqModelFamily x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

instance Phenomena.ScalarImplicatures.WeakEvidenceEffect.instBEqModelFamily :

BEq ModelFamily

Equations

Phenomena.ScalarImplicatures.WeakEvidenceEffect.instBEqModelFamily = { beq := Phenomena.ScalarImplicatures.WeakEvidenceEffect.instBEqModelFamily.beq }

def Phenomena.ScalarImplicatures.WeakEvidenceEffect.instBEqModelFamily.beq :

ModelFamily → ModelFamily → Bool

Equations

Phenomena.ScalarImplicatures.WeakEvidenceEffect.instBEqModelFamily.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

Instances For

def Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprModelFamily.repr :

ModelFamily → ℕ → Std.Format

Equations

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

Instances For

instance Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprModelFamily :

Repr ModelFamily

Equations

Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprModelFamily = { reprPrec := Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprModelFamily.repr }

inductive Phenomena.ScalarImplicatures.WeakEvidenceEffect.ModelVariant :

Model variant (how individual differences are handled)

homogeneous : ModelVariant
heterogeneous : ModelVariant
speakerDependent : ModelVariant

Instances For

instance Phenomena.ScalarImplicatures.WeakEvidenceEffect.instDecidableEqModelVariant :

DecidableEq ModelVariant

Equations

Phenomena.ScalarImplicatures.WeakEvidenceEffect.instDecidableEqModelVariant x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.ScalarImplicatures.WeakEvidenceEffect.instBEqModelVariant.beq :

ModelVariant → ModelVariant → Bool

Equations

Phenomena.ScalarImplicatures.WeakEvidenceEffect.instBEqModelVariant.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

Instances For

instance Phenomena.ScalarImplicatures.WeakEvidenceEffect.instBEqModelVariant :

BEq ModelVariant

Equations

Phenomena.ScalarImplicatures.WeakEvidenceEffect.instBEqModelVariant = { beq := Phenomena.ScalarImplicatures.WeakEvidenceEffect.instBEqModelVariant.beq }

instance Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprModelVariant :

Repr ModelVariant

Equations

Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprModelVariant = { reprPrec := Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprModelVariant.repr }

def Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprModelVariant.repr :

ModelVariant → ℕ → Std.Format

Equations

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

Instances For

structure Phenomena.ScalarImplicatures.WeakEvidenceEffect.ModelComparisonDatum :

Model comparison result from Table 1

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

Instances For

def Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprModelComparisonDatum.repr :

ModelComparisonDatum → ℕ → Std.Format

Equations

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

Instances For

instance Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprModelComparisonDatum :

Repr ModelComparisonDatum

Equations

Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprModelComparisonDatum = { reprPrec := Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprModelComparisonDatum.repr }

def Phenomena.ScalarImplicatures.WeakEvidenceEffect.modelComparison :

List ModelComparisonDatum

Table 1 data

Equations

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

Instances For

theorem Phenomena.ScalarImplicatures.WeakEvidenceEffect.rsa_speaker_dep_best_likelihood :

12 > 82 / 10

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

theorem Phenomena.ScalarImplicatures.WeakEvidenceEffect.rsa_speaker_dep_best_waic :

-164 / 10 < -133 / 10

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

structure Phenomena.ScalarImplicatures.WeakEvidenceEffect.FittedParams :

Fitted parameters for the best model (RSA speaker-dependent)

betaMAP : ℚ
betaCV : ℚ
responseOffset : ℚ
pragmaticMixWeight : ℚ
literalMixWeight : ℚ

Instances For

instance Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprFittedParams :

Repr FittedParams

Equations

Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprFittedParams = { reprPrec := Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprFittedParams.repr }

def Phenomena.ScalarImplicatures.WeakEvidenceEffect.instReprFittedParams.repr :

FittedParams → ℕ → Std.Format

Equations

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

Instances For

def Phenomena.ScalarImplicatures.WeakEvidenceEffect.bestModelParams :

Equations

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

Instances For

theorem Phenomena.ScalarImplicatures.WeakEvidenceEffect.beta_positive :

bestModelParams.betaMAP > 0

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

theorem Phenomena.ScalarImplicatures.WeakEvidenceEffect.pragmatic_group_uses_j1 :

bestModelParams.pragmaticMixWeight > 9 / 10

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

theorem Phenomena.ScalarImplicatures.WeakEvidenceEffect.literal_group_uses_j0 :

bestModelParams.literalMixWeight < 2 / 10

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