Johannes B Mahr1

Olivier Mascaro2

Hugo Mercier3

Gergely Csibra4

Johannes Mahr
email: jmahr@fas.harvard.edu

The effect of disagreement on children's source memory performance

Keywords: Source memory, belief transmission, disagreement

Source representations play a role both in the formation of individual beliefs as well as in the social transmission of such beliefs. In this study, we investigated whether young children are sensitive to the communicative functions of source information. Three experiments with an identical design (one original study and two replications) with 3-to 4-year-old-children (N = 100) assessed whether children's source memory performance would improve in the face of disagreement and whether such an effect interacts with different types of sources (first-vs. second-hand). Four-year-olds (but not three-year-olds) performed better in response to an open source memory question when their interlocutor had disagreed with them compared to when it had agreed with them. Children were also better recalling 'having been told' than 'having seen'. These results suggest that by 4 years of age children are sensitive to the communicative functions of source information.

Introduction

The ability to 'know how we know'-to know the sources of our beliefs-plays an important role in belief formation and transmission. The source of a piece of information can have a dramatic impact on its cognitive effects in belief formation: for instance, people update their beliefs on the basis of sources they view as reliable, and tracking where a belief comes from allows people to adjust their trust in the source if it turns out that the belief was false (e.g. [START_REF] Cosmides | Consider the source: The evolution of adaptations for decoupling and metarepresentation[END_REF][START_REF] Mercier | Not born yesterday: The science of who we trust and what we believe[END_REF]. Apart from playing a role in belief formation, knowing where our beliefs come from also influences how we communicate those beliefs to others. Claims can be undermined if they are linked to an inappropriate source (e.g., if someone asserts that it will rain tomorrow because they dreamt it), or bolstered if they are attributed to an authoritative source (e.g., if your doctor tells you that you are sick; see [START_REF] Sperber | The guru effect[END_REF].

When children expect that source information will play an important communicative role, they might be more likely to explicitly remember source information. In particular, source information will especially be useful in interpersonal disagreement, as one can report sources in an attempt to convince a disagreeing conversational partner (e.g., "I saw it"), or to mitigate the disagreement by hedging one's position (e.g., "someone told me"). In order to assess whether preschoolers understand these social functions of source information, we studied whether disagreement facilitates the explicit retrieval of source information.

Before introducing our experimental design, we offer a short overview of the cognitive requirements of source representation and how these capacities might be brought to bear in communication.

The Cognitive Requirements of Explicit Source Memory

In spite of its apparent simplicity, the capacity to report the sources of our beliefs is cognitively demanding. Consider the simplest and most common sources people attribute their beliefs to: perception, hearsay, and inference. If you form the belief that it is going to rain tomorrow after watching a weather report, did you form the belief based on perception of the map, hearsay from the presenter, or inference from this information? Competently retrieving source information is particularly challenging because it is often not obvious what the appropriate source is in a given context and different sources can have different cognitive and conversational consequences (e.g. Ozturk & Papafragou, 2016;Papafragou et al., 2007;Casetlain, Floyd, & Mercier, 2020).

Partly as a result of the difficulty in attributing sources to our beliefs, people seem to leave most of their beliefs without source tags when they are acquired [START_REF] Johnson | Memory and reality[END_REF]. Even if sources are taken into account in belief formation (people tend to update their beliefs on the basis of sources they view as reliable), they are only explicitly represented as sources whenever they are needed after the fact [START_REF] Haigh | What children know about the sources of their knowledge without reporting it as the source[END_REF]. To do so, dedicated source monitoring mechanisms infer sources from memories of learning events and other information [START_REF] Johnson | Source monitoring[END_REF], such as their understanding of what sources are appropriate for what beliefs (for example, that "feeling" can't be the source of knowing the color of an object; [START_REF] Pillow | Preschool children's understanding of the relationship between modality of perceptual access and knowledge of perceptual properties[END_REF].

Source recall is thus a cognitively sophisticated and demanding ability. Consequently, children start developing the capacity to accurately report the sources of their beliefs relatively late (between three and five years of age, see [START_REF] Drummey | Developmental changes in source memory[END_REF][START_REF] Gopnik | Knowing how you know: Young children's ability to identify and remember the sources of their beliefs[END_REF][START_REF] O'neill | Young children's ability to identify the sources of their beliefs[END_REF] compared to other social skills such as mindreading (e.g., Király, Oláh, Csibra, & Kovács, 2018;[START_REF] Kovács | The social sense: susceptibility to others' beliefs in human infants and adult[END_REF]Southgate, Chevalier, & Csibra, 2010). What are the functions of source representation hat warrant this cognitive complexity?

The Cognitive Functions of Explicit Source Memory

Source representation might serve several functions, which can be broadly classified into two categories: individual and social functions [START_REF] Cosmides | Consider the source: The evolution of adaptations for decoupling and metarepresentation[END_REF]. As mentioned above, source representation might enhance individual cognition by allowing people to appropriately update their beliefs. By comparing the sources of beliefs held in memory and of novel pieces of informationin particular communicated information (see, [START_REF] Mercier | Not born yesterday: The science of who we trust and what we believe[END_REF][START_REF] Sperber | Epistemic Vigilance[END_REF] people might make better decisions about how to weigh these beliefs and when to revise them. Directly or not, it is chiefly this individual function that has been the focus of the developmental literature on source memory (e.g., [START_REF] Giles | Source monitoring reduces the suggestibility of preschool children[END_REF][START_REF] Gopnik | Knowing how you know: Young children's ability to identify and remember the sources of their beliefs[END_REF][START_REF] Robinson | Children's working understanding of knowledge sources: Confidence in knowledge gained from testimony[END_REF].

For example, [START_REF] Whitcombe | Children's decisions about what to believe and their ability to report the source of their belief[END_REF] as well as [START_REF] Robinson | Children's suggestibility in relation to their understanding about sources of knowledge[END_REF] investigated whether 3-to 5-year-old children would accept a contradiction from an experimenter who was either better or less well informed than themselves. They tested whether children's ability to accurately remember the source of their own belief would help them make the right decision about what to believe when the experimenter contradicted them.

The results suggested that children were sensitive to how well informed a speaker was relative to themselves in their belief updating decisions. For instance, in Whitcombe and Robinson's tunnel game studies, the participants had to identify which one of a pair of toys differing either in color, or in hardness, was hidden in a tunnel. The children and an experimenter sometimes saw the hidden toy, or they felt it. Children who had only uninformative access (e.g., felt a toy identified by color) were more likely to defer to an experimenter's claim about the toy's identity when the latter had informative access (saw the toy), than when she did not (felt it). However, the results did not reveal a strong link between source representation and belief revision: many children were able to update their beliefs appropriately without being able to accurately remember the source of their own beliefs.

Related evidence comes from a large literature investigating how children learn from testimony. Preschoolers have been shown to have sophisticated capacities for tracking the trustworthiness and competence of informants and to use such information for assessing the reliability of assertions in belief formation [START_REF] Mascaro | The moral, epistemic, and mindreading components of children's vigilance towards deception[END_REF][START_REF] Koenig | Preschoolers mistrust ignorant and inaccurate speakers[END_REF][START_REF] Koenig | Trust in testimony: children's use of true and false statements[END_REF]; for recent reviews see Harris et al., 2017;Stephens, Suarez, & Koenig, 2016). While explicit source memory has not been the focus of studies investigating how children learn from testimony, these topics are closely related. Studies of children's capacities to evaluate the reliability of speakers, for example, suggest that children track where information comes from for long enough to revise trust when a statement turns out to be inaccurate. Moreover, preschoolers have been shown to not only monitor the reliability of speakers but to also appropriately revise their beliefs when new information about the speaker's reliability is revealed (Luchkina, Corriveau, & Sobel, 2020;Scofield & Behrend, 2008). We term these functions 'individual' because they mainly concern the way a given individual manages their beliefs in the face of new information.

Besides these individual functions, however, source information also has important social functions; that is, functions concerning the exchange of beliefs between individuals.

Being able to remember the sources of their beliefs allows people to communicate these sources to others, thereby serving a variety of goals: one can use sources to convince ("I saw it with my own eyes"), to gain credit ("I found the solution on my own"), or on the contrary, to hedge one's statements ("It's only something I've heard") (for a more general argument regarding the social functions of episodic memory, see [START_REF] Mahr | Why do we remember? The communicative function of episodic memory[END_REF]; see also Altay & Mercier, in press;[START_REF] Silver | No harm, still foul: Concerns about reputation drive dislike of harmless plagiarizers[END_REF][START_REF] Shaw | Whose idea is it anyway? The importance of reputation in acknowledgement[END_REF]. The importance of the social functions of source representation is also suggested by the fact that over one-quarter of the world's languages employ obligatory grammatical markers, known as evidentials, specifying the source of the speaker's assertion [START_REF] Aikhenvald | Evidentiality[END_REF] de Haan 2013 gives an estimate of over 50% of the world's languages). Even languages that do not encode evidentiality grammatically possess numerous ways of communicating the sources of a speaker's beliefs [START_REF] Degen | Definitely, Maybe: A New Experimental Paradigm for Investigating the Pragmatics of Evidential Devices across Languages[END_REF].

Moreover, there are reasons to believe that children's ability to use source information for social ends is closely related to the development of source memory. It has been shown that children's production of accurate evidentials (arguably serving a social function of source memory) develops in parallel with their source memory [START_REF] Ünal | Evidentiality, Information Source, and Cognition[END_REF], and precedes their full comprehension of similar expressions (arguably serving a more individual function of source memory) [START_REF] Ünal | Monitoring sources of event memories: A cross-linguistic investigation[END_REF].

How does source information contribute to communicative exchanges? First, source information helps audiences calibrate their trust in whatever the speaker is asserting (e.g., [START_REF] Nagel | The social value of reasoning in epistemic justification[END_REF]. By communicating their source, speakers leave it up to their audience to weigh the evidence according to their own estimate of the source's credibility. Second, source claims are relevant to assess who is accountable for the validity of the communicated information. By claiming to have first-hand evidence, a speaker makes themselves directly accountable, while referring to a second-hand source allows the speaker to defer such responsibility to someone else (see, e.g., Altay, Majima, & Mercier, in press;[START_REF] Mahr | The effect of source claims on statement believability and speaker accountability[END_REF].

The capacity to know the source of one's belief is therefore not only important to enable efficient belief revision: explicit source memory also plays a crucial role in helping speakers effectively communicate their beliefs to others.

Disagreement and the Social Functions of Source Memory

When someone is asked to provide a justification-and thus potentially to provide source information-for their beliefs, the ease with which they do so, and the accuracy with which they do so (in terms of providing accurate source information) should vary based on how much they have anticipated having to provide such justification. Moreover, the speaker who asks for a justification might exert more scrutiny of the justification provided if the justification request follows a disagreement. As a result, a disagreement should lead people to anticipate not only that they might need to provide a justification but also that they will need to provide accurate justifications. If source memory serves social functions, when facing disagreement speakers might thus be prompted to spend more cognitive resources on retrieving and reporting their source accurately than in other conversational contexts.

Existing evidence shows that preschoolers are sensitive to some features of disagreement: 4-year-olds have been shown to detect when someone contradicts them [START_REF] Doebel | Young children detect and avoid logically inconsistent sources: The importance of communicative context and executie function[END_REF], and to adjust their communication to convince an interlocutor who keeps disagreeing [START_REF] Mascaro | Nonverbal Rhetoric: 2-to 4-Year-Old Children Select Relevant Evidence When Trying to Influence Others[END_REF]. Given that the preschool years are crucial in the development of source memory [START_REF] Gopnik | Knowing how you know: Young children's ability to identify and remember the sources of their beliefs[END_REF], and that children of this age appear to be able to react appropriately to disagreement, they provide the most relevant age at which to test our hypothesis, namely, that source memory performance will be facilitated in a context of interpersonal disagreement, compared to a context of interpersonal agreement.

The Present Study

In the current study, the children were made aware of the contents of a container either by looking inside the container themselves, or by being told what the contents were by the experimenter. The children then met an interlocutor (a puppet) who asked them about those contents. Once the child had said what they believed was in the container, the puppet either agreed or disagreed with the child's answer. Finally, the puppet asked an open ("How do you know"?) followed by a closed ("Did you see it or did someone tell you?") source memory question. We conducted three separate experiments with the same design: the original study (with 4-year-olds), a replication with the same age group, and a replication with younger children (3-year-olds).

While [START_REF] Whitcombe | Children's decisions about what to believe and their ability to report the source of their belief[END_REF] and [START_REF] Robinson | Children's suggestibility in relation to their understanding about sources of knowledge[END_REF] investigated whether children would appropriately revise their own belief in the face of a contradiction by an interlocutor, they did not test the effects of this contradiction on source memory performance. Moreover, in contrast to previous studies, in our paradigm, the source memory question was not asked by the experimenter but by the interlocutor puppet who was engaged in a game with the child. This difference is important because children might interpret questions asked by a 'third party' experimenter as test questions [START_REF] Grosse | Two-year-old children differentiate test questions from genuine questions[END_REF], rather than as a natural request for justification which was our target here.

While test questions assume that the speaker herself already knows the answer, requests for justification can be interpreted as a speaker's genuine requests for more information that could potentially change their minds.

Our central prediction bore on the effect of agreement: We predicted that disagreement would facilitate source memory performance, making children more likely to recall the source of their beliefs when their interlocutor disagreed with them compared to when the interlocutor agreed with them.

Methods

We conducted three experiments: Experiment 1 constituted the original study with 4year-old children. Its results tended to confirm our hypothesis about the effect of agreement on source memory, by showing marginally significant statistical trends in the expected direction. Thus, in order to confirm our results, we ran Experiment 2, which was a pre-registered replication of Experiment 1. Experiment 3 was designed to test the ontogeny of the behaviors observed in Experiments 1 and 2. It used the same procedure as Experiments 1 and 2 with a younger age group (3-year-olds). Since the three experiments were identical in terms of procedure and design, we report their methods together. All experiments were carried out in the same environment, and Experiments 2 and 3 were performed after Experiment 1.

Participants

For Experiment 1, we recruited 34 4-year-old children. Two of these children had to be excluded because of experimenter error (see Coding and Analyses), so that the final sample included 32 children (age range: 48-59 months-old; mean age: 54 months; 16 females). We chose this number of participants so as to ensure that at least four children completed each counterbalancing order (see Design).

In Experiments 2 and 3, we aimed for a sample size superior or equal to that of the original study for each age group. We had a pre-registered stopping rule of 40 participants for each of our experiments which we exceeded due to a scheduling miscommunication between the research assistants running the study. Thus, we recruited 42 4-year-olds for Experiment 2 and 43 3-year-olds for Experiment 3. Children were excluded from analysis if they contributed fewer than four valid trials (Experiment 1: 0 children; Experiment 2: 6 children; Experiment 3: 6 children). Further, we had to exclude 2 children from Experiment 2 due to technical difficulties and 1 child from Experiment 3 for not fulfilling the age criterion. Thus, Experiment 2's final sample included 34 4-year-olds (age range: 48-59 monthsold; mean age: 56; 18 females) and Experiment 3's final sample included 34 3-year-olds (age range: 36-47 months-old; mean age: 43; 11 females).

Design

All three experiments employed the same within-subjects design with two two-level independent variables: Agreement (interlocutors agrees/interlocutor disagrees) and Source (seeing/being told). Participants completed three familiarization trials and six test trials, which exposed them to each combination of factors at least once. We chose to expose children to six rather than four test trials in order to maximize the amount of data points we could collect per participant and piloting revealed that increasing the trial number to eight test trials caused children to lose focus in the last two trials.

The order in which Agreement and Source factors varied was counterbalanced within as well as across participants, and so was the order of sources mentioned in the closed source memory question. Moreover, whether children received an 'agreement' or 'disagreement' and a 'seen' or 'told' trial first was counterbalanced across children. All in all, we employed eight counterbalancing orders, aiming for a minimum of four participants per order in each group (for the full counterbalancing information see Supplementary Information).

Each child was asked three test questions per test trial: a 'contents question' about the contents of the container, an open source memory question ("how do you know that there is a […] inside ?"), and a closed source memory question ("did you see or were you told that there is a […] inside?"). We included both an open and a closed test question in order to have two separate measures of children's source memory. While the open source question was intended to assess children's source memory through free recall, the closed source question was intended to serve as a recognition memory test for source.

Procedure

Before the start of the experiment, the children were asked if they wanted to participate in a game and only participated in case both they and their parents agreed to do so (parents received and signed an informed consent form). Children were seated on a chair at a table which was placed in front of a curtain. A first experimenter sat next to the table, while a second experimenter was hidden behind the curtain controlling a puppet serving as the interlocutor for the child. Caregivers were allowed to stay in the room but asked not to interfere with the procedure in any way. The whole procedure was video recorded. Detailed scripts for the familiarization and test procedures can be found in the Supplementary Information.

Familiarization Trials

Children completed three familiarization trials introducing them to the setting of the task, their interlocutor ('Zirmi the cat'), the different sources (finding out about the contents of a box either by looking inside or by being told), and the fact that Zirmi sometimes disagrees without necessarily being correct.

In the first familiarization trial, children were introduced to Zirmi and asked if they wanted to play a game in which they have to find out what was inside a box placed on the table in front of them. Next, Zirmi opened the box and showed its contents to the child.

In the second familiarization trial, the experimenter removed the box from view and placed a new object inside it. The experimenter then asked the child whether they wanted to have a look inside and tell them what was in the box. The children were then allowed to look into the box and answered the question. If the child gave an incorrect answer, the experimenter corrected them. After the child gave the correct answer, the experimenter asked the child the open source question ("How did you find out what was inside?") and corrected them if they gave the wrong answer. Next, the experimenter turned away and Zirmi appeared from behind the curtain. Zirmi asked the child about what was inside before disagreeing with the child and suggesting a different, wrong answer. Finally, the child and Zirmi opened the box together to find out that the child had been correct about its contents.

The third and last familiarization trial was similar in structure to the second one.

However, in this trial the experimenter told the child about the contents of the box and Zirmi agreed with the child about the contents.

Test Trials

At the beginning of each test trial, only the first experimenter and the participant interacted, and the puppet ("Zirmi") was not present. The experimenter removed the object from the last trial from the box, in full view of the child. Next, she hid a new object inside the box underneath the table, so that the hiding (but not the object itself) was visible to the child.

In each trial, a different object was hidden inside the container. Which object was hidden in Next, in all conditions, the experimenter turned away and Zirmi appeared from behind the curtain. The puppet asked the child what was inside the box by saying: "Hello! Oh! There is the box again… What do you think is inside?" ('contents question'). Zirmi repeated the contents question until the child gave an answer. After the child had answered, Zirmi's reaction differed across conditions. In the 'agreement' condition, Zirmi agreed by saying: "You are right! There must be a [name of object that she child said to be inside the box, e.g., a car] inside." In the 'disagreement' condition, Zirmi disagreed by saying: "No! I don't think there is an [name of object that she child said to be inside the box, e.g., a car] inside! I think there is a [name of an alternative object, e.g., a watch] inside!". In each disagreement trial, Zirmi suggested a different alternative object. The alternative object Zirmi suggested to the child when disagreeing was predetermined for each trial and stayed consistent across children.

In all conditions, after either agreeing or disagreeing with the child, Zirmi asked the child the open source question ("How do you know that there is a [name of object that she child said to be inside the box, e.g., a car] inside?"). If the child did not answer, Zirmi repeated this question once. If the child still did not answer, the trial was coded as an incorrect answer (see below). Regardless of the child's answer to the open source question, Zirmi then asked the child the closed source question ("Did you see or were you told that there is a [name of object that she child said to be inside the box, e.g., a car] inside?"). The order in which sources were mentioned in the closed source question was counterbalanced across trials within subjects. Again, if the child did not answer the closed question, Zirmi repeated the question once. In the disagreement condition, in response to the child's answers, Zirmi said: "Hm.. if you [saw/were told] then you must be right… there must be an [name of object that she child said to be inside the box, e.g., a car] inside".

Next, in all conditions, Zirmi and the child opened the box together to check its contents. Finally, Zirmi said: "Oh! I have to go…!" and went away behind the curtains.

Participants then proceeded to the next test trial, till the end of the experiment.

Coding

Responses were double-coded by coders unfamiliar with the hypotheses of the study.

Disagreements between the two primary coders were resolved by a third coder (the first author; Cohen's kappa across all studies and measures was .833).

A first preliminary coding served to exclude participants and trials for which the experimental protocol had not been followed correctly, or if parents had interfered in a relevant way in the procedure. For the remaining participants/trials, the children's answers were transcribed by two different coders unfamiliar with the hypotheses of the study.

Children's answers to three test questions were coded: (1) the contents question, ( 2) the open source question, (3) the closed sources question.

Regarding (1), children's responses were coded as correct when they mentioned what was inside the container or when they referred to objects looking closely similar to the actual objects inside the container (e.g., "a bus" for a tram car).

Regarding (2), responses to the open source question were coded for two measures.

First, we generated a binary variable coding for whether children mentioned a source (irrespective of correctness) in response to the open source question (0 = no source mentioned; 1 = source mentioned). Second, we created a binary variable coding for whether children referred to the correct source in a given trial (0 = incorrect response; 1 = correct response). The first measure quantified the children's willingness to provide a relevant response, while the second measure quantified the accuracy of this response. Coders were instructed to code any reference to visual perception (e.g., "I looked", "I peeked" etc.) in response to the question as a reference to having seen the contents of the container.

Conversely, any reference to the experimenter (such as pointing or addressing her) or to testimony (e.g., "someone told me") were coded as references to having been told about the contents of the container. Finally, a lack of response after the question had been repeated

once, an answer not referring to either perception, the experimenter, or testimony (such as "I just know"), as well as professions of ignorance (such as "I don't know"), were coded as incorrect answers.

Regarding (3), the closed source question responses were coded in a similar way as the responses to the open source question (2). However, for this test question, we did not code separately whether children mentioned a source but only whether their response was correct.

Responses of children in the final sample were excluded from analysis if the experimenter failed to repeat the question in case the child had not given a response to the initial query (Experiment 1: 6 responses; Experiment 2: 11 responses; Experiment 3: 14 responses).

A trial would also have been excluded from analysis if the children had not answered the contents question correctly. Since all children in all trials were able to provide a correct response to the contents question, no trials had to be excluded in this way. Trials were also excluded when either experimenter significantly departed from the experimental protocol, when the child did not cooperate, or when a caregiver interfered with the proceduree.g., by giving hints to the child (Experiment 1: 2 trials; Experiment 2: 0 trials; Experiment 3: 2 trials).

Results

Analysis

We fit separate logistic linear mixed models with a binomial distribution (logit link) for each dependent measure in each experiment to participants' individual responses coded as binary outcomes. In order to take into account repeated measures explicitly, we added Participant Identity and Trial Number as random intercepts in a step-wise fashion (see below). Where a lack of variance in a given measure did not allow for the inclusion of both of these random effects, we dropped Trial Number and only included Participant Identity.

We employed a step-wise selection approach to model selection. For each measure, we fit five different kinds of models: (1) a First Null Model, featuring Participant Identity as the only predictor, (2) a Second Null model, adding Trial Number as a second random intercept; (3) a Source Model, which added a fixed effect for Source (seen vs. told), (4) a Source + Agreement Model, which in addition to Source included the fixed effect of Agreement (interlocutor agreed vs. disagreed) and (5) a Full Model, which added an interaction effect between Agreement and Source to model (4).

We used likelihood ratio tests (LRTs) to compare the overall fit of each of these models. The results of this analysis for the open and closed source memory questions are summarized in Tables 1 and2. For the estimates of the model parameters, the 95% confidence intervals were assessed by computing a likelihood profile and finding the appropriate cutoffs based on the LRT. Statistics were computed using R 3.6.2 (R Core Team, 2019) with the lme4 package (v1.1-21; Bates, Maechler, Bolker, & Walker, 2015).

Since in our pre-registration we planned an analysis based on Wilcoxon-Signed Rank tests, we also computed non-parametric statistics for all measures and all experiments in addition to the mixed modelling approach reported below. These analyses can be found in the Supplementary Materials and show the same pattern of results as the regression-based analysis reported here (see Figure 1). All the statistical tests reported in this paper were twotailed. Model comparison suggested that the Second Null Model provided the best fit for this measure improving model fit over the First Null Model (LRT: χ2(1) = 7.12 , p = .008). This suggests that the number of sources children mentioned was not affected by any of our experimental factors. a standard method for combining p-values from multiple studies, while controlling for false positives (Whiltlock, 2005). This analysis yielded a statistically significant result (p = .009).

Closed Source Question

Children reported the correct source in response to the closed source question in a proportion of 0.8 (SE = 0.04) of trials on average. Model comparison suggested that the Source model provided the best fit to children's responses for this measure significantly improving model fit over the Second Null Model (LRT: χ2(1) = 13.22, p < .001). This model revealed a significant effect of Source (β = 1.52, SE = 0.46, 95%CI = 0.67-2.5, Z = 3.33, p <

.001) such that children were more likely to report the correct source when they had been told about the contents of the container (Mtold = 0.90, SEtold = 0.03) compared to when they had seen them (Mseen = 0.7, SEseen = 0.03).

Experiment 3 (Younger Children)

Open Source Question Null Model (LRT: χ2(1) = 9.32, p = .002). This model revealed a significant effect of Source (β = 1.31, SE = 0.45, 95%CI = 0.45-2.24, Z = 2.9, p = .004) such that children were better at answering the open source question correctly when they had been told about the contents of the container (Mtold = 0.37, SEtold = 0.07) compared to when they had seen them (Mseen = 0.21, SEseen = 0.06).

Closed Source Question

Younger children reported the correct source in response to the closed source question might have been interpreted as a retrieval cue for the events at the beginning of the trial (when children had found out about the contents of the container). Thus, it might have been easier for children to think of the event during which they found out about the contents of the container as a source of their belief [START_REF] Haigh | What children know about the sources of their knowledge without reporting it as the source[END_REF]. In contrast, it might have been pragmatically less clear to children how to interpret the open source question in the context of agreement (for example, it might have been a 'test question, [START_REF] Grosse | Two-year-old children differentiate test questions from genuine questions[END_REF]. Under this interpretation, our results suggest that 4-year-olds understand the justificatory function of source information.

Second, Agreement might have impacted children's motivation to either convince their interlocutor or hedge their bets about their own claim. Children might have been prompted to be more careful in answering correctly to a disagreeing (i.e., epistemically vigilant) interlocutor than to an agreeing one. As a result, the participants might have spent more cognitive resources on recovering the exact source of their belief about the contents of the box in the context of disagreement. In other words, children had stronger incentives to calibrate their commitment correctly when facing a disagreeing rather than an agreeing interlocutor. The fact that children made more source errors in the agreement than the disagreement condition despite the fact that they did not mention fewer sources, lends support to this interpretation.

Note that this second interpretation of the results attributes a higher degree of communicative competence to children. The 4-year-old children in Experiments 1 & 2 would not only have to have understood that questions in the context of disagreement can be interpreted as requests for justification and that sources can provide such justification: they would also have to have understood that sources can serve the more specific function of modulating speaker commitment.

It is also worth noting that, since in any given trial the children did not know whether their interlocutor would agree or disagree with them, the effect of Agreement on 4-year-olds' performance has to be attributed to the retrieval, and not to the encoding, of source information. One might think that our data could be explained by the fact that children might have come to expect to encounter disagreement in subsequent trials after the first 'disagreement trial,' and encoded source information more deeply as a result. Such a generalized expectation should, however, have resulted in increased performance across trials, and not only in disagreement trials. Moreover, since we controlled for the effect of Trial Number as a random effect in our models, it is unlikely that the effect we observed was driven by children who received a disagreement trial first. An effect driven by the retrieval phase is to be expected under the assumption that source monitoring processes specifically occur at retrieval and operate over episodic representations [START_REF] Johnson | Source monitoring[END_REF].

Regardless of the exact mechanisms leading to the effect of disagreement on source recall, the present results therefore support the idea that retrieval of source information is sensitive to communicative context [START_REF] Mahr | Why do we remember? The communicative function of episodic memory[END_REF]. As such, the effect of communicative context on source memory performance observed here might contribute to our understanding of the underlying reasons for the common finding that source memory performance significantly increases between three and five years of age. In the present study, older children did not only perform better but also became sensitive to agreement with their interlocutor in their responses to the open source memory question.

The improvement in source memory performance between three and five years is often attributed to children's developing theory-of-mind abilities (e.g., [START_REF] Gopnik | Knowing how you know: Young children's ability to identify and remember the sources of their beliefs[END_REF][START_REF] Perner | Episodic memory and autonoetic consciousness: Developmental evidence and a theory of childhood amnesia[END_REF]. On this view, explicit representation of the sources of one's own beliefs requires the capacity for representing one's own beliefs in the first place. Even though evidence for implicit theory of mind abilities in young children is controversial (Kulke et al., 2018), a considerable amount of research has indicated that 3-year-olds already possess such capacities (see, e.g., Király et al., 2018 for a recent example relevant to the current context).

Thus, while it is possible that source memory performance increases as a function of proficiency in mental state reasoning, another possibility is that children's increasing source memory performance is related to their developing communicative competence. In particular, it has been shown that children develop a range of important communicative capacities related to epistemic vigilance during this time (e.g., [START_REF] Mascaro | The moral, epistemic, and mindreading components of children's vigilance towards deception[END_REF]. Our results add to this work by suggesting that 4-year-olds might be sensitive to the communicative function of knowing the source of their own beliefs as providing a potential justification of their assertions to their interlocutor.

The Effect of Source

In both age groups, the children were more likely to accurately say that they had been told something, rather than that they had seen something. Although we did not predict this result, it deserves discussion given that it contrasts with other findings suggesting that children have a tendency to over-attribute their own beliefs to perception rather than testimony or inference. In particular, [START_REF] Whitcombe | Children's decisions about what to believe and their ability to report the source of their belief[END_REF], as well as [START_REF] Robinson | Children's suggestibility in relation to their understanding about sources of knowledge[END_REF], found a trend opposite to that of the present study: in their studies, children of the same age group seemed to be biased to over-report first-hand over secondhand sources of information (for similar results with adults, see Ünal et al., 2015).

In our view, this result can be explained in one of two main ways. On the one hand, differences in the way the information was presented between different source conditions in the present study might have made it easier for the children in our experiment to encode that they had been told the answer, or more difficult to encode that they had seen the contents of the container. In particular, 'seeing' something may not have been encoded as a unique event while the interlocutor's communicative act might have made event boundaries easier to differentiate. However, the differences between the protocols of the current and of past studies in this respect were not large, and so it is not clear why such differences at encoding would emerge.

On the other hand, this effect could have been due to a response bias towards answering having been told, independently of the actual source. That is, children might have been better at reporting having been told because they were choosing this answer more often overall and not because they were actually better at remembering having been told. One reason for such a response bias in the present study might be that the children either wanted to hedge their bets or increase their authority by referring to the experimenter as a source.

This possibility is supported by results suggesting that preschool children generally view testimony as highly trustworthy [START_REF] Jaswal | Young children have a specific, highly robust bias to trust testimony[END_REF][START_REF] Jaswal | Believing what you're told: young children's trust in unexpected testimony about the physical world[END_REF]. In the current context, results such as those by Jaswal and colleagues suggest that children perceived the adult informant as authoritative, and might therefore have judged it as 'safer' to refer to testimony when asked for their source. The main difference between our current design and previous studies such as those by Whitcombe and Robinson is that source memory questions were asked in a naturalistic conversational context by a 'second party' interlocutor rather than in a test situation by a 'third party' experimenter. This might have biased children to want to manage conversational risk in their answers. If that was the case, it would further support the idea that children of this age can recognize how source report modulates speaker commitment. Alternatively, a response bias might have been caused by the fact that many of the children's beliefs do in fact come from testimony. Children might therefore have reported having been told whenever they were unsure about their actual source because they have a baseline assumption that any given piece of knowledge they have is likely to come from others.

Conclusion

The current study suggests that, by four years of age, children understand the justificatory function of source information, which facilitates their retrieval of such source information in the face of disagreement. This ability likely forms the basis of an understanding of the costs and benefits of source report for the purposes of hedging one's bets or claiming authority. Future studies should thus aim to disentangle whether children of this age group are already sensitive to the communicative costs and benefits of different source reports.

  each trial stayed consistent across children. Next, the experimenter asked the child if they wanted to know what was inside the box by saying: "Look, I put something new inside! Do you want to know what it is?". The rest of the procedure varied depending on condition. In the 'told' condition, the experimenter told the participant what object she had hidden by saying: "I will tell you! It's a [name of object hidden inside the box, e.g., a car]! There is a [name of object hidden inside the box, e.g., a car] inside this box!". Next, the experimenter asked: "What's inside? Can you tell me?". In case the child did not give the correct answer, the experimenter told her again what was inside the box until the participant gave the correct answer. In the 'seen' condition, the experimenter allowed the child to look inside the box. She said: "Do you want to look inside to find out what's inside?". Next, she let the child open the box and look inside it, before asking: "Did you see what's inside? Can you tell me?". If the child answered correctly, the experimenter said: "Wow! That's exciting!". In case the child did not give the correct answer, the experimenter asked her to look inside again until the participant gave the correct answer.

Figure 1 :

 1 Figure 1: Results of the non-parametric analysis for the effect of Agreement on children's performance in the open source memory question. Middle lines depict means.

  Sources mentioned: Younger children on average provided 0.41 (SE = 0.07) sources per trial in response to the open source question. Of the sources mentioned, a proportion of 0.68 (SE = 0.07) referred to having been told. The First Null Model provided the best fit to these responses suggesting that neither Agreement nor Source had an effect on how many sources the younger children mentioned. Accuracy: On average, the younger children provided a correct source in response to the open source question in a proportion of 0.28 (SE = 0.05) trials. Due to insufficient variance we dropped Trial Number and instead only included Participant Identity as a random effect in the models for this measure. The Source Model provided the best fit for children's accuracy in answering the open source question significantly improving model fit over the

  in a proportion of 0.53 (SE = 0.05) trials. Again, due to a lack of variance we dropped Trial Number and instead only included Participant Identity as a random effect in the models for this measure. Model comparison suggested that the Source Model provided the best fit to these responses with a marginally significant improvement over the First Null Model (LRT: χ2(1) = 3.29, p = .07). The model revealed a marginally significant effect of Source (β = 0.59, SE = 0.32, 95%CI = -0.05-1.25, Z = 1.8, p = .071): children were marginally better at recognizing the correct source when they had been told about the contents of the container (Mtold = 0.58, SEtold = 0.073) compared to when they had seen them (Mseen = 0.46, skills serve social functions, they should be more strongly activated in the context of interpersonal disagreement and, as a result, source memory performance should improve in such a context. In the present study, 3-and 4-year-old children were asked by a puppet how they knew about the contents of a box, which they had either seen or been told about. The results of Experiments 1 and 2 indicate that 4-year-old children performed better in answering an open-ended source question when the puppet had disagreed rather than agreed with them about the contents of the box. In contrast, 3-year-old children did not show this effect. Our results do not reveal whether the effect of Agreement on 4-year-olds' source memory is due to (i) an increase in performance in the disagreement condition, (ii) a decrease in performance in the agreement condition, or (iii) a combination of these two factors. Nevertheless, regardless of the respective effects of agreement and disagreement, our results indicate that source memory performance was comparatively enhanced when children needed to justify their claims (in the disagreement condition) compared to when they did not (in the agreement condition), thus supporting the view that source memory can serve a social function in childhood.The effect of Agreement on 4-year-olds' source memory performance can be explained by two non-mutually exclusive phenomena. First, disagreement might have made it easier than agreement for children to understand what kind of response would be appropriate to the open source memory question via cueing children to interpret the question as a request for justification. As a consequence, in the context of disagreement, the open source question

Table 1 :

 1 Results of Likelihood Ratio Test-based model comparison for children's performance in the open source memory question in Experiments 1, 2, and 3. Trial number was omitted as a random intercept in cases where variance was too lowfor the model to converge otherwise. Predictors mentioned in the 'Model' column were sequentially added.

	Dependent Variable	Experiment	Model	Df	2	p
			Random Intercept: ID
	Open		Random Intercept: Trial Number	1	2.49	.114
	Source Question	Experiment 1	Source (seen/told)	1	5.52	.019
	Accuracy		Agreement (agreed/disagreed)	1	3.42	.064
			Source * Agreement	1	.070	.402
			Random Intercept: ID
	Open		Random Intercept: Trial Number	1	4.45	.035
	Source Question	Experiment 2	Source (seen/told)	1	15.49	>.0001
	Accuracy		Agreement (agreed/disagreed)	1	3.93	.047
			Source * Agreement	1	.011	.737
			Random Intercept: ID	1
	Open Source Question Accuracy	Experiment 3	Source (seen/told) Agreement (agreed/disagreed)	1 1	9.32 0.59	.002 .441
			Source * Agreement	1	0.00	.982

Table 2 :

 2 Results of Likelihood Ratio Test-based model comparison for children's performance in the closed source memory question inExperiments 1, 2, and 3. Trial number was omitted as a random intercept in cases where variance was too low for the model to converge otherwise. Predictors mentioned in the 'Model' column were sequentially added.

	Dependent Variable	Experiment	Model	Df	2	p
			Random Intercept: ID
	Closed Source Question Accuracy	Experiment 1	Source (seen/told) Agreement (agreed/disagreed)	1 1	1.33 0.73	.249 .391
			Source * Agreement	1	2.9	.087
			Random Intercept: ID
	Closed		Random Intercept: Trial Number	1	0.03	.866
	Source Question	Experiment 2	Source (seen/told)	1	13.22	<.001
	Accuracy		Agreement (agreed/disagreed)	1	0.24	.624
			Source * Agreement	1	0.00	.946
			Random Intercept: ID
	Closed Source Question Accuracy	Experiment 3	Source (seen/told) Agreement (agreed/disagreed)	1 1	3.29 0.00	.069 .976
			Source * Agreement	1	0.79	.375

Accuracy: On average, children provided the correct source in a proportion of 0.64 (SE = 0.05) of trials in response to the open source question. Model comparison suggested that the Source + Agreement Model provided the best fit to the data marginally increasing model fit over the Source Model (LRT: χ2(1) = 3.42, p = .064). This model revealed a significant effect of Source (β = 0.92, SE = 0.55, 95%CI = 0.15 -1.75, Z = 2.3, p = .021) and a marginally significant effect of Agreement (β = 0.72, SE = 0.402, 95%CI = -0.04 -1.54, Z = 1.81, p = .07).

Children were thus marginally better at reporting a correct source after the puppet had disagreed (Mdisagreed = 0.7; SEdisagreed = 0.05) compared to when it had agreed with them (Magreed = 0.59; SEagreed = 0.07). Children were also better at reporting the correct source when they had been told about the contents of the container (Mtold= 0.7; SEtold = 0.06) compared to when they had seen the contents (Mseen = 0.57; SEseen = 0.08).

Closed Source Question

Children answered the closed source question correctly on average for a proportion of 0.8 (SE = 0.04) of trials. On average, children mentioned that they 'were told' in a proportion of 0.57 (SEtold = 0.04) of trials and that they 'had seen' in a proportion of 0.34 (SEseen = 0.03) of trials. In the remaining proportion of trials, children did not provide an answer that fit our criteria for source report (such as providing no answer or answering "I don't know"). This model performed significantly better than the Source model (LRT: χ2(1) = 3.93, p = .047). The Source + Agreement model revealed an effect of Source (β = 1.7, SE = 0.47, 95%CI = 0.08 -2.68, Z = 3.63, p < .001) and an effect of Agreement (β = 0.83, SE = 0.43, 95%CI = 0.01 -1.72, Z = 1.93, p = .05). Children were better at recalling the source when they had been told about the contents of the container (Mtold = 0.73, SEtold = 0.6) compared to when they had seen them (Mseen = 0.5, SEseen = 0.07). Children were also better at recalling the source when their interlocutor had disagreed with them (Mdisagreed = 0.66, SEdisagreed = 0.06) compared to when it had agreed with them (Magreed = 0.56, SEagreed = 0.06).

Because the effect of Agreement was of primary interest to us, we assessed its overall significance across Experiment 1, and its replication (Experiment 2). As mentioned above, model comparisons by Likelihood Ratio Tests indicated that adding Agreement to the Source model improved its fit in a marginally significant manner in Experiment 1 (p = .064), and in a significant manner in Experiment 2 (p = .047). To assess the overall significance of this pattern of results, we used the weighted Z-methodweighting each study by its sample size

In addition, we also found that, in contrast to earlier studies, children performed better at reporting their source when their belief was based on testimony than when it was based on perception. This effect might have been due to a bias on the children's part to over-report testimony as the source of their belief. Such a bias could be explained either by children's attempt to manage conversational risk or by a baseline assumption about the origins of their knowledge in social sources.