Preverbal infants expect agents exhibiting counterintuitive capacities to gain access to contested resources

Claims to supernatural power have been used as a basis for authority in a wide range of societies, but little is known about developmental origins of the link between supernatural power and worldly authority. Here, we show that 12- to 16-month-old infants expect agents exhibiting counterintuitive capacities to win out in a two-way standoff over a contested resource. Infants watched two agents gain a reward using either physically intuitive or physically counterintuitive methods, the latter involving simple forms of levitation or teleportation. Infants looked longer, indicating surprise, when the physically intuitive agent subsequently outcompeted a physically counterintuitive agent in securing a reward. Control experiments indicated that infants’ expectations were not simply motived by the efficiency of agents in pursuing their goals, but specifically the deployment of counterintuitive capacities. This suggests that the link between supernatural power and worldly authority has early origins in development.


Participants
The final sample included ninety-six 12-16 month old Japanese infants (i.e., n = 24 for each experiment). The sample size was determined based on a priori power analyses taking into account the results of previous infant studies on social dominance (especially, Pun, Birch & Baron, 2016) 1-4 . Specifically, a minimum of 24 participants in each experiment was required to detect potential effects using three-way repeatedmeasures analysis of variance (ANOVA) with effect size between the medium and large level: partial η 2 = .10, α = 0.05, and 1-β = 0.80 5 . Written consent was obtained from all caregivers before the experiment. All participants were recruited and tested at the BabyLab in Kyushu University Hospital. The study was approved by the ethical committee of Kyushu University (2017-012), and was conducted in accordance with the Declaration of Helsinki. Below is detailed information about the participants in each experiment.

Experiment 1
Twenty-four infants participated (15 girls and 9 boys; Mage = 423.9 days, SD = 43.92, range = 351-496). Eleven additional infants were excluded because they did not direct their attention to the animation (n = 7), because they did not watch the critical event in which one agent took the reward and thus missed the onset of coding in test phase (n = 3), or because the coder accidentally ended the test before the infant looked away from the screen for 2 seconds (n = 1).

Experiment 2
Twenty-four infants participated (13 girls and 11 boys; Mage = 424.6 days, SD = 43.50, range = 370-496). Eleven additional infants were excluded because they were fussy and did not direct their attention to the animation (n = 5), because their eyes were out of the camera so that coding was impossible (n = 3), or because the caregivers adjusted the infants' positions while they were watching the test video which made it difficult to judge whether infant faced the screen due to their own will or parental intervention (n = 3).

Experiment 3
Twenty-four infants participated (13 girls and 11 boys; Mage = 443.8 days, SD = 45.20, range = 366-516). Seven additional infants were excluded because they did not direct their attention to the animation (n = 3), because the caregivers interfered with the infants' looking behavior toward the screen in test phase by making eye contact or adjusting infants' position (n = 3), or because the infant's sibling talked outside the experiment booth and thus interfered the infant's attention towards the videos (n = 1).

Experiment 4
Twenty-four infants participated (14 girls and 10 boys; Mage = 450.8 days, SD = 48.11, range = 372-513). Nine additional infants were excluded because they did not direct their attention to the animation (n = 2), because their eyes their eyes were outside of the viewing range of the camera so that coding was impossible (n = 2), because they did not watch the critical event in which one agent took the reward and thus missed the 3 onset of coding in test phase (n = 2), because their attention was drawn by the voice of the sibling outside the booth (n = 1) because they were paying attention to something else (e.g., their shoes) (n = 1), or because of an experimental error regarding video presentation order (n = 1).

Set-up
The infants were presented video stimuli that were identical to that in Experiment 1 and 3, whereas neither of the test outcomes could be considered as expectation-consistent or expectation-violated, given that both agents appeared in these tests were physically intuitive, as detailed below (see also Fig. 1 in the main article).

Stimuli and procedure
Caregivers were briefed and informed consent was obtained outside of the experimental booth prior to the study. Entering the experimental booth, caregivers were instructed not to interfere with infants by uttering, pointing, or making eye contact if infants tried to engage the caregiver during the experiment. Infants were seated on the lap of the caregivers who were seated on a floor pillow, 145 cm away from the screen.
During all experiments, it was dimly lit inside the booth. After a pre-experimental calibration phase, the video stimuli were presented. The experiments each consisted of three phases: the warm-up phase, familiarization phase (4-8 trials) and the test phase (2 trials). In each phase, the corresponding type of video stimuli was presented. Each experiment lasted approximately 6 minutes.

Calibration
The calibration phase aimed to create referential indexes of infant gazing patterns to enable the coders to judge whether or not infants were watching the screen during offline coding. Specifically, we recorded the scenes in which each infant was looking at each end of the screen, and used them as the individual based referential index. The calibration phase comprised a white screen with six yellow diamond-shaped geometric figures which sequentially appeared on each ends of the screen, and spun around accompanied by a chiming sound to get the attention of infants (See Movie S1).

Warm-up phase
The warm-up phase was included to familiarize infants to the competitive context of the test phase. The videos used in this phase were based on Thomsen et al.'s (2011) study, which demonstrated that 10-month-old human infants use body size as a cue to infer social dominance in competitive context 1 .
We included the warm-up phase to habituate infants to the paradigm of the test phase for a few reasons. First, we wanted to reduce infants' confusion after they saw the test videos pause at the end of each trial, during which time we recorded their gazing time. In a pilot study, we presented similar experimental stimuli four times to infants without the warm-up phase. We found that infants frequently looked alternately to the caregivers and the screen when the test video paused in the initial trial. But, these behaviors were scarcely observed in the following three tests. Therefore, infants probably felt confused when the video stopped for the first time. Such response may lead to larger variance in infants' looking time across trials, and reduce the power of detecting the possible effects of experimental manipulation. Thus, to avoid these responses, we inserted a warm-up-phase to habituate infants that the screen will stop after viewing the competition. Second, we wanted to familiarize infants to the competitive context of the test, and that the socially dominant agent should obtain the reward in this context.
Specifically, two agents in obviously large and small sizes appeared and competed for a reward.
The warm-up phase consisted of the three parts (see Movie S2). In the first, infants watched a video in which a small (7.5 cm in diameter) and a big (13 cm in diameter) spherical agent appeared in the center of the screen, and then moved in the opposite direction and exited the screen while saying "Hm" in a negative tone. The agents different only in body size: each had a dark green spherical body with two eyes and a nose.
In the second part, infants were presented with videos that displayed agents collecting a reward. Videos started with a yellow cube-shaped reward falling down on one side of the stage. Then either the small or big agent appeared from the other side of the stage, collected the reward, then went back and exited the screen from the side it appeared. Then the other agent repeated the same event. The starting location and order 6 of the agent (whether the big or the small agent appeared the first) were counterbalanced (see Fig. S1).
The final part consists of two warm-up test trials almost identical to the actual test phase. Here, infants watched both the small and big agent compete for the reward: the big agent always outcompeted the small agent by obtaining the reward. Videos started with a yellow cube-shaped reward falling into the middle of the screen. Then the two agents appeared together simultaneously from the either side of the screen. Both agents approached the reward at the same speed. After approaching, both agents stopped and gazed at each other, and again they slowly moved forward as though cautious of one another, before stopping again. Then, the big agent moved forward slightly, whereas the small agent took a step backward with an averted gaze while saying "Hmmm..." in a disappointed tone. Subsequently the big agent took the object back to the side it came from, stopped and lightly jumped while saying "Ahaha!" in a positive tone. Then the animation paused for 5 seconds before ending. This trial was repeated twice (with the big agent obtaining the rewards both times), and the sides that agents appeared were counterbalanced (for the counterbalance information, see Fig. S1). The length of the entire warm-up phase was 83 seconds.

Familiarization phase
Following the warm-up phase, the familiarization phase began. In the familiarization phase, the infant watched two agents obtain the reward by using different methods. Two pairs of agents, similar to those in the warm-up phase featured in these events.
In Experiment 1 and 3, we manipulated the way in which the agents overcame the obstacles: one agent-the physically intuitive agent-collected in a way that did not for the inefficient event).

8
In Experiment 3, the movement of the physically counterintuitive agent was faster than the physically intuitive agents. Thus, in Experiment 4, the physically counterintuitive event was modified so that the agent's disappearance and re-appearance was occluded from view by two grey boards placed specifically for this purpose: the agent therefore still moved more quickly than the physically intuitive agent, but without necessarily violating intuitive expectations about object permanence (see Movie S11; see also Movie S10 for the inefficient event).
The experimental manipulation aimed to test whether counterintuitive behaviour affects expectations of social dominance. Therefore, any difference on low-level visual characteristics of the agents' movements (e.g., speed) between the conditions -factors we were not focusing on but which could affect the attribution of social dominance -should be eliminated. That is, agents in both experimental and control conditions (e.g., intuitive agents in Exp1 and Exp 2) should advance at the same rate. To achieve this, we ensured that agents exhibited the same visual characteristics in terms of trajectories and speed across conditions. We also used different contexts (i.e., different stages in the animation) to manipulate counterintuition of the movements. These manipulations resulted in several points regarding agents' movements which might be perceived as slightly "anomalous".
Specifically, the counterintuitive/efficient agents in Exp 1 and 2 slightly moved sideward towards the background before crossing the valley. This manipulation was applied to ensure that we could remove/insert a bridge above the valley without modifying agents' movement trajectories cross conditions. Furthermore, the counterintuitive/efficient agents in Exp 3 and 4 disappears not all at once but by sliding behind an invisible/visible occluding object. This manipulation was applied to ensure that we could remove/insert the boards without modifying agents' movement trajectories. It could be argued that these manipulations made the unexpected movements less like levitation or teleportation.
However, we believe that they were required to achieve the intended experimental design allowing us to test the main hypothesis while avoiding other factors we were not focusing on. More importantly, measures of social looks suggested that infants were surprised by agents suspended in mid-air with no apparent source of support, but not by other agents moving with physical support (see Results in the main article), which showed that the stimuli we adopted succeeded in manipulating infants' evaluations of the events in terms of intuitive/counterintuitive properties.

Test phase
The animation was identical to that in the last two trials of the warm-up test, except the following: First, instead of the big and small agents, infants watched the agents from the previous familiarization phase. Second, each trial ended if infants looked away from the screen for >2 s, or after 60 s elapsed from the time point the screen paused.

Coding
All the sessions were both coded online and offline. The entire experiment was recorded with four video cameras. Online coding was conducted to manage the timing of experimental procedure. The coders measured if infants looked away for consecutive 2s, which is the criterion for terminating the current trial and proceed to the next trial. In the familiarization phase, this coding was applied from the fifth trial. In the test phase, this coding was applied to both test trials. Two coders measured the time by pressing a key while infants were looking away from the screen with an aid of the computer programme built on Visual Basic (https://github.com/YNakawake/timewatcher_socdominance). The familiarization and the test trials were coded by different coders. Each coder only watched their part, thus the coder of the test phase was blind to the events in the familiarization phase. In case of ambiguity (e.g. not clear whether infants were looking at the screen or were looking away), the coder was instructed to consider it as infants were looking at the screen; thus the coder reset (stopped pressing the key) and waited for another extra 2s to terminate and proceed to the next step.
In the calibration phase, we created an individual based referential index to establish a method of coding instances in which infants were looking at the screen versus looking away. Using this referential index in the test phase, precise looking time was coded offline by measuring frame-by-frame whether or not infants were looking at the screen. One coder coded the whole recorded test trials and another coder independently recoded 50% of the data. The test was coded separately from the familiarization, thus coders were blind to the hypothesis and events of familiarization. Looking time at the test event were measured as the time interval between the moment the agent took the reward and the moment infants began to consecutively look away for 2s or 60s had elapsed from the time point when the screen had paused. The interclass correlation of coders was 0.973 [CI (0.960, 0.982), P < 0.001]. No trials were terminated before the cutoff point coded offline, except one trial. We excluded the data of this participant from data analyses due to an operation error of the experimenter (n = 1, Experiment 1).
Based on this coding scheme, we checked if the participants met two exclusion criteria. Firstly, we included the data of participants whose visual exposure to the videos (i.e., total duration of fixation on the events) exceeded the length of one whole familiarization trial for both agents (Experiment 1 and 2

Infants' visual exposure to the videos in the familiarization phase
To (1) confirm that the infant attended to each video stimulus for both agents and (2) investigate whether the results of test phase was influenced by the length of visual exposure to the events in familiarization, we coded and analyzed the total duration of fixation towards each event in the familiarization phase. Duration of fixation at each trial during the familiarization phase was measured from the time point that a reward dropped into the ground to the point that the agent disappeared from the screen.
To achieve the first aim, we calculated the percentage of the total fixation of gaze duration for the first four trials. We plotted total duration of fixation for the final sample in Fig. S2. On average, infants looked at the familiarization stimuli >95% for first two trials of both events (presented to every participants). Thus, we consider that infants' exposure to the videos is sufficient to create a mental representation for the physically intuitive and physically counterintuitive events in familiarization. To achieve the second aim (testing whether the results of test phase was influenced by the length of visual exposure to the events in familiarization), we analyzed the total duration of gaze fixation during each event in the familiarization phase. Note that because the events were presented successively, and the presentation order was fixed, we predicted that infants would show longer total duration of fixation on the physically intuitive (or inefficient) events than the physically counterintuitive (or efficient) events.
There were two reasons for this prediction. First, the current design was a departure from previous studies designed to measure differences in infants' looking time with respect to physically intuitive versus counterintuitive event 7-9 . In previous studies, events freeze and infants have enough time to watch the screen until they "lose interest" and look away. These studies find that it takes longer for infants to "lose interest" in the frozen counterintuitive events than the frozen intuitive events. In addition, infants generally continue to look at the frozen screen for > 20 seconds. In contrast, in the familiarization phase of the current study, events were presented one by one without the events freezing, making it possible to present a new event before infants "lost interest". Given this design, we did not predict that infants would look longer at the counterintuitive event. Second, the fixed presentation order may had led to a primacy effect, such that the intuitive (or inefficient) events always elicited longer total duration of fixation than the counterintuitive (or efficient) events, because the familiarization ended once infants had looked away from the screen for 2 seconds regardless of the properties of the events being presented.
The total duration of fixation was log-transformed for data analysis as a previous research has recommended 10 . Results showed that total duration of fixation in the familiarization phase with regard to both events consistently differed. As predicted, physically intuitive (or inefficient) events in the familiarization phase evinced longer total duration of fixation in all four experiments. A three-way ANOVA on total duration of fixation (Table S1)

Overall analysis of all experiments (on looking time of the test phase)
We merged the data of all four experiments, and analyzed it to confirm that the effect appears only in experimental condition and that it is independent of domain. We used the log-transformed looking time for the statistically analyses 10 . Results of the ANOVA were shown in Table S2-4.     Figure 3 in the main article indicated that several data of looking time should be treated as outliers. We did not, prior to the experiment, plan to exclude outliers from the sample because, discarding data is considered to be detrimental to statistical efficiency 10 .
We have applied logarithmic transformation to the data before statistical analysis to increase the validity of the analysis. However, to confirm that outliers did not influence the findings, we further conducted an ANOVA on the data in which outliers were excluded (Table S5-7). The results indicated that whether or not the outliers were included as the dependent variables did not change the findings.

Exploratory analyses of the test phase
We used the log-transformed looking time for the statistically analyses 10 . For each experiment, we conducted exploratory analyses with ANOVA to rule out possible effects of the order of presentation of test trials (test order) and sex of participants (sex).
Specifically, the looking time of the two test trials were compared with the property of the agent as the within-subject variables, and test order and sex as the between-subject variables (eta-squared η² and partial eta-squared ηp² were calculated for the effect size).
Visual presentation of data were mainly conducted with R (https://www.r-project.org), and ANOVA was conducted with JASP (https://jasp-stats.org/) and jamovi    As the previous experiment, the same three-way ANOVA was performed on looking times. No main effects and no interaction effects were found [Ps > 0.245, see Table S10-11], suggesting that neither the order of presentation of test trials nor sex of participants influenced infants' evaluation of social dominance.

Experiment 4 (domain: continuity, control condition)
As the previous experiment, the same three-way ANOVA was performed on looking times. No main effects and no interaction effects were found (ps > 0.078, see Table S14-15), suggesting that neither the order of presentation of test trials nor sex of participants influenced infants' evaluation of social dominance.