2.1 Mirror Model

A common wisdom shared amongst discourse researchers is that interlocutors represent the ongoing discourse by constructing a mental model and continually updating it as they process the discourse (e.g., Lambrecht 1996). As discourse unfolds, representations of certain discourse referents are likely to be more active in memory and attention than others.

Traditional approaches to discourse anaphora posit that referents can be ranked according to the activation status of their mental representations in memory. This activation status is thought to guide speakers’ choice of which referent to mention and the type of referring expression to use. These approaches propose hierarchies mapping different referential forms to various activation statuses of referents (e.g. Givón 1983; Ariel 1990; Gundel et al. 1993). In general, they tend to associate more reduced expressions such as pronouns with referents that are more activated in memory and attention i.e. more salient (see Table 1 for the Givenness Hierarchy in Gundel et al. 1993 as an example). The underlying assumption is that when referents are easily accessible in memory for both speakers and listeners, facilitated by contextual and cognitive information, speakers can more effectively use less explicit referring expressions. As such, the choice of referring expression is driven by speakers’ assumptions regarding the cognitive status of the intended referent in listeners’ minds. This implies that both speakers and listeners use the same cues to determine referent salience and rely on a shared concept of referent salience for production and interpretation. Therefore, during interpretation, it is assumed that listeners reverse-engineer the speaker’s production process, interpreting pronouns by considering what entities the speaker would most likely refer to using a pronoun as opposed to a competing referential form.

Following previous research, we adopt the term Mirror Model to refer to these types of approaches. In these approaches, pronoun production and pronoun interpretation align on the same notion of referent salience, essentially mirroring each other. We define this model as per Equation I, as done in prior studies (e.g., Rohde & Kehler 2014; Bader & Portele 2019; Zhan et al. 2020; Patterson et al. 2022). Interpretation bias, denoted as P(referent | pronoun), represents the probability of a specific referent being the intended reference for a given pronoun. On the other hand, production bias, denoted as P(pronoun | referent), represents the probability of a pronoun being used to refer to a particular referent. The sum in the denominator is computed over all possible referents such that P(pronoun | referent) is calculated for each candidate referent and those probabilities are summed. This summation ensures that the probabilities across all possible referents add up to 1, normalizing the probabilities. However, for the purpose of our discussion, we can disregard this denominator as it acts as a constant factor (i.e., it is the same for P(referent | pronoun) for all referents). Therefore, in the Mirror Model, the interpretation bias towards a referent is directly proportional to the likelihood of the speaker using a pronoun to refer to that referent i.e., production bias.

2.2 Bayesian Model

Challenging the assumption of a unified salience notion in pronoun production and interpretation, the proposal put forth by Kehler et al. (2008) and Kehler & Rohde (2013) suggests a Bayesian framing for the relationship between pronoun interpretation and production. This model provides a plausible explanation for the observed asymmetries between pronoun production and interpretation in empirical studies (e.g., Rohde & Kehler 2014; Mayol 2018). For example, story continuation data from Stevenson et al. (1994) found no strong interpretation bias for the ambiguous pronoun he in (1a) towards either the subject John or the non-subject Bill (a roughly 50/50 interpretation preference). However, for (1b), there was a strong bias towards using a pronoun when participants referred to the previous subject John, and a strong bias toward using a name when they referred to a non-subject Bill.

According to the Bayesian Model, this asymmetry can be characterized using Bayes’ Rule, as shown in Eq. II. Such a formulation allows for the differentiation between the bias in pronoun production observed by Stevenson et al. (1994) and the pattern of pronoun interpretation. While the latter is related to the production bias, it also incorporates the next mention bias.

More specifically, pronoun interpretation bias, represented by P(referent | pronoun) in the formulation, is determined by two probabilities: (i) P(referent), the listener’s estimate that a referent will get mentioned next, and (ii) P(pronoun | referent), the listener’s estimate that the speaker will use a pronoun to refer to that referent. In other words, the Bayesian Model predicts that if we have separate estimates of P(referent), P(pronoun | referent), and P(referent | pronoun), then we would expect Eq. (II) to hold approximately. This claim is known as the weak claim of the Bayesian Model, henceforth referred to as Weak Bayes (e.g., Kehler & Rohde 2013; Rohde 2019; Zhan et al. 2020; Hoek et al. 2021; Patterson et al. 2022).

The strong form of the Bayesian Model, henceforth referred to as Strong Bayes, further specifies the types of contextual factors that affect each term on the right-hand side of Eq. II (see the references just given for Weak Bayes). Strong Bayes reflects an empirical observation that a set of meaning-driven factors (e.g., verb type, coherence relations) influence the next-mention bias and accordingly affect the pronoun interpretation bias. However, the speaker’s decision regarding the pronominalization of a referent is insensitive to these factors. Instead, pronoun production is primarily influenced by grammatical factors (e.g., subjecthood) and/or factors associated with information structure (specifically, topichood). These factors together essentially lead to a preference for sentential subjects.¹

However, empirical studies have produced conflicting evidence concerning whether certain semantic and pragmatic factors like verb type and discourse relation, actually influence pronoun production. In the following section, we will present the Expectancy Hypothesis, an alternative theory to Strong Bayes, along with a pronoun interpretation model derived from this theory, known as the Expectancy Model.

2.3 Expectancy Model

In contrast to Strong Bayes, the Expectancy Hypothesis (Arnold 1998; 2001; Arnold et al. 2007; Arnold 2010; Arnold & Tanenhaus 2011) posits that both next-mention bias and pronoun production bias are influenced by meaning-driven factors. According to the Expectancy Hypothesis, next-mention bias, which refers to the expectations about the next mention from listeners, is closely tied to speakers’ choice of referring expression. Specifically, it suggests that listeners’ estimate of the likelihood that a particular referent will be mentioned next strongly influences the activation level of that referent in the interlocutors’ mental representation of discourse. Speakers can thus calculate the former as an estimate of the latter, using more reduced forms, such as pronouns, for referents that are expected or highly predictable to their listeners.

Furthermore, as the Expectancy Hypothesis suggests a direct link between listeners’ estimate of the likelihood that a referent will be continued in the discourse and the activation level of that referent in their mental representation (referent accessibility), it predicts that reference interpretation is strongly influenced by the expectancy of a referent. Given this and following previous research, we define a third model of pronoun interpretation, termed as Expectancy Model. In this model, pronoun interpretation bias primarily depends on the next-mention bias, as shown in Eq. III.

In the following section, we present the methods and materials employed in previous studies, which bear upon various aspects of the present study.

2.5 Previous findings

This section summarizes findings from previous studies that aimed to quantitatively assess the three models of pronoun interpretation and evaluate the Strong Bayes hypothesis. These studies employed standard experimental paradigms with bare and pronoun prompts (e.g., Ex. (2) and (3)). Their findings are directly relevant to our research questions, which we will elaborate on in Section 3.

The study by Rohde & Kehler (2014) marked the first quantitative evaluation of the three pronoun interpretation models. Their approach involved manipulating verb type by using subject-biased and object-biased implicit causality verbs in English (e.g., Ex. (6) and (7)). They assessed the correlations between predicted interpretation biases (obtained from bare-prompt data) and observed biases (collected from pronoun-prompt data) using R². Further details on this metric, along with two others below, are provided in Section 5.4. Notably, the Bayes-derived estimates consistently exhibited the strongest correlation with observed data. Additionally, they observed the influence of verb type on next-mention and pronoun interpretation biases, while pronoun production biases remained unaffected, giving rise to the Strong Bayes hypothesis.

Expanding the research scope, Zhan et al. (2020) investigated overt and null pronouns in Mandarin Chinese. They conducted three experiments using implicit causality verbs and introduced additional variables such as voice (active vs. passive) and syntactic construction in the second and third experiments. No evidence supporting the influence of verb type on pronoun production biases was found throughout the study, consistent with the Strong Bayes hypothesis. To evaluate pronoun interpretation model performance, they employed R² alongside Mean Squared Error (MSE) and Average Cross Entropy (ACE) metrics, offering a more comprehensive assessment. Across nine evaluations, the Bayesian model outperformed both the Mirror Model and the Expectancy Model, ranking best in six and second best in three.

In a more recent study, Patterson et al. (2022) further demonstrated the superior predictive accuracy of the Bayesian Model for the German personal pronoun er and the German demonstrative pronoun dieser when compared to the Mirror Model and the Expectancy Model. They improved the assessment of model performance by incorporating Bayesian methods that propagated data uncertainty to predictions, producing distributions of possible values rather than point estimates like the ones in the metrics employed by Zhan et al. (2020) and Rohde & Kehler (2014). Furthermore, Patterson et al. evaluated the Strong Bayes hypothesis through contrasts between accusative and dative verbs, as well as stimulus-experiencer versus experiencer-stimulus verbs. In both cases, no interaction between verb type and referent was found in pronoun production likelihoods, supporting the Strong Bayes hypothesis.

In summary, the body of evidence consistently points towards the Bayesian Model outperforming the other two models across various languages and experimental setups. Furthermore, these studies also consistently provide support for the Strong Bayes hypothesis.

4.1 Corpora

4.1.2 Rhetorical Structure Theory Discourse Treebank (RST-DT)

RST-DT consists of 385 Wall Street Journal articles (176k words) from the Penn Treebank (Marcus et al. 1993), annotated with discourse relations in the framework of Rhetorical Structure Theory (RST, Mann & Thompson 1988).⁴ Under the RST framework, texts are represented as a tree and are broken down into minimal discourse units (often corresponding to clauses), which are called elementary discourse units (EDUs). As illustrated in Figure 1, each leaf of the tree corresponds to an EDU. Adjacent EDUs are connected by discourse relations to form larger segments.

Figure 1

Graphical representation of an RST analysis (own production using text from the RST website, www.sfu.ca/rst).

The inventory of discourse relations annotated in RST-DT is fairly fine-grained, with 78 relations in total. In our study, we use a coarser-grained taxonomy of relations (Carlson & Marcu 2001), in which the 78 RST relations are partitioned into 16 broad categories based on their rhetorical similarity. For instance, one of the major categories is Contrast, which is the umbrella term for the relations Contrast, Concession, and Antithesis in the original inventory.

4.3 Results

The results from both corpora support Hypothesis 1: the subject referent is more frequently re-mentioned in Narration than in other relations, as follows. Figure 2 shows the distribution of coreference types by relation in OntoNotes and in RST-DT, where subject coreference is higher in Narration than in Result and Contrast (raw counts for each type are presented in Section B of the Supplementary file).

Figure 2

Coreference type by discourse relation in OntoNotes (left; total samples = 4,887) and RST-DT (right; total samples = 568).

We built mixed-effects logistic regressions where the dependent measure was whether the context continued with the subject referent or not, and a fixed effect for the 3-level discourse relation type, with Contrast as the reference level.⁸ In our analysis of the OntoNotes sample, random intercepts for individual verbs were included, along with random slopes for relation types by verb, given that the effect of discourse relation types have been shown to vary across different verbs (e.g., Kehler et al. 2008). The analysis of the RST-DT sample, on the other hand, included only random intercepts for verbs. Random slopes for relations by verb were not incorporated due to insufficient data to accurately estimate them. In both analyses, we also included random intercepts for the document ID to account for potential variations associated with e.g. author style.

The results of the statistical analysis are reported in Tables 7 and 8 for OntoNotes and RST-DT respectively. The effect of Narration on the likelihood of subject re-mention in both analyses is positive and significant at the chosen .05 alpha level, indicating that the subject referent is more frequently mentioned again in the Narration relation compared to the Contrast relation. Pairwise comparisons using the estimated marginal means show the subject referent is more frequently re-mentioned in Narration compared to Result (OntoNotes: β = 0.50, z = 3.14, p = 0.005; RST-DT: β = 1.37, z = 3.77, p < 0.001), while there is no difference between Contrast and Result (OntoNotes: β = 0.13, z = 1.03, p = 0.56; RST-DT: β= –0.01, z = –0.02, p ≈ 1).

In terms of Hypothesis 2, we find no evidence that discourse relations affect the choice of referring expression, that is we find support for Strong Bayes, as follows. Figure 3 shows the raw data, which do not indicate a higher pronominalization rate in the Narration relation, despite the higher rate of subject re-mention in this relation; and this is supported by a statistical analysis. We conducted mixed-effects logistic regression analyses on subject and non-subject samples. The dependent measure in this analysis was whether the next mention was pronominalized or not. The fixed effects included discourse relation types, coreference types (subject or non-subject), and their interaction, with Contrast as the reference level for relation type and non-subject as the reference level for coreference type. In our analysis of the OntoNotes sample, we included random intercepts for both verbs and document IDs, consistent with the first set of models. Random slopes for relations by verb were not incorporated due to singular fit issues. In contrast, the analysis of the RST-DT sample involved only random intercepts for document IDs, omitting random effects for verbs also due to singular fit concerns. As shown in Tables 9 and 10, the analyses on both OntoNotes and RST-DT revealed no significant difference in pronominalization patterns among the three examined relations. Additionally, our findings replicate the widely attested observation that subjecthood affects pronominalization. Specifically, we observe a higher frequency of pronoun usage when referencing the preceding subject (see the three left bars in figures (a) and (b) in Figure 3) compared to non-subject entities (represented by the three right bars). We conducted an additional robustness test to check a potential confound related to analyzing pronoun production in corpus passages: whether the antecedent is a pronoun or not. We found that the rates of pronoun production do not exhibit variations across discourse relations, even after accounting for the influence of the antecedent’s form (see more details in Section B.2 of the Supplementary file.

Figure 3

Pronominalization rate of next mention by relation in OntoNotes (left) and RST-DT (right). The graphs show the pronominalization rates when the next-mention corefers with the subject and when it corefers with a non-subject. Raw counts of samples with a pronominal next mention are presented on top of each bar, with the corresponding percentage in parentheses.

However, traditional null hypothesis testing aimed at identifying statistically significant differences, and this approach could be problematic when addressing hypotheses like Strong Bayes, which focus on the absence of an effect. This is because this method primarily assesses the presence rather than the absence of effects, potentially conflating true absence with undetected effects.

To address this, we adopted a Bayesian framework using Bayes Factors, which shifts the focus from finding evidence for a difference (i.e., rejecting the null hypothesis that there is no difference, as in traditional null hypothesis testing) to quantify support for true null hypotheses (e.g., Kass & Raftery 1995; Schad et al. 2022). Specifically, we assess how much more likely the data is under the model which represents the null hypothesis compared to the other which represents the alternative.

For both analyses with OntoNotes and RST-DT, we compared two Bayesian models: Model 1 (H1: alternative hypothesis) and Model 2 (H0: null hypothesis). Model 1 incorporates the same fixed effects and random effects as the models presented in Table 9 (for OntoNotes) and Table 10 (for RST-DT). Specifically, Model 1 incorporates both Relation Type and Coreference Type as predictors, as well as their interaction. Model 2, in contrast, excluded Relation Type and considered only Coreference Type as a predictor.

The models were fit using the brm function from the brms (v2.18.0; Bürkner 2017) package in R (R Core Team 2021). To ensure stable inferences, we utilized weakly informative priors, specifically Cauchy distributions with a center of 0 and a scale of 2.5 (Gelman et al. 2013). The fits were run with 4 chains, each comprising 4000 iterations, with half as warm-up. Prior to analysis, thorough diagnostic checks were conducted to rule out any potential pathologies in the estimation process.⁹ For Bayes factors analysis, we used the bridgesampling package (Gronau et al. 2020; version 1.1.2) in R.

The results from both analyses strongly supported Model 2 (H0). In the analysis with OntoNotes, the Bayes Factor in favor of Model 2 (H0) over Model 1 (H1) was estimated to be 32,984 (in favor of Model 1 over Model 2: 0.00003). Similarly, in the analysis with RST-DT, the Bayes Factor in favor of Model 2 (H0) over Model 1 (H1) was estimated to be 86.75 (in favor of Model 1 over Model 2: 0.01). Therefore, our analyses indicate that the inclusion of Relation Type in the model does not contribute significantly to explaining pronoun production biases, and the simpler Model 2, representing the null hypothesis or Strong Bayes, is the preferable model in both cases.

4.4 Interim discussion

To sum up, our corpus-based evidence confirms that discourse relations can induce varying degrees of bias in subject re-mentioning. Specifically, Narration exhibits a greater bias towards the continuation with a subject referent compared to Contrast and Result; and we do not find evidence that re-mention likelihood influences pronoun production within contexts of discourse relations. This disconnect between the likelihood of next mention and the likelihood of pronominalization aligns with the Strong Bayes theory.

As a side note, we observe from a comparison between the two figures in Figure 2 that, while the distribution of coreference types is comparable in the two corpora, there is a peculiar shortage of Narration contexts in the RST-DT corpus (71 samples only, which represents merely 12.5% of the total samples across all three relations, compared to 985 in OntoNotes, accounting for 20.2% of the total). This discrepancy is not likely to be due only to the difference in corpus size: OntoNotes is approximately ten times the size of RST-DT. While samples for both Contrast and Result suffer a proportionate decrease in RST-DT, the drop in Narration instances is more substantial. We suggest that there is a second factor at play, namely a genre effect. RST-DT is comprised solely of news texts, while the OntoNotes corpus includes a wider range of genres. Figure 4(a) shows that the primary source of Narration contexts in OntoNotes is the Bible, a significant portion of which is narrative. In fact, around 70% of the Narration contexts are found in the Bible, despite the Bible constituting only 17% of the corpus texts, as shown in Figure 4(b). The next most frequent source of Narration contexts is transcripts of spoken conversations. News articles and other written texts, which make up almost half of the OntoNotes corpus, contribute the least. This pattern confirms the relative infrequency of Narration contexts in news texts, which accounts for their scarcity in the RST-DT corpus. We leave further exploration of this aspect to future work.

Figure 4

The left figure (a) presents the distribution of Narration coreference samples by genres in OntoNotes. The pie chart on the right (b) shows the genre distribution in OntoNotes.

5.2 Analysis

The data were analyzed utilizing mixed-effect logistic regressions with centered predictors. We built three models: (1) one focused solely on the bare-prompt data, with the dependent variable being whether the continuation continued with the subject referent or not and a fixed effect for the 3-level discourse relation type; (2) one where the dependent variable assessed whether the next mention was pronominalized, incorporating fixed effects for discourse relation types, grammatical role types (subject or non-subject), and their interaction; and (3) another that considered both the bare-prompt and pronoun-prompt data, using the same dependent variable as the first model but including fixed effects for discourse relation types, prompt types (bare or pronoun), and their interaction. Model building began with a maximal random structure and subsequently simplifying the random-effects structure until convergence was attained (Barr et al. 2013). To assess the significance of the fixed effects, we employed likelihood ratio tests, comparing the full model with the effect in question against a counterpart model devoid of said effect.

The fitting of these models was conducted using the lme4 package (Bates et al. 2015) in R (version 4.1.2, R Core Team 2021). For each of the variables in the model, we report the coefficients in log odds. Null-hypothesis significance testing was employed to ascertain the statistical significance of the results (alpha level: 0.05).

In instances where the lme4 package encountered convergence failure, we employed a Bayesian approach using the brms R package (Bürkner 2017). To ensure stable inferences, we utilized weakly informative priors, specifically Cauchy distributions with a center of 0 and a scale of 2.5 (Gelman et al. 2013); and a maximal random structure. All fits were run with six chains, each comprising 2000 iterations, with half as warm-up. Prior to analysis, thorough diagnostic checks were conducted to rule out any potential pathologies in the estimation process. For the Bayesian models, we reported the estimated mean and the corresponding 95% Credible Intervals (CIs) of the posterior distribution in log odds. The 95% CI represents the range within which the outcome is likely to fall with a 95% probability, based on the observed data. A null hypothesis is rejected if the interval does not include zero (Gelman et al. 2013).

5.3 Results

In Section 3, we outlined our research questions and hypotheses. We state them again here. Our first question asks which model for pronouns (i.e., Bayesian, Expectancy, or Mirror) best accounts for the observed interpretation biases. Additionally, we have put forth two hypotheses regarding next-mention biases. Hypothesis 1 posits that, in Narration contexts, the likelihood of the subject referent being mentioned again is higher than in Contrast or Result contexts. If our data supports Hypothesis 1, it leads us to Hypothesis 2, which concerns pronoun production biases. Specifically, we hypothesize that discourse relations do not influence pronoun production biases, aligning with the predictions of the Strong Bayes model.

Next-mention biases. Raw proportions of subject references by discourse relation and prompt type are shown in Figure 6. We first evaluated the next-mention biases (red bars) in the bare-prompt condition. Analyses of the binary outcome of subject coreference showed a main effect of Relation Type (χ²(2) = 22.48, p < .001). Further pairwise comparisons revealed that Narration relations yield the most subject continuations, more than Contrast (z = 4.29, p < .001) and Result (z = 3.73, p < .001) in the bare-prompt condition; no difference was found between Contrast and Result (z = 0.06, p ≈ 1). A model summary is presented in Table 11. Therefore, Hypothesis 1 receives support from the data: subject referents are more predictable in Narration than in Contrast and Result.

Figure 6

Proportion of subject references by discourse relations and prompt types. Subject references in the bare-prompt condition represent participants’ expectations about the subject being the next mention, while subject references in the pronoun-prompt condition allow us to measure participants’ interpretation biases when encountering an ambiguous pronoun. Error bars are standard errors over by-participant means.

Pronoun production biases. The bare-prompt condition also allows us to measure participants’ pronominalization rates (see Figure 7). To model the binary outcome of whether the participant produced a pronoun or not, we built a full Relation Type × Grammatical Role model and replicated the well-known effect of grammatical role on pronoun production, with more pronouns produced referring to subjects than non-subjects (β = 2.71, [2.11, 3.40]). As for Hypothesis 2, we found no evidence of an effect of Relation Type on pronominalization, in keeping with the findings from our corpus-based observational analyses. A model summary is presented in Table 12.

Figure 7

Pronominalization rates by grammatical roles and relation types.

Beyond traditional hypothesis testing, we further evaluate evidence in favor of the null hypothesis (i.e., the absence of the effect) using Bayes Factors, similar to our approach in the corpus analyses discussed in Section 4.3.

We compared two Bayesian models: Model 1 (H1: alternative hypothesis) and Model 2 (H0: null hypothesis). Model 1 incorporates both Relation Type and Grammatical Role as predictors, as well as their interaction, same as the fixed effect items in the model presented in Table 12.¹⁷ Model 2, in contrast, excluded Relation Type and considered only Grammatical Role as a predictor. The Bayes Factor in favor of Model 2 (H0) over Model 1 (H1) was estimated to be 36432.67 (in favor of Model 1 over Model 2: 0.00003), indicating strong evidence in support of Model 2. Therefore, our analysis indicates that the inclusion of Relation Type in the model does not contribute significantly to explaining pronoun production biases, and the simpler Model 2, representing the null hypothesis or Strong Bayes, is the preferable model. This is consistent with the finding in our corpus analyses.

Pronoun interpretation biases. Next, we compare participants’ interpretation biases measured in the pronoun-prompt condition (depicted in the blue bars of Figure 6) to their next-mention biases (already seen in the red bars of Figure 6). To do this, we constructed a mixed-logit model of the binary outcome of subject versus non-subject continuation, incorporating the fully crossed factors of Relation Type × Prompt Type. The summary of this model is presented in Table 13.

We find a main effect of Relation Type (χ²(2) = 45.4, p < .001) whereby Narration yields the most subject continuations, more than Contrast (z = 6.52, p < .001) and Result (z = 5.79, p < .001); no difference was found between Contrast and Result (z = 0.08, p ≈ 1). We also replicate the well-known effect of Prompt Type (χ²(1) = 72.5, p < .001) whereby the presence of a pronoun increases subject continuations; the interpretation bias is more skewed towards the subject in this condition than in the bare-prompt condition. The mean score for interpreting an ambiguous pronoun as subject in Narration was significantly higher than the score in Contrast (z = 6.37, p < .001), and in Result (z = 5.85, p < .001). No difference was found between Contrast and Result (z = 0.01, p ≈ 1).

The interaction between Prompt Type and Relation Type shows that Prompt Type, changing from the bare-prompt condition to the pronoun-prompt condition, has the biggest effect in increasing subject continuations in the Narration condition. Although this initially appears counter-intuitive when comparing the raw proportions of differences between the bare and pronoun prompts (21% in Narration relations versus 31% in Contrast and 24% in Result relations), it can be better understood when considering the following perspective. In the bare-prompt condition, subject references in Narration relations sit high at 71%, limiting further increase. Transitioning to the pronoun-prompt escalates this to 92%, nearing saturation. This marginal potential for growth heightens the interaction effect.

5.4 Quantitative model comparisons

To address our research question on model evaluation, as formulated in Section 3, we conduct a quantitative analysis to assess the performance of three models by comparing their predictions against the observed interpretation biases: Bayes, Expectancy (relying primarily on the next-mention bias), and Mirror Model (based on a claim that speakers use pronouns when referring to entities whose salience makes them the preferred referent for a listener). The models are formalized in Table 14.

Table 14

Formulations of the three models of pronoun interpretation.

(a) Bayes:
(b) Mirror:
(c) Expectancy:	P(referent | pronoun) ← P(referent)

It follows from the formalization that, to determine model predictions, we need to estimate two probabilities for each of the 90 experimental stimuli (30 items × 3 relations): next-mention biases, P(referent), and pronoun production biases, P(pronoun|referent). These quantities are estimated based on the bare-prompt condition of our experiment, wherein participants have the freedom to select both the referent and the form employed to refer to the referent. To prevent zero-probability estimates, which could result in undefined model predictions for certain stimuli, we use simple additive smoothing (Schutze et al. 2008). We add a pseudo-count of one to our stimulus-specific experimental data for each logically possible combination of the V = 2 referents (subject and non-subject referents) and the W = 2 forms (pronoun, non-pronoun) that could be used in a re-mention. This approach yields stimulus-specific probability estimates as follows:

Following Zhan et al. (2020), we computed stimulus-by-stimulus predictions of the three models for pronoun interpretation preferences, and compared them against stimulus-by-stimulus observed behavior in the pronoun-prompt condition. As in Zhan et al. (2020), we used three statistical metrics to conduct a comprehensive evaluation of how well the predictions of these models align with the observed interpretation biases. These metrics, each focusing on a different aspect of model performance, include: R-squared (R²), Mean Squared Error (MSE), and Average Cross Entropy (ACE). We explain them below.

R² measures the proportion of the variance in the observed interpretation biases that can be explained by the predicted interpretation preferences of each model in a linear regression model. It is used to gauge the goodness of fit of these models. The R² value ranges from 0 to 1, where a value closer to 1 indicates a stronger fit. However, this metric may still indicate a high fit even when the model predictions are poorly calibrated (if the model systematically underestimates or overestimates the observed biases), hence additional metrics are necessary to assess the models’ performance.

We use Mean Squared Error (MSE), which calculates the average squared difference between the predicted and observed values. It is employed to estimate the average magnitude of the errors made by the models. Lower MSE values are indicative of a better model fit and reduced prediction errors. It is defined as (VI), where y_i and ŷ_i are respectively the observed and predicted interpretation preferences for the i-th stimulus and n is the total number of stimuli.

Similar to MSE, the Average Cross Entropy (ACE), defined as (VII), quantifies the dissimilarity between the observed rate y_i and the predicted rate ŷ_i. While MSE weights the discrepancies equally throughout all items, ACE more heavily penalizes predictions that are close to 0 when the observed rate is actually close to 1, as well as predictions that are near 1 when the observed rate is close to 0. In other words, ACE assigns greater importance to evaluating extreme cases.

Hence, when evaluating three models for pronoun interpretation, a better model is indicated by a higher R-squared (R²) value and lower Mean Squared Error (MSE) and Average Cross Entropy (ACE) scores.

Results. The results from all three metrics suggest that the Bayes Model outperforms the two competing models, as displayed in Table 15.¹⁸ Mirror Model demonstrates inferior performance when evaluated using the R² metric. However, when the evaluation is based on the MSE and the ACE metrics, Expectancy Model exhibits comparatively weaker performance.

Figure 8 illustrates the observed pronoun interpretation rates against stimulus-specific predictions from each model separately in three distinct plots, with the dotted x = y line representing an ideal model fit. A significant number of predictions cluster above the perfect-fit dotted line, suggesting that the models tend to underestimate subject interpretation. The Bayes Model shows a noteworthy performance particularly when the human biases towards interpreting pronouns as referring to the subject are approaching 1.

Figure 8

Quantitative model evaluation for subject referents only. The figure consists of three separate plots, each showing the predicted pronoun interpretation rates from a different model. In total, there are 270 datapoints. Each datapoint represents a prediction made by each model for each of the 90 stimuli (30 items × 3 relations in the pronoun-prompt condition).

In addition to the metrics from Zhan et al. (2020), we expanded our evaluation of the three pronoun interpretation models by incorporating the Bayesian method from Patterson et al. (2022). The results obtained using this Bayesian method were consistent with those using the metrics of Zhan et al. (2020). For more details on the use of the Bayesian method, see Section D of the Supplementary file.

6.1 Summary

We used both corpus-based and experimental methodologies to assess whether the Bayesian probabilistic framework adequately captures pronoun production and interpretation, and the relationship between them in naturalistic contexts. According to this framework, listeners utilize Bayesian principles to reverse-engineer the intended referent of a speaker. Additionally, a strong form of this framework proposes that next-mention bias and pronoun production bias are influenced by distinct contextual factors.

Our observational corpus analyses reveal that while the frequency of subject re-mentions varies across distinct discourse relations (Narration, Contrast, and Result), the rate of pronominalization remains consistent, in line with the prediction of the Strong Bayes. This observation is consistent irrespective of whether relations are explicitly signaled by connectives or inferred by human coders.

To further investigate these findings, we conducted a passage completion experiment utilizing corpus passages as stimuli. Manipulating discourse relation (Narration, Contrast, and Result) and prompt type (bare and pronoun), we obtained empirical evidence that favors the Bayesian Model over two competing models in predicting the observed pronoun interpretation bias. Moreover, our results once again highlight a separation between the factors influencing next-mention bias and those influencing pronoun production bias, in line with the prediction of the Strong Bayes.

In summary, our data provide broad support for the predictions of the Bayesian Model, both in its weak and strong forms. We discuss them in more detail below.

6.2 Weak Bayes

The central claim of the Bayesian Model, in its weaker form, is that the relationship between pronoun production and interpretation biases can be modelled through Bayes’ theorem. This proposition asserts that listeners, upon encountering a pronoun, undertake the task of reverse-engineering the speaker’s targeted referent using Bayesian mechanisms, as formulated in Eq. II. Interpretation biases thus should reflect both next-mention biases and production biases. This was substantiated by our experimental findings, where the variation pattern in interpretation biases is the same as that in next-mention biases, suggesting that the variation in next-mention biases shaped by the discourse relation manipulation became apparent through their influence on interpretation biases. Moreover, interpretation biases are much more skewed towards the previous subject across relations, in contrast to the corresponding next-mention biases, indicating the expected effect of pronoun production biases.

Further, we analyzed the predictions of the Bayesian Model along with two other models – the Expectancy Model and the Mirror Model. The bare-prompt condition data was employed to estimate the predictions of these three models, and three metrics — R², MSE, and ACE — were used to evaluate model performance. The Bayesian Model typically outperformed both rival models. In general, the Expectancy Model underestimated the bias towards interpreting a pronoun as referring to the previous subject. This tendency is visible in Figure 8, where Expectancy Model points are above the x = y perfect-prediction line: this is due to the Expectancy Model not including a term for pronoun production, which biases pronouns towards previous-subject interpretations. In contrast, the Mirror Model often underestimated cross-stimuli variability in interpretation preferences, observable in Mirror Model points clustering surrounding the x = 0.75, regardless of the actual stimulus-specific interpretation bias. This pattern is due to the Mirror Model disregarding the effect of next-mention bias, which shows more variability across stimuli than the pronoun production bias.

On the other hand, the alignment between Bayesian Model predictions and observed interpretation rates isn’t perfect either. The Bayesian Model tended to underestimate the interpretation bias towards the previous subject, though not as much as the Expectancy Model. We note that in 16 out of 90 stimuli (10 Occasion, 3 Result, and 3 Contrast), the observed interpretation rate reaches the maximum limit of 1, implying that all human participants interpreted the pronoun as referring to the previous subject. However, after applying our smoothing method, the predicted interpretation rate by all three models is unlikely to reach 1, rendering a perfect match unattainable in these instances. Bayesian Model predictions tend to be concentrated in the upper right corner, suggesting superior performance in these extreme cases, especially in Occasion scenarios. In fact, in 26 out of 30 Occasion scenarios, the observed interpretation bias towards the previous subject exceeded 0.90, while the proportions were 14 out of 30 for Contrast, and 12 out of 30 for Result. Therefore, with our stimuli, there was a clear inclination for participants to interpret the ambiguous pronoun as the subject. This can be attributed to the fact that our stimuli of discourse relations typically represent natural discourse where subject continuity is much more common. Scatter points in Figure 8 would less likely be gathered in the upper right corner if we used object-biased implicit causality verbs (such as admire) or transfer-of-possession verbs (like give) in our stimuli.

In the context of these observations, it’s worth noting that previous studies (Rohde & Kehler 2014; Zhan et al. 2020; Patterson et al. 2022) have consistently found that the Bayesian Model of pronoun interpretation outperforms alternative models across diverse languages and experimental setups. Our study, while employing a different approach by using corpus passages as stimuli instead of constructed material, aligns with this prevailing trend. By bridging the gap between constructed material and more naturalistic language, our findings contribute to the growing body of evidence that supports the role of Bayesian inference in pronoun interpretation.

6.3 Strong Bayes

Our results from both observational and experimental studies are in keeping with the prediction of Strong Bayes that the likelihood of next mention and the likelihood of pronoun production are conditioned by different sets of factors. Specifically, we show that the likelihood of re-mentioning the subject is influenced by factors related to discourse coherence, while the likelihood of pronoun production appears to be insensitive to differences between discourse relations, but primarily subject to grammatical role, whereby subject re-mentions were pronominalized significantly more often than non-subject re-mentions.

In the literature, this question is frequently reframed as an investigation into whether the production of pronouns is influenced by the referent predictability induced by a set of semantico – pragmatic factors. Assuming that addressees can (to some extent) predict which referent will be mentioned next, speakers could exploit addressees’ expectations: They could use less costly expressions, like pronouns, more frequently when referents are more expected or predictable to their addressees. This exploitation of predictability is often associated with the view of language as an efficient code for communication (Tily & Piantadosi 2009). In fact, predictability has been broadly shown to account for reduction processes in many areas of language production, such as attenuated pronunciations for more predictable words (e.g. Jurafsky et al. 2001).

Contradicting this perspective, our findings in this task show that speakers do not use more pronouns in Narration scenarios where the subject referent is more predictable. The fact that speakers do not exploit predictability is prima facie counter-intuitive because it looks like it makes them less efficient. One explanation may be that, when speakers produce language, their cognitive load is such that they can only rely on comparatively shallower cues (such as grammatical role) rather than combining them with predictability. Therefore, speakers might ignore cues that their addresses are sensitive to. Another potential reason is that the influence of predictability is so minor that it becomes eclipsed by other factors, such as the grammatical role or topichood, which is the main driver of a speaker’s choice of referential form.