Why does decreased likeability not deter adolescent bullying perpetrators?

Abstract This study examines why the lower likeability of bullying perpetrators does not deter them from engaging in bullying behavior, by testing three hypotheses: (a) bullying perpetrators are unaware that they are disliked, (b) they value popularity more than they value likeability, (c) they think that they have nothing to lose in terms of likeability, as they believe that their targets and other classmates would dislike them anyway, regardless of their behavior. The first two hypotheses were examined in Study 1 (1,035 Dutch adolescents, M age = 14.15) and the third hypothesis was examined in Study 2 (601 Dutch adolescents, M age = 12.92). Results from regression analyses showed that those higher in bullying were not more likely to overestimate their likeability. However, they were more likely than others to find being popular more important than being liked. Moreover, those higher in bullying were more likely to endorse the belief that the victimized student or the other classmates would have disliked a bullying protagonist (in vignettes of hypothetical bullying incidents) before any bullying started. These findings suggest that adolescent bullying perpetrators may not be deterred by the costs of bullying in terms of likeability, possibly because they do not value likeability that much (Hypothesis 2), and because they believe they hardly have any likeability to lose (Hypothesis 3).

and gains in social dominance (Reijntjes et al., 2013b). Moreover, those who bully tend to strive for popularity more than others (Caravita & Cillessen, 2012;Sijtsema et al., 2009). Thus, the widespread and continued high prevalence of bullying, which is a goal-directed behavior (Volk, Dane, & Marini, 2014), may be explained by the highstatus bullying confers on its perpetrators, which is something they aim to obtain. To the extent that it provides access to desired resources, bullying is both rewarding from a social learning perspective (Bandura, 1971) and adaptive from an evolutionary perspective (Volk et al., 2012(Volk et al., , 2014. Nevertheless, bullying others also incurs social costs for the perpetrators: It is negatively associated with social preference (or likeability), indicating that adolescents who bully are generally disliked by their peers (Caravita, Di Blasio, & Salmivalli, 2009;Dijkstra, Lindenberg, & Veenstra, 2008;Pouwels et al., 2016;Sentse, Kiuru, Veenstra, & Salmivalli, 2014;Sijtsema et al., 2009;Vaillancourt et al., 2003; Van den Broek et al., 2016). It remains unclear, however, why this lower likeability does not discourage these adolescents from bullying. It is surprising, as being liked by one's peers provides individuals with feelings of affection and helps them fulfill their desire for interpersonal attachment, which is a fundamental human need (Baumeister & Leary, 1995;Pendell, 2002). Being liked should, therefore, also be rewarding and adaptive for human beings. Identifying cognitions underlying the lack of responsiveness of bullying perpetrators to the social costs of their behavior could guide future antibullying efforts.
The current study investigates why lower likeability does not act as a deterrent for adolescents engaging in bullying, by putting three possible explanations to the test. First, bullying perpetrators may not be aware of being disliked. In other words, they may overestimate their likeability. We refer to this explanation as the inaccuracy of selfperceived likeability hypothesis. Second, lower likeability may not matter to them because they value being perceived as popular more than they value being liked by their peers, which we refer to as the superiority of popularity hypothesis. Third, we considered the possibility that bullying perpetrators might think that they have no likeability to lose anyway. Though they might believe that high perceived popularity is within their reach, they might also believerightly or not-that their targets and other classmates would not like them, irrespective of their behavior. In this case, they would only have something to gain by bullying-perceived popularity-and nothing to lose in terms of likeability. We refer to this explanation as the unreachability of likeability hypothesis. As the three hypotheses are not mutually exclusive, it is possible that we will find evidence for more than one hypothesis.

| The inaccuracy of self-perceived likeability hypothesis
The first reason why lower likeability does not discourage bullying adolescents from engaging in such behavior may be a lack of awareness of their lower status. Perpetrators who are disliked by peers may believe that they are relatively well-liked, possibly because they might mistake the fear that they instill in others for a form of respect (Vaillancourt, McDougall, Hymel, & Sunderani, 2010). To our knowledge, no study has examined the link between bullying behavior specifically and overestimation of likeability (or peer acceptance) in adolescents. Nevertheless, several studies examining aggressive behavior in children indicate that positively biased perceptions of peer acceptance are associated with higher levels of both overt and relational aggression (David & Kistner, 2000;Lynch, Kistner, Stephens, & David-Ferdon, 2016) and general aggression (Sandstrom & Herlan, 2007;. This positive association was found when biased self-perceptions of peer acceptance were operationalized as the variance in children's self-perceived likeability unexplained by their actual (or peer-perceived) likeability (David & Kistner, 2000;Lynch et al., 2016) as well as when operationalized as difference scores between actual and self-perceived likeability (Sandstrom & Herlan, 2007;Stephens et al., 2016).
However, not all studies on aggression and overestimation of likeability provide evidence for a positive link between the two: When children's reactive and proactive aggression were examined separately and teachers were used as informants of the children's levels of likeability among peers (White & Kistner, 2011), no significant association between positively biased perceptions of peer acceptance and proactive aggression was found.
Furthermore, as evaluating how liked we are by others relies on the capacity to infer what others think about us, self-perceptions of likeability might be related to the theory of mind skills, defined as abilities to understand the mental state of others. Studies investigating the link between bullying and theory of mind (ToM) skills found that early adolescents who bully others had no more difficulty than their nonbullying counterparts in these tasks (Gini, 2006), and boy "ringleader bullies" were even found to have higher ToM skills (Caravita, Di Blasio, & Salmivalli, 2010). Taken together, these studies seem to hint that overestimation of likeability is more likely in reactively aggressive than proactively aggressive youth and in those with poor ToM skills. As bullying in adolescence is more strongly associated with proactive than reactive aggression (Pouwels et al., 2016), and bullying perpetrators do not have impaired ToM skills (Caravita et al., 2010;Gini, 2006), a positive link between bullying and overestimation of one's likeability may not be as likely as suggested by the studies not distinguishing between reactive and proactive types of aggression.
In the present study, we will test the effects of bullying in adolescence on the overestimation of one's likeability. As it has been suggested that the positive link between aggression and overestimation of one's social competence held only for disliked children (e.g., De Castro, Brendgen, Van Boxtel, Vitaro, & Schaepers, 2007), we will also examine whether these effects vary depending on adolescents' actual levels of likeability.

| The superiority of popularity hypothesis
It is also possible that lower likeability does not discourage bullying perpetrators from engaging in bullying because they are more interested in being popular than they are in being liked. In other GARANDEAU AND LANSU | 349 words, they may endorse the Machiavellian view that it is "much safer to be feared than loved" (Machiavelli, 1513(Machiavelli, /1981. Numerous studies on peer bullying and aggression in adolescence support this suggestion: Research directly investigating status goals (i.e., selfreported importance of being popular and importance of being liked), have shown that endorsement of the popularity goal was positively related to peer-reported aggression (Dawes & Xie, 2014;Faris & Ennett, 2012) and to self-reported relational aggression (Dumas, Davis, & Ellis, 2017;Li & Wright, 2014). Other studies have examined the effects of adolescents' prioritizing of popularity over other personals goals (such as friendship, achievement, and romance) on their social behaviors. Cillessen, Mayeux, Ha, De Bruyn, and LaFontana (2014) found that prioritizing popularity predicted higher levels of aggression, controlling for actual popularity. Using the same measure of prioritizing popularity, Van den Broek et al. (2016) found a positive correlation between bullying and prioritizing popularity.
When examining links between aggression and likeability goals, a very different pattern emerges: The more adolescents endorse the social preference goal, the less likely they are to report engaging in overt and relational aggression (Li & Wright, 2014). In addition, endorsing communal goals, which capture the desire to be close to others, was found to be either unrelated to aggression (Ojanen et al., 2005), negatively correlated with aggression in adolescent boys (van Hazebroek, Olthof, & Goossens, 2017), or predictive of decreased physical aggression (Ojanen & Findley-Van Nostrand, 2014).
Taken together, these findings indicate that bullying perpetrators appear to favor popularity rather than likeability. Several of these studies further show that the positive association between valuing popularity and engaging in aggressive behavior varies depending on whether adolescents are actually popular. Those who prioritize popularity or strongly endorse the popularity goal tend to be especially engaged in bullying if they are also perceived as popular by their peers (Cillessen et al., 2014;Dawes & Xie, 2014). According to the studies by van den Broek et al. (2016) and Duffy et al. (2017), gender also plays a role. The finding that combining prioritizing popularity with high popularity predicted the highest levels of bullying held for adolescent boys only. In the present study, we expect that high engagement in bullying will be associated with favoring popularity over likeability, and we predict that this positive association will be stronger for more popular adolescents. Moreover, we will test whether these effects are further moderated by gender.

| The unreachability of likeability hypothesis
A third possible explanation for why lower likeability does not prevent bullying perpetrators from engaging in the behavior is that they may believe they have no likeability to lose. They might assume that the peers who dislike them would not have liked them more had they not engaged in bullying. Whereas bullying perpetrators might believe that they have the capacity to achieve high popularity among peers, they might also think (correctly or not) that they would never be liked whether they bully or not. If this hypothesis were true, they would feel that they can only benefit by bullying others (by increasing their popularity), since they would have nothing to lose in terms of likeability. Therefore, it would be logical that low likeability as a side effect of bullying does not prevent them from bullying, as they feel they already are not well-liked. When Machiavelli wrote that it is safer to be feared than to be loved, he specified "if one cannot be both." Strangely, the idea that adolescent bullying perpetrators may believe that perceived popularity is within their reach, but likeability is out of their reach has not yet been considered in the scientific literature on bullying (or aggression) or in the literature on peer status. Evidence for this explanation would provide new avenues for interventions aimed at changing the cognitions of youth engaging in bullying.
In the literature, the studies that come closest to the current question regarding bullying/aggressive youth's peer-focused social cognitions are studies that examine the link between a hostile attribution bias and aggression. The hostile attribution bias is defined as the tendency to interpret others' behavior as having hostile intent in ambiguous social situations, and according to the meta-analysis by De Castro, Veerman, Koops, Bosch, and Monshouwer (2002), aggressive children are generally more likely to exhibit it. However, there is some indication that this positive association may hold only for reactively aggressive children, and not for children engaging in proactive aggression (Crick & Dodge, 1996;Dodge & Coie, 1987;Martinelli, Ackermann, Bernhard, Freitag, & Schwenck, 2018;Schwartz et al., 1998). Consistent with these early findings, studies comparing perpetrators, targets, and "bully-victims" have shown that, when presented with ambiguous scenarios, "bully-victims"-but not those who perpetrate bullying without being victimized themselves-were more likely than other peers to attribute hostility to the perpetrators, in childhood (Camodeca, Goossens, Schuengel, & Terwogt, 2003;Pouwels, Scholte, van Noorden, & Cillessen, 2015) and in adolescence (Guy, Lee, & Wolke, 2017).
Research on the link between aggression or bullying and hostile attribution bias offers precious information regarding the social cognition of perpetrators of bullying. However, attributing a harmful intent to other people's behavior in ambiguous situations is different from assuming that people would dislike oneself regardless of whether one bullies or not. To our knowledge, no study has yet captured this type of cognition. In the present study, participants are presented with hypothetical bullying scenarios and asked to evaluate the extent to which the target and other classmates (in the story) would have disliked the bullying protagonist before any bullying started. We expected that adolescents who score higher on bullying engagement themselves would be more likely than others to endorse this belief.

| STUDY 1: TESTING THE INACCURACY OF SELF-PERCEIVED LIKEABILITY AND THE SUPERIORITY OF POPULARITY HYPOTHESES
The objective of this first study was to try and determine why being disliked would not prevent adolescent bullying perpetrators from engaging in bullying behavior, by testing two hypotheses. First, to examine whether bullying is associated with not being aware of being disliked (the inaccuracy of self-perceived likeability hypothesis), we test the effects of bullying on an overestimation of one's likeability. We further test if this effect is moderated by actual likeability. No specific expectation is formulated due to inconsistencies in previous research. Second, to examine whether bullying is associated with endorsing popularity goals more strongly than likeability goals (the superiority of popularity hypothesis), we test the effects of bullying on the difference between the importance attached to popularity and the importance attached to likeability. We expect this effect to be positive. In addition, we test whether this effect is moderated by adolescents' peer status (popularity and likeability) and whether this moderating effect is further qualified by gender. In all analyses, we controlled for victimization, so as to capture the cognitions of those who bully but are not also being victimized.

| Participants
The data used in the present study were part of a Dutch larger research project on children at risk for social and emotional problems, the Kandinsky Longitudinal Study. This project involves annual assessments of pupils in Grades 7-10, which are the first 4 years of secondary school in the Netherlands. There were 1,035 participants (495 boys and 540 girls). Their age ranged from 11.43 to 17.8 (M = 14.15; SD = 1.26). Ninety-five percent of the participants were born in the Netherlands.

| Procedure
The parental consent procedure was under the responsibility of the school principals. Permission from parents was requested at the beginning of the school year for all tests/surveys deemed beneficial to the students. Schools sent parents a letter that included a description of the objective and procedure of the assessment, and a request to respond if they wanted their child not to participate. None of the parents expressed disapproval of the participation of their child. In addition, adolescents were asked to give their assent at the beginning of the assessment. None of them declined to participate, nor decided to opt out during or after the assessment. The data used by the researchers were anonymous.
Questionnaires were completed during regular teaching hours with the use of individual netbook computers. Right before the participants started to answer the questions, a survey administrator explained the goal of the study and informed participants of the anonymous processing and confidentiality of the data. Adolescents were told that they could stop participating at any time, had to answer the questions as honestly as possible and should not share these answers with others. Computerized peer nominations were used to assess adolescents' peer status, bullying behavior, and victimization. For each nomination question, participants were presented with the full list of their classmates' names and the number of nominations was unlimited (with a minimum of one). Selfnominations were not possible, as the participant's own name did not appear on the screen. Nominating a peer was done by clicking on his or her name.

| Measures
Bullying and victimization were assessed with peer nominations.
Peer-reported bullying was assessed with the item Who bullies others?
and peer-reported victimization with the item Who is being bullied by others? The total number of received nominations for each item was divided by the number of participants within each classroom to obtain proportion scores.
The two types of peer status-likeability and perceived popularity -were both measured with peer ratings. Participants were asked to rate the extent to which they liked each classmate and the extent to which they found each classmate popular on a 6-point scale from not at all to very much. To obtain a score of likeability and popularity for each individual, received ratings were averaged per type of status per participant. Self-perceived likeability was assessed by asking participants "How much do your classmates like you?" on a 6-point scale from not at all to very much. An "overestimation of likeability" variable was computed by subtracting the self-perceived likeability score from the average rating on likeability received from all classmates.
Importance of likeability and importance of popularity were each measured with one question; How important is it for you to be liked by your classmates? and How important is it for you to be popular among your classmates?, respectively. The questions again could be answered on a 6-point scale from not at all to very much. The variable "favoring perceived popularity over likeability" was computed by subtracting the importance attached to likeability from the importance attached to popularity.

| Do bullies overestimate their likeability?
Descriptive statistics and correlations for the main study variables are presented in Table 1. To examine whether bullying was significantly associated with overestimation of likeability, we ran a first regression analysis testing for the main effects of age, gender, actual (i.e., peer-perceived) likeability, bullying, and victimization (Model 1) on an overestimation of likeability. All continuous variables were mean-centered. The model was significant, F(5, 1004) = 56.11, p < 0.001, explaining 22% of the variance (Table 2). There was a significant effect of gender: Boys were more likely than girls to overestimate their likeability, p = 0.003. In addition, adolescents were GARANDEAU AND LANSU | 351 more likely to overestimate their own likeability when they were younger, p = 0.004, lower in actual likeability, p < 0.001, and lower in victimization, p < 0.001. However, there was no significant effect of bullying, p = 0.604, suggesting that adolescents higher in bullying were not more likely than others to overestimate their likeability.
A second model was run (Model 2), which included the interaction between bullying and actual likeability in addition to all the predictors of the first model. This model was significant, F(6, 1003) = 46.92, p < 0.001, explaining 22% of the variance ( Table 2).
The interaction between bullying and actual likeability was not significant, p = 0.322, suggesting that the effects of bullying on an overestimation of one's likeability are not moderated by adolescents' actual likeability.

| Do bullying perpetrators favor perceived popularity over likeability?
To test whether those higher in bullying are more likely to favor popularity over likeability, we first tested for the main effects of age, gender, bullying, and victimization on favoring popularity over likeability in a regression analysis. All continuous variables were mean-centered. The model, presented in Table 3, was significant, F(4, 1005) = 12.25, p < 0.001, explaining 5% of the variance in predicting favoring popularity over likeability. There was a positive effect of age, p < 0.001; gender, p = 0.001; and bullying, p < 0.001, but no significant effect of victimization, p = 0.179. Adolescents higher in bullying, boys, and older adolescents were more likely to favor popularity over likeability.
To examine whether the association between bullying and favoring popularity would be moderated by adolescents' popularity or likeability, we ran two additional models including the main effect of popularity and the interaction between popularity and bullying (the "popularity" model) and the main effect of likeability and the interaction between likeability and bullying (the "likeability" model).
Models were conducted separately for popularity and likeability to prevent multicollinearity, since the correlation between the two types of status was high (r = 0.60, p < 0.001).
The "popularity" model was significant, F(6, 981) = 10.85, p < 0.001, explaining 6% of the variance. There was a positive main effect of popularity; higher popularity predicted a stronger tendency

| STUDY 2: THE UNREACHABILITY OF LIKEABILITY HYPOTHESIS
The goal of the second study was to examine whether bullying perpetrators might believe that they have no likeability to lose, which would explain why low likeability does not deter them from bullying.
To put this explanation to the test, we exposed participants to vignettes of hypothetical bullying scenarios followed by questions regarding the target's and other peers' disliking of the bullying protagonist in the story. Specifically, participants were first asked to which extent they believed the target (Question 1) and classmates (Question 2) disliked the bullying perpetrator. In addition, they were asked to assess the extent to which they believed the target (Question 3) and classmates (Question 4) disliked the bullying perpetrators before the bullying behavior started. We expected that adolescents higher in bullying would be more likely to endorse beliefs that targets and classmates would have disliked the bullying perpetrator before the bullying started.

| Procedure
The participants were recruited by contacting individual teachers from 15 secondary schools in various cities across the Netherlands.
The data were collected as part of a larger study designed to test the effectiveness of a small intervention. It consisted of three assessments (two preintervention and one postintervention). Only the data collected at the two preintervention assessments, which took place about 1 week apart, were used in the current report: Measures of peer status and vignette questions designed to assess beliefs regarding likeability were collected at the first data collection moment, and measures of aggression and victimization were collected at the second data collection moment (i.e., these measures were thus not assessed longitudinally). Active parental consent was used: About 2 weeks before data collection, parents received a letter describing the general objective of the study, and a request to return the signed form if they gave permission to their child to participate.
On the first day of data collection, adolescents who had received parental consent were asked to give their assent before survey administration. Data collection took place during regular school Note. The two way interaction between bullying and gender, as well as three-way interactions between bullying, gender and each type of status were nonsignificant and are not included in the models above. *p < 0.05. **p < 0.01. ***p < 0.001.

| 353
hours. It was conducted by university undergraduate assistants in the presence of the participants' teacher. Participants were informed that they could stop participating at any time and the data would remain anonymous (only code numbers-and no names-were used to enter the data). During data collection, nonparticipants were given a general knowledge questionnaire to complete to preserve the anonymity of their nonparticipation.

| Measures
The data used in the current study consisted of peer nominations for bullying and victimization, as well as self-reports of beliefs regarding

| Results
The descriptive statistics and correlations for all variables are presented in Table 4. To test the hypothesis that adolescents higher in bullying would be more likely to endorse beliefs that victimized students and classmates would have disliked the bullying perpetrator before any bullying started, we ran four regression models. In each model, we tested the effects of bullying on answers to each of the four vignette questions, controlling for age, gender, and victimization.
We were particularly interested in the effects of bullying on answers to Questions 3 and 4, but also investigated answers to Questions 1 and 2 for comparison purposes. Results are shown in Table 5.

| DISCUSSION
Understanding the psychological mechanisms underlying bullying perpetration among youth is essential for effective antibullying intervention efforts. That bullying tends to be rewarded with high perceived popularity in adolescence is now widely acknowledged as a key explanation for adolescents' engagement in bullying (e.g., Pouwels et al., 2016;Reijntjes et al., 2013aReijntjes et al., , 2013bVaillancourt et al., 2003). However, research also suggests that bullying is associated with losses in likeability (e.g., Pouwels et al., 2016). Our aim was to elucidate why such a cost in terms of likeability does not deter bullying perpetrators from engaging in bullying behavior. Three possible explanations were put to the test across two studies. In Study 1, we investigated the possibility that adolescent bullying perpetrators may overestimate their likeability (the inaccuracy of selfperceived likeability hypothesis), and the possibility that decreased likeability may not matter to them because they value being popular more than they value being liked (The superiority of popularity hypothesis). In Study 2, we explored the possibility that adolescents who bully others might think that they would not be liked whether they bully or not and therefore have no likeability to lose by bullying (the unreachability of likeability hypothesis).

| Support for two of the three explanations
No support was found for the inaccuracy of self-perceived likeability hypothesis: While victimized adolescents had a tendency to underestimate their likeability, adolescent bullying perpetrators were no more likely than their peers to overestimate how much they were liked by their classmates, regardless of their own likeability.
Adolescents' accuracy at evaluating their own likeability was thus not related to their bullying behavior. To our knowledge, our study is the first to examine this question with regard to bullying specifically rather than aggressive behavior in general. Indeed, our finding does not reflect the typical finding in research linking aggressive behavior to self-enhancing tendencies in children (e.g., De Castro et al., 2007).
Such links, however, are more likely to be observed when examining reactive aggression. In fact, children with ADHD, who tend to use reactive rather than proactive aggression (Murray, Obsuth, Zirk-Sadowski, Ribeaud, & Eisner, 2016), also tend to overestimate their social acceptance (Hoza, Pelham, Dobbs, Owens, & Pillow, 2002). Our results are consistent with studies showing that those who engage in bullying or proactive aggression, do not lack the ability to understand the mental state of others (Caravita et al., 2010;Gini, 2006). They indicate that youth's engagement in bullying cannot be attributed to their blindness for their (low) likeability level among their classmates.
The results of the current study show that bullying others is positively associated with a tendency to value being popular more than being liked. This finding adds to the increasing number of studies showing that aggressive youth aim for high popularity among peers but are not necessarily concerned with being liked (e.g., Li & Wright, 2014) by showing a similar effect for bullying in adolescence.
In addition, results indicated that being popular was associated with valuing popularity more strongly than likeability. Although some previous studies showed that actual status and bullying interacted in predicting boys' prioritizing of popularity (Duffy et al., 2017;Van den Broek et al., 2016), the current study did not find such moderation effects. One strength of our study was to combine ratings of the importance of being popular and the importance of being liked in a single measure, quantifying the degree to which one was more strongly pursued compared to the other. To our knowledge, this is the first study to quantify the prioritizing of popularity over likeability so precisely.
The most likely explanation for the finding that bullying perpetrators prefer popularity is that it is associated with greater social power (Vaillancourt et al., 2003). This explanation is consistent with an evolutionary approach. Proactively aggressive youth's preference for popularity may also reflect their Machiavellian approach to social interactions, according to which individuals find How likely is it that the victim dislikes the bully?
How likely is it that others in the class dislike the bully?
How likely is it that the victim would have disliked the bully before the bullying started?
How likely is it that others would have disliked the bully before the bullying started? it safer to be feared when faced with choosing between being loved and being feared (Machiavelli, 1513(Machiavelli, /1981. However, several points remain to be clarified in future research: Although the desire for interpersonal attachment may be a fundamental human need (Baumeister & Leary, 1995), it is possible that bullying perpetrators value having the social connections that perceived popularity provides but are indifferent to the quality or depth of these relationships. Moreover, it is unknown whether this higher value attached to popularity is a stable personality trait present early in life or whether it is acquired and can be potentially unlearned.
The current set of studies took the exploration of bullying students' cognitions and motivations in relation to peer status a step further. Support was found for the hypothesis that bullying perpetrators might believe that targets of bullying and other peers would not like them anyway, whether they engage in bullying or not.
When exposed to hypothetical bullying scenarios, adolescents higher in bullying were not more likely than others to think that the hypothetical target and classmates disliked the bullying protagonist.
However, they were more likely than others to report thinking that the target and the classmates would have disliked the bullying protagonist even before any bullying started. This implies that adolescent bullying perpetrators may not be deterred by the costs of bullying in terms of likeability possibly because the perceived costs are relatively low. They might think that their likeability will not decrease much when they engage in bullying, as they already think that they are being disliked. What remains to be determined is whether the fact that bullying perpetrators find popularity more important than likeability might be a consequence of their perception of likeability as being out of reach. The reasons why bullies tend to prefer popularity are still unclear. Our finding that they may believe they have no likeability to lose provides a new, testable explanation and sheds light on a cognitive process that can potentially be modified by intervention. Another venue for further exploring this type of reasoning in bullying perpetrators would be to assess cognitions such as "Regardless of my behavior, I will always be disliked" more directly and more personally related, instead of having them judge others in a hypothetical situation. Ideally, youth whose cognitions and bullying behavior are measured would have to be followed longitudinally to examine whether this "likeability is unreachable" cognitions actually are predictive of increases in bullying engagement over time.

| Limitations and future research
As expected, in the data we analyzed the correlation between bullying and peer-perceived likeability was negative (r = −0.27).
Nevertheless, an important limitation of our study is that with these data we cannot provide evidence that bullying results in a loss of likeability over time. Despite multiple cross-sectional studies showing that adolescent bullying perpetrators tend to be disliked (e.g., Dijkstra et al., 2008;Pouwels et al., 2016;Vaillancourt et al., 2003) and longitudinal investigations of the effects of likeability on future bullying behavior (Sentse et al., 2014), the current literature is still lacking in longitudinal research on the link between bullying and changes in likeability over time. One exception is the study by Reijntjes et al. (2013a) which examined prospective links between bullying and social acceptance using joint trajectories analyses. Moreover, we have not examined by which type of peers those who bully thought they were disliked and by which type of peers they were actually disliked (e.g., friends vs. nonfriends and victims vs. nonvictims), as our measure of actual likeability resulted from averaging ratings across peers, and our measure of self-perceived likeability only considered general likeability among peers. However, research suggests that the rejection of bullying perpetrators may not be equally shared among their classmates, but is restricted to their targets (Hafen, Laursen, Nurmi, & Salmela-Aro, 2013) and to peers for whom they represent a threat (e.g., Veenstra, Lindenberg, Munniksma, & Dijkstra, 2010). To more accurately test whether bullying perpetrators are aware of being disliked (first hypothesis), future studies should include dyadic analyses to investigate whether they report being disliked by the specific peers who actually report disliking them. Similarly, our global measure of reported importance of being liked did not enable us to capture by whom participants found it important or not to be liked. It is conceivable that students who bully do not find it important to be liked by some others, their targets in particular, but still care about being liked by a group of friends for instance. Using more specific questions, such as "I only find it important that my friends like me, whether other classmates like me or not is not important to me" would provide useful information.
Finally, the current study used an ethics committee-approved passive consent procedure and had nonparticipating students still on the nomination roster. A benefit of this procedure is a high participation rate, which increases the reliability and validity of the peer nominations.
It also protected the nonparticipants from identification by their participating classmates. However, passive consent is not the most ethically rigorous approach, as classmates could nominate nonparticipating classmates and, therefore, some information about nonparticipants was initially available to the researchers.

| CONCLUSIONS
Achieving a significant breakthrough in the fight against school bullying calls for a more precise understanding of the cognitions that underlie youth's decisions to instigate bullying against peers. By focusing on the construct of perceived popularity, the literature of the past two decades has emphasized the importance of status rewards in explaining aggression and bullying behavior in adolescence. The present set of studies provides new insight into the role of peer status in perpetrators' decision to engage in bullying by examining the role of three different types of cognitions related to likeability among peers. It demonstrates that the behavior of bullying perpetrators cannot be attributed to their lack of awareness of their own likeability, and thereby sheds light on the mixed body of literature on aggressive adolescents' self-perceptions. Using a new measure that quantifies the degree to which one type of status (popularity or likeability) is considered more important than the other, it even more strongly corroborates previous findings that proactively aggressive youth strongly value popularity but not likeability. Moreover, the current study demonstrates these patterns for bullying specifically, whereas most of the previous work on accuracy of perception of likeability and the importance of popularity and likeability has focused on aggression more generally, most distinguishing in the nature of (overt vs. relational) or motivation for (proactive vs. reactive) aggression.
Furthermore, our results suggest that bullying perpetrators may be apt to believe that likeability is out of their reach. This possibility has, to our knowledge, never been examined before, and might add to our ability to explain why lower likeability does not deter some youth from engaging in bullying. Should this finding be replicated with more