@cite{burnett-2019} — Signalling Games, Sociolinguistic Variation, and #
the Construction of Style
Linguistics and Philosophy 42: 419–450.
Overview #
Social Meaning Games (SMGs) model how sociolinguistic variant choice conveys social information. A speaker's use of -ing vs -in' induces listener inferences about persona traits (competent, friendly, etc.). The framework combines @cite{lewis-1969}'s signalling games with RSA-style Bayesian reasoning to derive both style shifting (intra-speaker variation across contexts) and social stratification (inter-speaker variation across classes) from the same principles.
Architecture #
The meaning function is grounded in the Eckert–Montague lift from
EckertMontague.emMeaningMI: each variant's Eckert field (a set of
indexed properties) is lifted to persona compatibility via intersection
semantics. The grounding theorem ingMeaning_eq_emMeaningMI verifies
that the study's meaning function matches the theory-layer derivation.
Each context is an RSAConfig INGVariant Persona with beliefBased S1
scoring (S1(v|π) ∝ L0(π|v)^α, α=6) and context-specific worldPrior.
All predictions are verified by rsa_predict.
Key predictions #
- Per-persona variant preference: cool-guy prefers -in' ~69%
- Style shifting: casual→careful flips the cool-guy's preference
- Stern-leader exclusion: -in' is incompatible with stern leader
- Listener interpretation: Rice/Pelosi/Bush /t/ release predictions
- Bulletproofing: strong prior overwhelms variant effects (Bush)
- Cross-reference: model predictions close to @cite{labov-2012} data
Social properties (Burnett example (5)). Two bipolar dimensions: competence (competent/incompetent) and warmth (friendly/aloof).
- competent : PersonaTrait
- incompetent : PersonaTrait
- friendly : PersonaTrait
- aloof : PersonaTrait
Instances For
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- Burnett2019.instDecidableEqPersonaTrait x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
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- Burnett2019.instReprPersonaTrait = { reprPrec := Burnett2019.instReprPersonaTrait.repr }
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- Burnett2019.instDecidableEqPersona x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
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- Burnett2019.instReprPersona.repr Burnett2019.Persona.doofus prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Burnett2019.Persona.doofus")).group prec✝
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- Burnett2019.instReprPersona = { reprPrec := Burnett2019.instReprPersona.repr }
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Eckert fields (Burnett example (10)):
- [-ing] = {competent, aloof}
- [-in'] = {incompetent, friendly}
The meaning function is derived via the Montagovian Individual / intersection semantics (Burnett footnote 14, Table 1): persona p is compatible with variant v iff p shares at least one property with v's Eckert field.
The property space for Burnett's simplified example.
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Persona membership as a Finset.
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- Burnett2019.Persona.coolGuy.toFinset = {Burnett2019.PersonaTrait.competent, Burnett2019.PersonaTrait.friendly}
- Burnett2019.Persona.sternLeader.toFinset = {Burnett2019.PersonaTrait.competent, Burnett2019.PersonaTrait.aloof}
- Burnett2019.Persona.doofus.toFinset = {Burnett2019.PersonaTrait.incompetent, Burnett2019.PersonaTrait.friendly}
- Burnett2019.Persona.asshole.toFinset = {Burnett2019.PersonaTrait.incompetent, Burnett2019.PersonaTrait.aloof}
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Eckert fields for (ING) (Burnett example (10)).
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The ING grounded field: both Eckert fields are consistent.
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- Burnett2019.ingField = { indexedProperties := Burnett2019.ingEckertField, indexed_consistent := Burnett2019.ingField._proof_1 }
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Meaning via the EM intersection lift: persona p is compatible with variant v iff p shares ≥1 property with v's Eckert field.
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- Burnett2019.ingMeaning Phenomena.SocialMeaning.ING.INGVariant.velar Burnett2019.Persona.coolGuy = true
- Burnett2019.ingMeaning Phenomena.SocialMeaning.ING.INGVariant.velar Burnett2019.Persona.sternLeader = true
- Burnett2019.ingMeaning Phenomena.SocialMeaning.ING.INGVariant.velar Burnett2019.Persona.asshole = true
- Burnett2019.ingMeaning Phenomena.SocialMeaning.ING.INGVariant.velar Burnett2019.Persona.doofus = false
- Burnett2019.ingMeaning Phenomena.SocialMeaning.ING.INGVariant.apical Burnett2019.Persona.coolGuy = true
- Burnett2019.ingMeaning Phenomena.SocialMeaning.ING.INGVariant.apical Burnett2019.Persona.sternLeader = false
- Burnett2019.ingMeaning Phenomena.SocialMeaning.ING.INGVariant.apical Burnett2019.Persona.asshole = true
- Burnett2019.ingMeaning Phenomena.SocialMeaning.ING.INGVariant.apical Burnett2019.Persona.doofus = true
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Grounding theorem: the inline meaning function equals the
theory-layer emMeaningMI applied to the ING Eckert fields.
-ing is compatible with 3 personae (Table 1: excludes doofus).
-in' is compatible with 3 personae (Table 1: excludes stern leader).
Each social context is an RSAConfig INGVariant Persona:
- Worlds = personae (what the listener infers)
- Utterances = variants (what the speaker chooses)
- Meaning = EM intersection lift
- S1 scoring = beliefBased: S1(v|p) ∝ L0(p|v)^α
- α = 6 (Burnett p. 435)
- worldPrior = context-dependent belief about the speaker
Construct an SMG as an RSAConfig with context-specific prior.
The meaning function incorporates the prior so that L0 matches Burnett's naive listener: L₀(π|v) ∝ Pr(π) · ⟦v⟧(π). Without the prior in meaning, L0 would be uniform over compatible personae (1/3 for all), erasing the context-dependence that drives style shifting.
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Casual-context prior (Burnett Table 2): voters at the barbecue think Obama is aloof (personae with aloof get more weight).
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Careful-context prior (Burnett Table 5): journalists think Obama is incompetent (incompetent personae get more weight).
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Rice: uniform prior — unfamiliar politician (Burnett Table 10).
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- Burnett2019.ricePrior x✝ = 1 / 4
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Pelosi: listeners believe she is inarticulate (Burnett Table 13).
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Bush: listeners almost certain he is {inarticulate, aloof} (Burnett Table 15).
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Cool-guy at the barbecue prefers -in' over -ing (~69% vs ~31%). Burnett (p. 435): "we predict that Obama will use -in' around 69% of the time [...] which is close to what Labov found" (72%).
Stern leader only uses -ing: -in' is incompatible (Table 1). This predicts ~0% -in' in formal contexts where Obama constructs the stern leader.
The doofus only uses -in': -ing is incompatible (Table 1).
In the careful context, the cool-guy now prefers -ing over -in'. The prior shift reverses the informativity ranking.
The /t/ release variable has the same mathematical structure as (ING). Relabeling: articulate↔competent, inarticulate↔incompetent (same friendly/aloof). Variants: released [tʰ]↔-ing, flapped [ɾ]↔-in'. The Eckert fields are structurally identical (Burnett example (19)): [tʰ] = {articulate, aloof}, [ɾ] = {inarticulate, friendly}.
We reuse the same types and meaning function, since the math is isomorphic. The personae reinterpret as: coolGuy ↔ {articulate, friendly}, sternLeader ↔ {articulate, aloof}, doofus ↔ {inarticulate, friendly}, asshole ↔ {inarticulate, aloof}.
The asshole prefers -in' in the casual context (both variants are compatible, but -in' is more informative given the prior).
Rice: released /t/ triggers {articulate, aloof} = stern leader (Burnett Table 11). With uniform prior, the exclusive variant (only -ing compatible) gets double the L1 weight.
Rice: flapped /t/ triggers {inarticulate, friendly} = doofus (Burnett Table 11). Symmetric to the released case.
Pelosi: released /t/ predominantly triggers {inarticulate, aloof} — the strong prior that she is inarticulate overwhelms the released /t/ association with articulateness (Burnett Table 14).
Pelosi: flapped /t/ triggers {inarticulate, friendly} (Table 14).
Bush "bulletproofing" (Burnett p. 444, Table 16): the prior is so extreme that variant choice has no practical effect. Both released and flapped /t/ yield >90% {inarticulate, aloof}.
Cross-reference: the SMG model's qualitative predictions match the directional pattern observed in @cite{labov-2012}'s data on Obama's (ING) rates. The model predicts the cool-guy persona prefers -in' in casual context and -ing in careful context; the data shows Obama's -in' rate decreasing monotonically from casual (72%) through careful (33%) to formal (3%).
The theory-layer SocialMeaningGame (Burnett Def. 4.1) captures the
signalling game structure: types, meaning, prior, and social evaluation.
We construct an SMG from the study's types and prove structural properties.
The SMG's naiveListener is Franke's literal L₀ — uniform over
compatible personae. This captures the exclusion structure (which
personae are ruled out by each variant) but not the prior-weighted
refinement. The quantitative predictions (69% -in' for cool guy,
style shifting) use the RSAConfig's belief-based S₁ (Burnett eq. 13:
P_S(m|π) ∝ L₀(π|m)^α), which incorporates the context-specific prior
into the meaning function to recover Bayesian conditioning.
Obama's social value function μ at the barbecue (@cite{burnett-2019}, Table 6, p. 438).
Cool guy ({competent, friendly}) is most valued (μ = 2); asshole ({incompetent, aloof}) is least (μ = 0). The μ function reflects what the speaker (Obama) most wants the listener to infer about him in this context.
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The (ING) Social Meaning Game for the casual context (@cite{burnett-2019}, Def. 4.1 + Table 2 + Table 6).
This connects the study's types to the theory-layer game
structure from SMG.lean, exercising SocialMeaningGame,
naiveListener, and toInterpGame.
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The SMG meaning is grounded in the Eckert–Montague intersection
lift — connecting the game structure to the compositional
semantics layer via ingMeaning_eq_emMeaningMI.
The naive listener excludes stern leader after hearing -in' (incompatible: stern leader = {competent, aloof} shares no property with [-in'] = {incompetent, friendly}).
The naive listener excludes doofus after hearing -ing (incompatible: doofus = {incompetent, friendly} shares no property with [-ing] = {competent, aloof}).
The naive listener assigns equal probability (1/3) to all compatible personae. Franke's literal L₀ is uniform over ⟦v⟧: since 3 personae are compatible with each variant, each gets 1/3.
This is the structural content of the meaning function: each variant partitions personae into compatible (1/3) and incompatible (0).