Developmental Science Developmental Science 15:3 (2012), pp 436–447 DOI: 10.1111/j.1467-7687.2012.01135.x PAPER Epistemic trust: modeling children's reasoning about others' knowledge and intent Patrick Shafto, Baxter Eaves,¹ Daniel J. Navarro² and Amy Perfors² 1. Department of Psychological and Brain Sciences, University of Louisville, USA 2. Department of Psychology, University of Adelaide, Australia Abstract A core assumption of many theories of development is that children can learn indirectly from other people. However, indirect experience (or testimony) is not constrained to provide veridical information. As a result, if children are to capitalize on this source of knowledge, they must be able to infer who is trustworthy and who is not. How might a learner make such inferences while at the same time learning about the world? What biases, if any, might children bring to this problem? We address these questions with a computational model of epistemic trust in which learners reason about the helpfulness and knowledgeability of an informant. We show that the model captures the competencies shown by young children in four areas: (1) using informants' accuracy to infer how much to trust them; (2) using informants' recent accuracy to overcome effects of familiarity; (3) inferring trust based on consensus among informants; and (4) using information about mal-intent to decide not to trust. The model also explains developmental changes in performance between 3 and 4 years of age as a result of changing default assumptions about the helpfulness of other people. Introduction Children face a daunting task in learning about the world; there are an almost unlimited number of things to learn, and the time available for learning through direct experience is limited. How might they overcome this limitation? One possibility relies on the fact that children are surrounded by people, which provides an opportu- nity for them to learn about the world through indirect experience. Although potentially very informative, indirect experience also poses a problem: it is not constrained to be veridical. Children must therefore be able to infer which information and informants are trustworthy if they are to take advantage of indirect experience. This is the problem of epistemic trust (Mas- caro & Sperber, 2009; Pasquini, Corriveau, Koenig & Harris, 2007; Corriveau, Meints & Harris, 2009b; Corriveau, Fusaro & Harris, 2009a; Corriveau & Harris, 2009a, 2009b; Koenig & Harris, 2005a, 2005b; Clement, Koenig & Harris, 2004; Harris & Corriveau, in press; Harris, 2007; Jaswal, Croft, Setia & Cole, 2010; Jaswal & Neely, 2006). Even preschool children can make sensible inferences about who to trust. Koenig and Harris (2005a) demon- strated that 4 year-old children can distinguish between accurate and inaccurate informants and can use this information to aid in the selection of a more accurate informant. Indeed, by 4 years of age children are quite sophisticated in their ability to monitor who to trust. For instance, Pasquini et al. (2007) systematically manipu- lated the relative accuracy of two informants in a labeling task, and found that children preferred to ask the more accurate informant about a label for a novel object (see Figure 2). Four year-olds can also use familiarity in judging informants, favoring informants with whom they have established a strong history of accuracy by default but switching to an unfamiliar informant if faced with evidence that the unfamiliar informant is more accurate (Corriveau & Harris, 2009a). In addition, children use information about consensus, trusting informants who label objects in the same way as the majority of others (Corriveau et al., 2009a). These studies provide strong evidence that children use a variety of information to guide who to trust. Researchers have interpreted these results as an indi- cator of children's abilities to infer which individuals are knowledgeable. Under this interpretation, individuals who label familiar objects correctly are inferred to be knowledgeable; whereas, individuals who label familiar objects incorrectly are inferred to be not knowledgeable. However, awareness of an informant's knowledge is not enough to justify epistemic trust: it is also important to understand their intent-whether they are trying to be helpful or deceptive. A knowledgeable but deceptive informant should be expected to consistently provide unreliable information, and should not be trusted. Given Address for correspondence: Patrick Shafto, 317 Life Sciences, University of Louisville, Louisville, KY 40292, USA; e-mail: p.shafto@louisville.edu © 2012 Blackwell Publishing Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA. this observation, one might reasonably ask, are children's abilities strictly due to inferences about knowledge, or do inferences about intent affect their judgments about who to trust? A separate line of experiments suggests that preschool children do use information about intent to guide infer- ence. Mascaro and Sperber (2009) presented children with a situation in which there were two different colored boxes, under one of which was hidden a candy. An informant then looked under both boxes, so the child knew that the informant knew where the candy was. In the test condition, a puppet entered and warned the child that the informant was a 'big liar' who always told lies. The informant then labeled one box, saying for example, 'The sweet is in the red box'. Their results showed that by 4 years-old children used information about the infor- mant's intent, showing a significant preference for the cup that the informant did not indicate. This study suggests that preschool children use intent, when it is clearly marked, to guide inference. Do inferences about intent play a role in children's epistemic trust? While researchers have interpreted pre- vious results as indicators of children's inferences about knowledgeability, evidence suggests that around the same ages children are developing the ability to use an infor- mant's intent to guide inference. We propose a theoretical framework within which we can investigate whether inferences about epistemic trust are due to knowledge alone (cf. Bovens & Hartmann, 2003) or whether intent plays a substantive role in children's judgments. The framework demonstrates how a learner might integrate inferences about others' knowledge and intent, while at the same time learning new labels. We formalize this framework as a probabilistic model and provide evidence that joint inference about informants' knowledge and intent provides an accurate account of 4 year-olds' behavior and explains developmental changes between the ages of 3 and 4 as a consequence of changing prior expectations about others' intent. We proceed by introducing the model, which formal- izes the relationship between evidence, inferences about knowledge and intent, and learning. Next, we demon- strate that our model of trust captures 4 year-olds' abilities but a simpler model based on knowledge alone does not. We then apply the model to 3 year-olds' per- formance, contrast the model's explanations for 3 and 4 year-olds' behavior, and conclude by discussing impli- cations for learning and development. A model of epistemic trust Formalizing the role of epistemic trust in learning requires specifying two inference problems. First, how would a learner expect an informant to choose infor- mation to provide, and how would that depend on the informant's knowledge and intent? Second, how would the learner use the information provided by the infor- © 2012 Blackwell Publishing Ltd. Modeling epistemic trust 437 mant to simultaneously make inferences about the true state of the world and about whether to trust the infor- mant? We present a model that unifies these problems under a single framework, and provides an account of how children may simultaneously learn about the world and whether to trust an informant. Because the studies we model involve learning the correspondence between objects and their labels,¹ the 'true state of the world' we seek to model is the set of correct labels in a word-learning task. We adopt a probabilistic modeling framework in which learning is based on data and formalized as Bayesian inference (Tenenbaum, Griffths & Kemp, 2006). In Bayesian inference, a learner's beliefs after observing some data (their posterior beliefs) are related to their prior beliefs as well as how well those beliefs explain the data (the like- lihood). In this case, the beliefs we seek to model include children's beliefs about their world (i.e. the correct label or labels for an object or objects) and their informant (i.e. how knowledgeable and helpful the informant is). It is necessary to specify prior beliefs about each of these characteristics. The other key component of our approach is the likelihood-specifically the sampling model underlying the calculation of the likelihood. Pre- cisely which label an informant provides depends on their knowledge and intent, as well as the true label; a learner, after observing the labels, can therefore reason back- wards about all three of these things, given certain (sampling) assumptions about how knowledge and intent translate into the choice of a label. In our model, epistemic trust is assumed to depend on the knowledgeability of the informant (denoted k) as well as the extent to which he or she intends to be helpful (denoted h). If we let / denote the actual label that the informant provides, then the goal of the learner is to infer the most likely state of the world s (i.e. the correct label for an object) and nature of the informant (k and h) given that label. Formally, this corresponds to calculating P(s,k,h|l), which according to Bayes' rule is given by: P(s,k,h|l) x P(l\s,k,h)P(s,k,h), = (1) where P(s,k,h) P(s)P(k)P(h) assuming the prior prob- ability of s, k, and h are independent of one another. Note that s and / correspond to possible object labels: s is the correct label and I is the label given to the learner by the informant. The two 'social' characteristics are binary: the informant is either knowledgeable (k 1) or not (k 0), and is either trying to help (h 1) or trying to hinder (h -1) (cf. Ullman, Baker, Macindoe, Evans, Goodman & Tenenbaum, 2010). However, learn- ers' beliefs about these characteristics are distributions over the possible values that they can take. - = = Viewed in this fashion, it becomes clear that different experimental manipulations correspond to different prior assumptions. For instance, if a child observes a new In one case, what is being learned is an object's location, but, as we will argue, the formal problem is the same. 438 Patrick Shafto et al. = informant labelling an object whose label is already known to the child, then P(s) is a point mass distribution which assigns probability 1 to the correct label and probability 0 to all other labels. When this happens, the learner can leverage their knowledge about the true state of the world to draw inferences about the informant's knowledge k and helpfulness h. Alternatively, the child might not know the true label; in this case, if there are n possible labels, it would be sensible to assume, as our model does, that P(s) 1/n for all possible states of the world (i.e., all possible labels). If the child is provided with a label from an informant whose knowledgeability and/or helpfulness is known from past experience, then the priors P(k) and P(h) can be adjusted to capture this information. In more complex situations where labels are provided (for unknown objects) by multiple informants whose knowledge and helpfulness are not known, the learner must simultaneously infer the correct labels, along with the knowledge k; and helpful intent h; of each informant i. All of the scenarios described above can be captured by the Bayesian learning rule in Equation 1, in which the link between prior beliefs P(s,k,h) and posterior beliefs P(s,k,h|l) is supplied by the likelihood function P(l\s,k,h). The likelihood function, in this case, reflects the learner's theory of how the informant would have generated a label, if the true state of the world was s, and the informant had knowledge level k and helpfulness h. As Figure 1 illustrates, the behavior of the informant also depends on a hidden variable, b, which corresponds to the informant's belief about what the true label is, where this belief depends on how knowledgeable the informant is as well as on the true label. We express this via a distribution over beliefs, P(b|k,s). Then, for any given belief b, the informant will generate the label in a manner that depends on how helpful they are, expressed by the distribution P(s|b,h). Because the learner cannot directly observe the beliefs b of any informant, he or she must (in effect) average over his uncertainty about what the informant really believes in order to calculate the likeli- hood of seeing that label 7. This is captured by the fol- lowing equation: P(I|s,k,h) = Σ P(I|b,h)P(b|k, s). b In order to complete the model, we need to specify these two distributions-one over the possible beliefs of the informant, and the other over what labels the informant might provide as a result of these beliefs. For the distri- bution over possible beliefs, we assume that: P(b|k, s) = 0 1/n if k = 1 and b = s if k = 1 and b s if k = 0. (3) That is, we assume that a knowledgeable informant al- ways has the correct belief, whereas a non-knowledgeable informant believes something chosen randomly from the © 2012 Blackwell Publishing Ltd. 2 set of possible labels. This is a simplification, of course, but it is sufficient for the current purposes. The subtle aspect to the model lies in the choice of P(lb,h), the probability that an informant would use the label / given that the informant believes the true label to be b and has degree of helpfulness h. The model assumes that a helpful informant (h 1) will try to select the label that maximizes the extent to which the learner comes to share the same belief as the informant, whereas an unhelpful informant (h -1) will try to minimize this. = = Formally, this is accomplished by choosing a distri- bution over labels P(lb,h) that satisfies the following 'communicative sampling' relationship (Shafto & Goodman 2008; Shafto, Goodman, & Griffths, under revision). In communicative sampling, the key idea is that the speaker actively seeks to shape the beliefs of the listener in a manner governed by a 'helpfulness' param- eter h, and both parties are assumed to be Bayesian reasoners. Formally this means that the probability that an informant (or speaker) with belief b chooses a label 1 is closely related to the probability that the learner will come to share the informant's beliefs as a consequence of this labelling: P(l|b,h) ∞ P(b|l,h)", (4) where the normalizing term is obtained by summing over all possible labels 7. Intuitively, the equation states that the learner expects the communicator to choose labels that tend to maximize the probability of the learner believing what the communicator believes in the helpful case, and minimize this probability in the unhelpful case. This is because when the communicator is being helpful, h = 1, they choose labels in such a way that tends to maximize P(b|l,h), the probability of the belief they actually hold. When the informant is not being helpful h -1, they choose labels in a way that tends to minimize the probability of the learner inferring the belief the communicator holds.² While Equation 4 does not directly tell us what kind of labeling distribu- tions actually satisfy this relationship, it is possible to discover this using numerical methods like fixed point iteration (see Shafto & Goodman, 2008; Shafto et al., under revision, for more detailed discussion). = In fact, although the underlying theory is complex, the behavior that results turns out to be quite simple. For instance, suppose that the informant can choose between four labels (A, B, C and D), and has the belief that the correct label is A. It turns out that, if the informant is trying to be helpful, then the probability that the informant will choose label A (that is, P(l A|b = A,h = 1)) is high. The other three labels are all equally likely, and chosen with low probability.³ On the = Note that in this equation, we assume that learners have uniform prior expectations about the informant's possible beliefs. When the informant's knowledge and intent is known, these proba- bilities are 1 and 0, respectively. Modeling epistemic trust 439 4 knowledge state of the world beliefs label helpfulness Figure 1 Graphical representation of the sampling model. Boxes indicate variables, and lines indicate probabilistic dependence. The variables of knowledge k, helpfulness h, and beliefs b are all properties of the informant: the informant's beliefs depend on whether they are knowledgeable about the world, and their beliefs and and helpfulness jointly determine the label they choose. other hand, if the informant is being unhelpful, this sit- uation reverses, with the probability of label A becoming low, and the probability of the other labels rising.4 Modeling results Modeling 4 year-olds' behavior in trust tasks We model the performance of 4 year-olds, contrasting the fits of the Knowledge & Intent model with the fits of a Knowledge-only model. In the experiments described above (Pasquini et al., 2007; Corriveau & Harris, 2009a; Corriveau et al., 2009a; Mascaro & Sperber, 2009), there are two types of question asked of children. Ask Ques- tions query children about which informant they would rather ask for information. Endorse Questions occur in situations in which multiple informants provide labels for an unfamiliar object, and children are asked what they believe the object is called. The first two experiments (Pasquini et al., 2007; Corriveau & Harris, 2009a) in- volved Ask Questions, which we model by evaluating which of the informants is more likely to provide the correct label. The second two experiments (Corriveau et al., 2009a; Mascaro & Sperber, 2009) involved En- dorse Questions, which we model by again asking it to choose between informants and assuming that the label is the one that the chosen informant previously generated. Full mathematical details can be found in Appendix A. Our model, like children, makes inferences about the informant's knowledge k and helpful intent h; like chil- dren, inferences in the model are shaped by prior expectations about whether informants are likely to be helpful and/or knowledgeable. Our modeling framework allows us to explore the nature of the expectations that children have by allowing us to determine which parameters best fit their observed behavior. Each com- The exact probabilities are 0 and 1/3, assuming four labels. © 2012 Blackwell Publishing Ltd. ponent, knowledge and intent, is captured by two parameters: balance and uniformity. Balance represents children's expectation about people on average, while uniformity captures the expected variability across indi- viduals. For the Knowledge & Intent model, we infer whether children believe that people are generally knowledgeable and helpful, and whether people are uniform or variable in those tendencies. These parameters have important implications for, among other things, children's ability to learn from evi- dence and consequently the changes in predictions across conditions. To the degree that children believe that peo- ple are uniformly knowledgeable or helpful, the model predicts that they will be relatively insensitive to evidence to the contrary. In contrast, if they expect people to vary in knowledge or helpfulness, the model predicts that they will be relatively sensitive to evidence, updating their beliefs about an individual given the information that they provide. Similarly, to the degree that children believe that people tend to be, but are not perfectly helpful, they will remain skeptical of even informants who provide truthful information, effectively reducing the variability in their behavior. To model behavior based on knowledge alone, we must make some assumption about how knowledgeable people choose labels. Previous empirical research is not explicit about this issue, but a sensible approach is to model children as assuming that informants choose information helpfully. To capture this, we fix beliefs about helpfulness at P(h) 1; that is, informants are assumed to be always helpful. The key question will be: is behavior adequately explained by inferences based on knowledge alone, or does the model with both knowledge and intent provide a significantly more accurate explanation of children's behavior? The results reported here are based on a single set of best-fit parameters for the Pasquini et al. (2007), Corri- veau and Harris (2009a), and Corriveau et al. (2009a) studies. For the Knowledge & Intent model, the best fitting parameters are .01 uniformity and .75 balance for knowledge, and .001 uniformity and .75 balance for helpfulness. The values of the balance parameters indi- cate that 4 year-olds assume that people are generally knowledgeable and helpful. The values of the uniformity parameters indicate that they assume that informants tend to be variable. Together the parameters indicate that informants are generally assumed to be knowledgeable and helpful, but there are informants who tend to be not knowledgeable and/or not helpful. For the Knowledge-only model, the best fitting parameters are .01 uniformity and .05 balance. Accord- ing to the Knowledge-only model, children assume that people as a group tend to be not particularly knowl- edgeable, but people do vary-individuals are either knowledgeable or not. These parameter values are sur- prising, and we discuss why these parameters best fit the data in greater detail below. Full details about the fitting procedure are reported in Appendix B. 440 Patrick Shafto et al. (၁) p(chooses with group) 0.5 0.5 Model Children 100 vs 0 100 vs 25 75 vs 0 75 vs 25 (b) p(asks familiar informant) 0.5 100 vs 0 100 vs 25 75 vs 0 K Only Children 75 vs 25 0.5 0 0.5 the tir pretest familiar 100% familiar 0% pretest familiar 100% familiar 0% pretest test (d) p(chooses with informant) 0.5 p(chooses with group) 0.5 pretest test 0 baseline liar Figure 2 Model predictions and observed results for 4 year-olds' choices in epistemic trust tasks. Black bars represent the predictions of the Knowledge & Intent model; gray bars represent predictions of the Knowledge-only model; white bars represent children's behavior.(a) In Pasquini et al. (2007), children were asked which of two informants they would trust to provide a new label. The informants differed in their accuracy on labels known to the children (shown on the x axes). Both children and the Knowledge & Intent model choose the more accurate informant, and the strength of the inference decreases when accuracy is probabilistic. The Knowledge-only model fails to capture the effects of variations in accuracy. (b) In Corriveau and Harris (2009), the children and both models initially prefer a familiar informant who has been known to be knowledgeable and helpful (PRE-TEST), and continue to prefer that informant if she ontinues to be accurate (FAM 100%). However, if she does not, they switch their preference to the novel informant (FAM 0%). (c) In Corriveau et al. (2009a) children are presented with a novel object that is labeled by groups of informants, a majority of whom (but not all) agree on the label. Both children and the Knowledge & Intent model use agreement among informants to infer that informants in the majority are more trustworthy. This is true both when asked about that label (PRE-TEST) as well as when deciding about a novel label provided either by the original dissenter or one of the original majority informants (TEST). Both models somewhat overestimate the difference between the questions; however, the Knowledge-only model performs con- siderably worse. (d) In Mascaro and Sperber (2009), after a baseline test, children were told that the informant was 'a big liar'. They, like the Knowledge & Intent model, use this information to choose consistently with the informant only if the informant is not a liar. The Knowledge-only model is omitted because it, by definition, cannot capture the effect of a knowledgeable but not helpful informant. © 2012 Blackwell Publishing Ltd./n

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Developmental Science Developmental Science 15:3 (2012), pp 436–447 DOI: 10.1111/j.1467-7687.2012.01135.x PAPER Epistemic trust: modeling children's reasoning about others' knowledge and intent Patrick Shafto, Baxter Eaves,¹ Daniel J. Navarro² and Amy Perfors² 1. Department of Psychological and Brain Sciences, Univers