Degen and Tonhauser (2021): Prior beliefs modulate projection #

This file formalizes Degen and Tonhauser's finding that a listener's prior belief in the content of a clausal complement modulates how strongly that content projects, the listener's inference about the speaker's commitment to it under a question. The hypothesis came from the by-item variability in Tonhauser, Beaver and Degen's projection ratings and had conflicting support, Mahler finding modulation for politically charged contents and Lorson none for the pre-state of stop. Across twenty clause-embedding predicates and twenty contents each paired with a fact raising or lowering its prior, projection was higher under the higher-prior fact for every predicate, both within participants (Experiment 1) and between (Experiment 2), and the participant's own prior predicted projection better than the group's or the categorical manipulation. The account the paper sketches is Bayesian, in the spirit of Goodman and Frank's rational speech acts and Qing, Goodman and Lassiter's projection model: projection is the posterior credence in the content, which by Bayes' rule is strictly increasing in the prior at fixed likelihoods, so a more likely content is taken to be more strongly committed to.

Main statements #

projection_strictMono: the posterior credence in a content is strictly increasing in its Bernoulli prior, whatever the speaker's production likelihoods.
fact_raises_prior: the fact manipulation raised every content's mean prior rating, in both designs.
prior_modulates_projection: every predicate's complement was rated more projective under the higher-prior fact, in both designs.

Implementation notes #

The means are the generated tables of Data/Experiments/DegenTonhauser2021.json, recomputed from the trial-level data of the paper's repository by scripts/check_experiments.py.
The regression coefficients are not encoded: the prior manipulation raised ratings (β = 0.45), projection rose with the categorical fact (β = 0.14), with the group-level prior (β = 0.31) and with the participant's own prior (β = 0.28), the individual-level model winning by BIC, and Experiment 2 replicated the effect between participants (β = 0.18).

References #

Projection as posterior credence #

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theorem DegenTonhauser2021.projection_strictMono {𝓤 : Type u_1} [MeasurableSpace 𝓤] [MeasurableSingletonClass 𝓤] (κ : ProbabilityTheory.Kernel Bool 𝓤) [ProbabilityTheory.IsFiniteKernel κ] {u : 𝓤} (htrue : (κ true) {u} ≠ 0) (hfalse : (κ false) {u} ≠ 0) :

StrictMono fun (p : ↑unitInterval) => ((ProbabilityTheory.posterior κ (ProbabilityTheory.bernoulliMeasure true false p)) u).real {true}

Bayes' rule makes projection prior-sensitive: for any speaker who can produce the utterance whether or not the content holds, the listener's posterior credence in the content is strictly increasing in the prior, so a content that is more likely a priori is more likely a posteriori.

The means of Experiments 1 and 2 #

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def DegenTonhauser2021.priorMean (d : Design) (f : Fact) (c : Content) :

ℚ

The mean prior probability rating of a content, given the fact.

Equations

DegenTonhauser2021.priorMean d f c = (DegenTonhauser2021.prior d f c).mean.toRat

Instances For

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def DegenTonhauser2021.certaintyMean (d : Design) (f : Fact) (p : Predicate) :

ℚ

The mean certainty rating of a predicate's complement, given the content's fact.

Equations

DegenTonhauser2021.certaintyMean d f p = (DegenTonhauser2021.certainty d f p).mean.toRat

Instances For

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theorem DegenTonhauser2021.fact_raises_prior (d : Design) (c : Content) :

priorMean d Fact.lowerProbability c < priorMean d Fact.higherProbability c

The manipulation worked: every content's mean prior rating was higher under its higher-probability fact, within and between participants, the pattern of Figures 2 and A2.

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theorem DegenTonhauser2021.prior_modulates_projection (d : Design) (p : Predicate) :

certaintyMean d Fact.lowerProbability p < certaintyMean d Fact.higherProbability p

For every predicate the complement's mean certainty rating was higher under the higher-probability fact, within and between participants, the pattern of Figures 3 and 6 that a prior-sensitive account predicts.