Documentation

Linglib.Studies.YoonEtAl2020

[YTGF20] — Polite speech emerges from competing social goals #

RSA model of [YTGF20] (Open Mind 4): polite speech arises from a speaker trading off three communicative goals — to be informative, to be kind, and to appear informative and kind. The experimental domain: Ann rates Bob's poem (states s₀–s₃, hearts) and chooses among eight utterances ({terrible, bad, good, amazing} × {plain, negated}).

The model stack (the paper's Figure 4): a literal listener P_L0(s|w) ∝ L(w,s)·P(s) over empirically elicited soft semantics; a first-order speaker with utility U_S1 = φ·ln P_L0(s|w) + (1−φ)·E_{P_L0}[V(s)] − c·l(w); a pragmatic listener jointly inferring state and goal weight, P_L1(s,φ|w) ∝ P_S1(w|s,φ)·P(s)·P(φ); and a second-order polite speaker with U_S2 = ω_inf·ln P_L1(s|w) + ω_soc·E_{P_L1}[V(s)] + ω_pres·ln P_L1(φ̂|w) − c·l(w).

Instantiated on the canonical pipeline: the S1 speaker is RSA.Canonical.S1 over (state × φ) speaker situations, and the pragmatic listener is RSA.Canonical.L1, the joint posterior over HeartState × Phi — the paper's eq. (4) by construction, with the U_pres marginal available as .snd. The paper's L0-gate (utterances with zero literal fit are unavailable to informativity-sensitive speakers) is the -utility branch.

Main statements #

Implementation notes #

Lexicon provenance. softSemantics stipulates acceptance proportions k/49 attributed to literal_semantics.csv in the paper's repository (the paper itself prints no θ table; N = 51 recruited per the supplement). -- UNVERIFIED: the k/49 values and the N = 49-after-exclusions claim await verification against the CSV. Negated utterances use graded negation ⟦not φ⟧ = 1 − ⟦φ⟧a compositional construction of this file, not the paper's lexicon: the paper elicits θ per utterance, including negated forms. The φ grid discretizes the paper's continuous φ ~ Uniform(0,1) to five points.

Findings policy. S1-level preferences are stated as theorems: they are parameter-free (any α > 0) and robust to lexicon perturbation. The S2-level negation preferences and the L1 state-inference orderings are numeric facts — α-dependent and, for S2, sensitive to the third decimal of single norming proportions — and are recorded as verified prose (§S2 below), per the library's policy on findings whose truth depends on exact parameter values. Notably, independent recomputation shows the paper's headline U_S2(not terrible) > U_S2(terrible) under both-goal weights at state s₀ is TRUE at the fitted parameters (margin ≈ 0.14) — correcting the previous version of this file, which left it sorryed with a docstring wrongly claiming it fails under point-estimate semantics (the old reflection tactic's interval arithmetic merely could not separate the sides).

States, utterances, goals #

World states: the true rating (number of hearts) deserved.

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      The eight utterances: four adjectives × {plain, negated}.

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          Speaker goal conditions from the experiment.

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              Discretized goal weight φ (informativity vs. kindness); the paper's φ ~ Uniform(0,1) discretized to five points.

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                instance YoonEtAl2020.instDecidableEqPhi :
                DecidableEq Phi
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                def YoonEtAl2020.instReprPhi.repr :
                PhiStd.Format
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                  The rational value of each φ level.

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                    The soft lexicon #

                    Soft semantic acceptance proportions for the four positive adjectives. -- UNVERIFIED: stipulated as k/49 from literal_semantics.csv in the paper's repository; not printed in the paper.

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                      Utterance semantics: positive forms from the norming data; negated forms by graded negation ⟦not φ⟧ = 1 − ⟦φ⟧. This construction is the formaliser's, not the paper's: the paper elicits per-utterance θ for all eight utterances; the derived profiles are qualitatively compatible with the paper's description of "not terrible" but are not its lexicon.

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                        The lexicon is soft: values in [0, 1].

                        The literal listener in closed form #

                        With a uniform state prior, P_L0(s|w) = meaning w s / Σ_s' meaning w s'. The closed rational forms below feed the speaker utility exactly.

                        The lexicon mass of an utterance (the L0 partition function).

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                          P_L0(s|u) in closed rational form (uniform state prior cancels).

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                            def YoonEtAl2020.ev (u : Utterance) :

                            E_{P_L0(·|u)}[V(s)]: the social value of u to the literal listener.

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                              The S1 speaker on the canonical pipeline #

                              noncomputable def YoonEtAl2020.util (α : ) (p : HeartState × Phi) (u : Utterance) :
                              EReal

                              S1 utility (the paper's U_S1 = φ·ln P_L0(s|w) + (1−φ)·E_{P_L0}[V] − c·l(w), c = 1), as an EReal score over speaker situations (s, φ). The branch is the paper's L0-gate: an utterance with zero literal fit is unavailable to any informativity-sensitive speaker (φ ≠ 0); for the pure-social speaker the φ-weighted log term vanishes, so the gate does not apply.

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                                noncomputable def YoonEtAl2020.speaker (α : ) :

                                The S1 speaker: the canonical softmax speaker over util.

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                                  S1 findings (Figure 2, S1 facets) — structural, every α > 0 #

                                  The pure-social speaker prefers indirect speech at the worst state: "it wasn't terrible" beats "it was terrible" (Figure 2, S1 social facet). A pure expected-value comparison: the social gain E[V] of the indirect form (53/24 vs 29/76) exceeds its one-word extra cost.

                                  The pure-social speaker prefers positive utterances: "it was amazing" beats "it wasn't amazing" (same cost direction reversed: here the positive form is both kinder and cheaper).

                                  The pure-informative speaker prefers direct speech at the worst state: "it wasn't terrible" is literally false at zero hearts (graded meaning 0), so the L0-gate excludes it for any informativity-sensitive speaker.

                                  Even slight informativity (φ = 1/4) suffices to exclude the literally false indirect form — a gate fact about the discretized model, not a claim of the paper's.

                                  The pure-informative speaker prefers the direct positive at the best state: "amazing" beats "not amazing" at three hearts — a genuine log-monotonicity comparison (P_L0(s₃|amazing) = 47/56 > 1/70 = P_L0(s₃|not amazing)), with cost also favouring the direct form.

                                  The pragmatic listener: the joint (state, goal) posterior #

                                  noncomputable def YoonEtAl2020.prior :
                                  PMF (HeartState × Phi)

                                  Uniform joint prior over state × φ (the paper's uniform P(s) and uniform P(φ), discretized).

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                                    theorem YoonEtAl2020.marginal_ne_zero (α : ) (u : Utterance) :

                                    Every utterance is literally compatible with some state, so every utterance has positive marginal probability.

                                    noncomputable def YoonEtAl2020.listener (α : ) (u : Utterance) :
                                    PMF (HeartState × Phi)

                                    The pragmatic listener (the paper's eq. (4)): the joint Bayesian posterior over (state, φ) given the utterance. The state marginal (.fst) is P_L1(s|w); the φ marginal (.snd) is P_L1(φ|w), the quantity inside the paper's presentational utility (eq. (3)).

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                                      L1 state inferences (prose) #

                                      The previous version of this file proved eight L1 state-inference orderings (e.g. P_L1(s₀|terrible) > P_L1(s₃|terrible): 0.686 vs 0.0003) by interval-arithmetic reflection. They are numeric facts about φ-marginalised sums of exponentials; independent recomputation confirms all eight at α = 3, seven robust over α ∈ [0.01, 100] and one (P_L1(s₁|bad) > P_L1(s₀|bad), 0.610 vs 0.390) reversing below α ≈ 1.19. Per the parameter-dependence policy they are recorded here as prose.

                                      The S2 polite speaker #

                                      S2 goal weights ω and projected goal φ̂. MAP estimates from the paper's Table 2 (main text); phiHat discretizes the fitted φ to the grid (0.36, 0.37 → ¼; 0.49 → ½).

                                      • wInf :
                                      • wSoc :
                                      • wPres :
                                      • phiHat : Phi
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                                        Both-goal condition (Table 2: ω = (0.36, 0.11, 0.54), φ = 0.36).

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                                          Informative condition (Table 2: ω = (0.36, 0.02, 0.62), φ = 0.49).

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                                            Kind condition (Table 2's "social" row: ω = (0.25, 0.31, 0.44), φ = 0.37).

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                                              noncomputable def YoonEtAl2020.s2Utility (α c : ) (W : S2Weights) (s : HeartState) (u : Utterance) :

                                              The S2 utility (the paper's eq. (2) with eq. (3)): ω_inf·ln P_L1(s|w) + ω_soc·E_{P_L1(s|w)}[V] + ω_pres·ln P_L1(φ̂|w) − c·l(w), over the joint listener's marginals. The cost sits inside the utility (and hence inside S2's α-scaling), as in the paper's Figure 4 — correcting the previous version, which moved it outside as an utterance prior.

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                                                S2 findings (prose, independently recomputed) #

                                                At the fitted parameters (α ≈ 4.47, c ≈ 2.64 — both attributed to the paper's supplement/repository and -- UNVERIFIED from the PDF, which states only the priors α ~ Uniform(0,20), c ~ Uniform(1,10)), with cost α-scaled as above:

                                                Sensitivity (the reason these are prose, not theorems): both negation preferences flip if the single norming proportion softSemantics .amazing .h0 = 1/49 ≈ 0.020 drops to ≈ 0.01 — they hinge on one participant's judgment in the norming task — and are α-dependent, unlike the S1 theorems above. The model-comparison content (Table 1: the full informational + social + presentational model beats all ablations, log BF ≥ 11) is Bayesian-fit material outside the formalisation's scope.

                                                Bridge to the subjectivity cline #

                                                The politeness model instantiates [TD02]'s intersubjectivity: for φ < 1 the speaker trades informativity for attention to the addressee's face, and S2 additionally manages how kind they appear — doubly intersubjective. [Nar10] connects this to modality: strong obligation is face-threatening because it is performative and volitive.

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