Testing the Roles of Perceived Control, Optimism, and Gratitude in the Relationship between General/Personal Belief in a Just World and WellBeing/Depression

Belief in a Just World (BJW) can be categorised into domains of how people view the fairness of their immediate social worlds (Personal Belief in a Just World–PBJW) and the wider world (General Belief in a Just World–GBJW). We conducted two studies with 179 (Study 1) and 364 (Study 2) participants to examine differential relationships that PBJW and GBJW could have in directly predicting mental wellbeing and depression and indirectly via three mediators of perceived control, optimism, and gratitude. Path analyses examined how well data from each study fit 13 different models. Models 1 to 4 tested whether PBJW directly and indirectly via the three mediators predicted wellbeing (Model 1) and depression (Model 3) and if GBJW likewise directly and indirectly predicted wellbeing (Model 2) and depression (Model 4). These four models had the best supported statistical fit for either Study 1 or 2 relative to other models. In both studies when explaining the effect of PBJW on wellbeing and depression, perceived control was the strongest mediator, followed by optimism, and then gratitude. When examining the effect of GBJW on wellbeing and depression, only perceived control and optimism were significant mediators. These studies affirm the need to assess GBJW and PBJW as separate phenomena, rather than combining these constructs or omitting PBJW, as is sometimes done.


Introduction
Belief in a Just World (BJW) is a ubiquitous and popular psychological construct that aims to understand complex phenomena relating to how fair and just people think the world is generally, and the ways in which injustices are explained and managed on cognitive and affective levels (Strelan & Callisto, 2020). For example, those with high levels of BJW may believe that wealthy and successful people have rightly earned this status, whereas those who are poor and generally struggle in life will be perceived as having deserved this fate. One of the key components of the BJW construct is that people are viewed as getting what they deserve, but also deserving what they get in the future (Kaliuzhna, 2020); this is to the extent that there is a perceived symmetry of negative events being a product of bad behaviours and present misdeeds being likely to precede further misfortune. Lerner (1980) described the BJW concept as consisting of different "illusions", pertaining to self-control and responsibility, due to the way people search for patterns and meaning in their lives, rather than accepting that many things could occur randomly and outside of their control. However, it is a concept with an important function to appease conflicts within the human psyche about the world people may feel they need to live in versus the state of the world that could exist as being rife with injustices and inequalities. Studies have shown that those with high levels of BJW appear to cope better when witnessing injustice or extreme misfortune (Furnham, 2003;Sutton & Douglas, 2005;Toews et al., 2019).
The BJW phenomenon came about, in part, with the paradoxical findings in studies showing some people generally saw the world as a fair place but still blamed seemingly innocent victims for their own misfortunes (Lerner, 1980). If people could attribute blame and identify causal mechanisms for injustices being witnessed, it could quell cognitive dissonance when believing that the world needs to be a fair place. This is particularly true if the event being witnessed is distressing and the victim cannot be easily helped, since this challenges people's Just World beliefs, which Lerner (1980) argued would be vital to people's sense of hope, trust, and confidence in the future. The function of BJW has been viewed as adaptive (Bartholomaeus & Strelan, 2019), in as much as people are motivated to maintain their levels of BJW, even in the face of any evidence to the contrary. This is because the incorporation of information that might lead someone to question the world as a fair place is likely to lead to feeling less hopeful and being unlikely to make efforts to succeed in the wake of any difficulty being experienced.

General Belief in a Just World (GBJW) versus Personal Belief in a Just World (PBJW)
Ever since the seminal work by Lerner and Simmons (1966) into the phenomenon of BJW, the key psychological patterns elicited in experimental work have been those characterised by derogation of unfortunate target persons and a certain motivational bias to achieve consistency in making sense of injustices. The BJW concept first emerged among scholars as a 'lens' through which people view the wider world and outside of one's sphere of influence-this concept has been termed as General Belief in a Just World (GBJW) or 'Just World-Other'; by having many reference points for finding and responding to unfairness globally, the chances of experiencing intra-psychic conflict are likely to be enhanced. By contrast, having a Personal Belief in a Just World (PBJW) (or 'Just World-Self') is a different 'lens' through which people can see levels of fairness or injustice within their immediate social confines and it could also be viewed as a type of world that is even more controllable (Dalbert, 1999). PBJW is thought to be related to GBJW but still relatively distinct (Lipkus et al., 1996). For instance, studies have shown that respondents' PBJW scores tend to be higher than their GBJW scores (Hafer et al., 2020;Jiang et al., 2017), although there is also evidence that the constructs can overlap considerably, as Yu et al. (2018) have found. With the PBJW phenomenon, an individual could maintain the view that their personal world is predictable, safe, and just, while not insisting it is so for everyone else. One of the key tenets common to both PBJW and GBJW is the 'personal contract'. This is the idea that good behaviour is appropriately rewarded, and there is a tacit expectation, as someone progresses through childhood and adolescence, of wider society having systems to reward appropriate behaviours and punish those who transgress societal norms (Dalbert, 1999). Although PBJW and GBJW have some psychological mechanisms in common, there are unique processes whereby each of these constructs could lead to different consequences.

The Differential Effects of GBJW and PBJW
Higher levels of GBJW have been linked to better mental health (Correia et al., 2009;Jiang et al., 2016) and other positive outcomes, such as self-forgiveness (Strelan, 2007), altruistic behaviour (Jiang et al., 2017), optimism (Littrell & Beck, 1999), and better wellbeing (Xie et al., 2011). However, the processes whereby better mental health and wellbeing can evolve because of high GBJW levels could be problematic from a social justice perspective. Sutton and Douglas (2005) found that higher GBJW scores predicted harsher attitudes towards the poor. Toews et al. (2019) found that higher GBJW levels predicted punitive attitudes and the attribution of responsibility and blame towards the target object of a mother whose child had been sexually abused. Moreover, 13 German studies have shown associations between GBJW and victim-blaming towards survivors of rape, those who have AIDS, cancer or disabilities, people in accidents, and those experiencing poverty (Montada, 1998).
Empirical evidence has pointed to different consequences for PBJW, which appear to be unrelated to some of the negative processes and outcomes involved with GBJW. In essence, PBJW appears to be more positively related to a range of outcomes such as better wellbeing and good mental health. Lipkus et al. (1996) conducted two studies to show that PBJW (relative to GBJW) had a more negative relationship with depression and stress, and a stronger positive relationship with life satisfaction. Moreover, Lipkus et al. (1996) uncovered that it was only PBJW that predicted life satisfaction, after controlling for the Five Factor personality traits. Similarly, Dalbert (1999), and Sutton and Douglas (2005) found that only PBJW predicted an increase in wellbeing. However, PBJW's differential impact when compared with GBJW is not just limited to wellbeing. In a 6.5-year longitudinal study on 65-87-year-olds, Fry and Debats (2011) found that PBJW uniquely predicted reduced mortality, but GBJW did not. This could be due to how PBJW helps with psychosocial adjustment; subscribing to the 'personal contract' and viewing one's world as fair tends to elicit a greater willingness to invest in one's future through health-promoting behaviours (Nudelman & Otto, 2021). Likewise, PBJW could help with people who are psychologically vulnerable. For instance, Valiente et al. (2010) were able to show that patients with persecutory delusions and higher levels of PBJW had fewer paranoia and depression experiences and reported higher life satisfaction when compared with patients who had similar symptoms, but lower levels of PBJW. By contrast, GBJW was not a contributing factor for either of these patient groups in Valiente et al.'s (2010) study.
Despite GBJW and PBJW having different effects, this has not always been acknowledged among scholars. Research by Correia and Vala (2004), Jiang et al. (2016), and Littrell and Beck (1999) is examples where GBJW was measured, but it would have been beneficial to know what differences PBJW would have brought to their findings. Likewise, Jiang et al. (2017) and Yu et al. (2018) measured both PBJW and GBJW but created one overall BJW score for the analyses. This approach is limiting, since it has been known for several decades that PBJW and GBJW are distinct factors, and yet the omission of analysing and addressing these two factors in any BJW research has been a persistent problem in the literature (Bartholomaeus & Strelan, 2019). One call that has also been made by Bartholomaeus and Strelan (2019) is for work to continue into the explanatory mechanisms underpinning BJW processes, including the use of mediation studies.

Potential Mediators of the Relationships between PBJW and GBJW with Wellbeing/Depression
Psychological wellbeing can be defined as comprising a range of elements. One model (Tennant et al., 2007) of psychological wellbeing includes "hedonic and eudaimonic aspects of mental health including positive affect…, satisfying interpersonal relationships and positive functioning". Conceptually, Tennant et al.'s (2007) model of psychological wellbeing can be seen as overlapping, to some extent with other frameworks, including those by Ryff (1989) and Seligman (2018), but there are differences too (Martela & Sheldon, 2019). For example, although Tennant et al.'s (2007) model has concepts in common with Ryff's (1989) approach by sharing selfacceptance and autonomy, there are other ways in which the models are distinct, such as Tennant et al.'s (2007) model also comprising energy and clear thinking. As a result, it is important to use only one type of measure of psychological wellbeing to avoid conflating concepts. In this instance, we have used Tennant et al.'s (2007) model. Furthermore, depression, as a subset of mental ill-health experiences, does not need be on the opposite end of the spectrum to that of wellbeing but could rather represent a separate spectrum of depressive experiences (Henry & Crawford, 2005). Indeed, just as research has demonstrated the componential structure of positive 1 3 affect and negative affect as being two separate dimensions (Kercher, 1992), depression tends to be inversely related to wellbeing, but it could also be very distinct.
The false and illusory nature of BJW has been known since the concept's inception. The inherent 'positive illusion' (Dalbert, 1999;Taylor & Brown, 1988;Wilson & Darke, 2012) within BJW can have the effect of impacting people's mental health and wellbeing in a positive way. However, BJW is not usually a direct predictor of wellbeing, but rather there is a series of direct and indirect paths from BJW to wellbeing. As an example, gratitude has been found to mediate the links between BJW and depression or wellbeing (e.g. Jiang et al., 2016) and there are many other studies that have shown similar indirect effects (e.g. Jiang et al., 2017;Ucar et al., 2019). In our research, we have examined three potential mediators-perceived control, optimism, and gratitude.

Perceived Control as a Mediator
One of the central claims of Justice Motive Theory (Lerner, 1980) is that BJW provides individuals with a sense of control. Bartholomaeus and Strelan (2019) provide a strong rationale for why perceived control should be further investigated as part of explanatory models into BJW and wellbeing by arguing as follows: if a person's immediate social world (or the wider world, in the case of GBJW) is seen as consistent and predictable, then they may feel control over their destiny and others' fate; this then elicits a virtuous cycle of expending effort towards worthy goals, perceiving a sense of control, and feeling subsequent emotions of pride in achieving one's goals, which then leads to affirmation of the belief in receiving one's just desserts (Kaliuzhna, 2020). Research has found that perceived control mediates the relationship that both PBJW and GBJW can have with various aspects of wellbeing (Donat et al., 2016;Fischer & Holz, 2010;Ucar et al., 2019;Yu et al., 2018). Furthermore, Skinner (1996) found that higher levels of perceived control, rather than objective measurable control, have been linked to higher levels of optimistic feelings, which could in turn lead to better states of wellbeing. This knock-on effect put forward by Skinner (1996) could mean possible double mediating relationships with perceived control predicting optimism and in turn predicting wellbeing, which would need to be empirically tested too. Feeling in control and seeing the benefits of one's efforts of being in control have been found to have knock-on effects on wellbeing (Muenscher et al., 2020). Conversely, degradations to people's sense of control have been implicated in the phenomenon of learned helplessness, which is a key mechanism underpinning the development of depression (Maier & Seligman, 2016).

Optimism as a Mediator
Optimism appears to be intrinsically linked to BJW in several important ways. Primarily, optimism is about expecting the future to be positive, and having confidence in achieving the right result (Kleiman et al., 2017). One can draw parallels with this dynamic and the 'personal contract' and 'positive illusions', which are core principles of BJW theory (Dalbert, 2001;Lerner, 1980). This particularly illusory, unrealistic and biased form of optimism is what Strelan and Callisto (2020) found in relation to PBJW and people's perceptions of experiencing positive outcomes. They found that people who believed in a just world for themselves also believed that more good things will happen to themselves when compared to other people. GBJW has been correlated positively with optimism among young adults (Correia & Vala, 2004), as well as among homeless African men (Littrell & Beck, 1999). Regarding causal relationships, experimental evidence has shown that higher PBJW improved students' perceptions of their career so that they viewed it more optimistically (Nudelman et al., 2016). Moreover, optimism was also found to mediate the relationship between GBJW and both wellbeing and depression (Jiang et al., 2016). Considering BJW's association with optimism, it is important to note that optimism has a well-documented association with wellbeing (Ferguson & Goodwin, 2010;Peterson & Bossio, 2001;Souri & Hasanirad, 2011) and subjective happiness too (Duncan et al., 2013). Given these associations, it would seem reasonable to infer that an optimistic explanatory style (Peterson & Steen, 2020) could be a result of having perceptions that one's personal world and the wider world are fair and, likewise, by expecting this to continue, wellbeing levels are more likely to increase accordingly.

Gratitude as a Mediator
Gratitude, in the context of BJW and wellbeing and depression, has been explored very modestly. Jiang et al. (2016) found that gratitude mediated the relationship between GBJW and wellbeing and depression, although the regression coefficients were relatively small. Gratitude has been found to mediate the relationship between GBJW and altruistic behaviour on the Internet and GBJW and self-esteem (Jiang et al., 2017). Gratitude has also been found to mediate the relationship between PBJW and forgiveness of others-another pro-social behaviour that may be linked to wellbeing (Strelan, 2007).
In relation to understanding gratitude as a potential mediator of PBJW/GBJW being related to wellbeing/depression, the following mechanisms could be at play. By seeing one's personal world as fair, the recipient of this perceived fairness is likely to feel grateful and blessed for receiving their just desserts (McCullough et al., 2002). From there on, feeling grateful would then lead to experiences of heightened wellbeing, or being protected from depressive feelings; both effects of gratitude predicting greater wellbeing and reduced depression have been wellestablished patterns obtained from a range of longitudinal and cross-sectional studies (e.g. Emmons & McCullough, 2003;Wood et al., 2008Wood et al., , 2010. There is also another potential mechanism, involving reciprocal altruism, which could explain how gratitude could act as a mediator in relation to PBJW/GBJW-wellbeing/depression links. For example, a person who perceives their world as being just and fair may engage in the thought process of 'people do kind acts for me (because I believe they do it in return for me doing good things to the world); they don't have to do kind acts, but because they do, this makes the world just'. Resultant feelings of gratitude could therefore have a possible role of 'filtering' someone's perceptions (i.e. as a mediator) and leading to certain knock-on reactions so that PBJW and GBJW are more likely to predict higher wellbeing levels and lower depression levels. Believing in the notion of reciprocal altruism in relation to being blessed with being in a Just World is what Ma et al. (2023) have argued is one mechanism whereby gratitude could have indirect effects in PBJW/GBJW-wellbeing/depression interrelationships.

Gratitude as a Moderator
However, feelings of being grateful because of BJW perceptions could have a different knock-on effect. While analysis of mediating relationships could help to explain how the effects of predictor exogenous variables on certain endogenous variableslike depression and wellbeing-can be 'filtered' through experiencing so-called third variables, there are other potential interrelationships. One such dynamic is when there is a synergy between the predictor variable and a potential moderating variable (see Hudek-Knežević et al., 2005) to increase or decrease the impact of this synergy on health-related outcomes. For example, by witnessing injustice and unfairness and viewing it as wrong, the observer may then attempt to make sense of it by recognising that the unfairness of the world might affect the observer at some point, if they are not vigilant. For a religious person, they might use the adage of "There, but for the grace of God, go I" to characterise this perception (Waples, 2016). This feeling of having escaped misfortune and seeing the world as unjust could then 'buffer' the observer as they attempt to craft a sense of meaning and purpose to make sense of a victim's misfortune (Frankl, 1985). This notion of being 'buffered' from depressive feelings by having perceived one as having a fortunate escape from misfortune could then mean that gratitude feelings are interacting with PBJW/GBJW levels and creating a new synergistic interrelationship between PBJW/GBJW and wellbeing/depression. By seeing the world as unjust, and having low levels of BJW, high levels of gratitude could interact with this low BJW experience to protect the individual and, in so doing, predict higher wellbeing and lower depression levels. Conversely, a person who believes fervently that they live in a just society (i.e. High GBJW) may not see any reason for being grateful (i.e. Low GBJW) and may view this as a natural phenomenon to be taken for granted. To our knowledge, there is not a great deal of literature into gratitude as a moderator in BJW relationships, but using allied literature into stress and coping (e.g. Gungor et al., 2021), we can see that the protective capabilities of gratitude in that domain may transfer to the BJW area too. However, given the lack of prior research into gratitude as a moderator of BJW predictive relationships, the testing of this possibility was mainly exploratory in our research.

The Present Study
To our knowledge, we are not aware of any studies that have simultaneously assessed PBJW's and GBJW's relationships with wellbeing and depression, along with the mediating roles of perceived control, gratitude, and optimism. There has been research into the role of gratitude and optimism as mediators (Jiang et al., 2016), or the sense of control as a mediator (Yu et al., 2018), but none that we could find that examined all three mediators. To this end, we sought to test several hypothesised models that would identify potential direct relationships between PBJW/GBJW and wellbeing/depression, along with indirect relationships via three potential mediating variables. We also sought to test the potential for moderating relationships occurring, whereby gratitude interacts with PBJW/GBJW and this would bring about a significant change to people's levels of wellbeing and depression.
Hypotheses Based on our review of extant theory and empirical findings, we tested the following models: Model 1 PBJW will be positively associated with wellbeing on a direct level, and this relationship will be mediated by PBJW predicting increases in optimism, gratitude, and perceived control, which, in turn, leads to increases in wellbeing.
Model 2 GBJW will be positively associated with wellbeing on a direct level, and this relationship will be mediated by GBJW predicting increases in optimism, gratitude, and perceived control, which, in turn, leads to increases in wellbeing.
Model 3 PBJW will be negatively associated with depression on a direct level, and this relationship will be mediated by optimism, gratitude, and perceived control so that PBJW will predict increases in these three mediators, which, in turn, will predict decreases in depressive symptoms.
Model 4 GBJW will be negatively associated with depression on a direct level, and this relationship will be mediated by optimism, gratitude, and perceived control so that GBJW will predict increases in these three mediators, which, in turn, will predict decreases in depressive symptoms.
Model 5 GBJW and PBJW will directly predict wellbeing (positively) and depression (negatively), while gratitude, optimism and perceived control will mediate these relationships. We allowed for wellbeing and depression to correlate.
We conducted exploratory tests of the possible presence of double mediation for the first mediator of perceived control then predicting the second mediator of optimism and then predicting wellbeing or depression. We also tested whether gratitude could act as a moderator for PBJW/GBJW relationships with wellbeing/depression. Results of these exploratory tests are included in the supplementary information.

Design and Analysis
Two studies were conducted. We used cross-sectional designs for both studies and obtained correlational data. The first study was aimed at uncovering tentative trends with the relationships between PBJW/GBJW and wellbeing/depression, while being mediated through three potential mediators. We then sought to confirm/disconfirm the trends obtained in Study 1 by obtaining a more expansive sample in Study 2. We examined the relationship-using path analysis (Streiner, 2005)-between (a) exogenous variables of PBJW and GBJW, and (b) endogenous variables of gratitude, optimism and perceived control (i.e. the mediators), and (c) wellbeing and depression (i.e. the outcome variables). With hypothesised mediation, the identity of the mediators was switched, and they were labelled as exogenous variables so that their impact on the endogenous variables of wellbeing and depression could be examined too. To test for moderation, with gratitude as the moderator, we used the recommended practice of generating the product term of the exogenous variables with the moderator (Memon et al., 2019) and we also kept the other two mediators in the path analysis to test for simultaneous relationships with these mediators as well.
Path analysis was performed in RStudio using the 'lavaan' package, which uses maximum likelihood estimation procedures. This method of analysis can be used to evaluate multiple mediating variables at once, giving it an advantage over multiple regression, in addition to depicting direct and indirect effects. Hooper et al. (2008) stipulate that the Root Mean Square Error of Approximation (RMSEA) value needs to be lower than 0.06, the Standardised Root Mean Square Residual (SRMR) value needs to be below 0.08 and the Comparative Fit Index (CFI) and Tucker-Lewis Fit Index (TLI) values need to be above 0.95. The Chi-square value is also a 'badnessof-fit' index (Kline, 2005), where lower values are better, and a non-significant p value is best as this shows there is not a significant discrepancy between the data obtained and the hypothesised model. As well as assessing model fit, we then followed the requirements set out by Hayes (2009) for testing total, direct and indirect effects when conducting mediation analyses.

Study 1
After data cleaning, 179 participants' responses to the online Qualtrics-based study were included in the final sample. The survey link was clicked by 225 people, but some of the would-be participants did not reach the end of the survey or they completed less than 80% of any given scale (which was grounds for exclusion). The mean age in years was 25.9 (SD = 10.73) and ranged from 18 to 66 years. Regarding ethnicity, 146 identified as 'white', 8 identified as 'mixed/multiple ethnic groups', 14 identified as 'Asian', 3 identified as 'black', 1 identified as 'Arab' and 7 identified as 'other'. A total of 140 participants lived in Europe, 35 in North America, 1 in Asia, 1 in the Middle East and 1 did not specify. Regarding gender, the sample consisted of 123 females (69%) and 54 males (30%). There were 2 people who identified as non-binary (1%) and were grouped with the females for the purpose of the analyses into the role of gender.
Participants were recruited through a variety of methods. Undergraduate psychology students were targeted via the researchers' university's research recruitment system, which rewards students with research credits for their participation. The study was also advertised on Psychological Research on the Net (https:// psych. hanov er. edu/ resea rch/ expon net. html) for no compensation. The crowdsourcing company 'Prolific' was also used to recruit 40 participants online; these people received £0.84 each for their time.

Study 2
After data cleaning, 364 participants' responses to the online Qualtrics-based study were included in the final sample. The survey link was clicked by 490 people, but some of these would-be participants did not reach the end of the survey or completed less than 80% of any given scale (which was grounds for exclusion). The mean age in years was 25.07 (SD = 9.18) and ranged from 18 to 76 years. Regarding ethnicity, 167 identified as 'white', 17 identified as 'mixed/ multiple ethnic groups', 57 identified as 'Asian', 16 identified as 'black', 87 identified as 'Chinese', 2 identified as 'Arab' and 18 identified as 'other'. A total of 110 participants lived in Europe, 110 in North America, 129 in Asia, 3 in the Middle East, 4 in Australasia, 1 in Africa and 7 did not specify. Regarding gender, the sample consisted of 243 females (67%) and 121 males (33%).
Recruitment was simpler for Study 2; it was listed on the websites Psychological Research on the Net (https:// psych. hanov er. edu/ resea rch/ expon net. html) and Social Psychology Network (www. socia lpsyc hology. org) for no compensation. Links to the study were also shared via Twitter (www. twitt er. com).
As the participants for both studies were obtained because of convenience sampling, we used G*Power version 3.1.9.2 (Faul et al., 2009) to conduct a post hoc power analysis to see what would be the likely effect sizes and acceptable statistical power that could be detected with the desired analyses. With seven predictor variables (i.e. including the exogenous variables of PBJW and GBJW, three mediators and two control variables), and acceptable power of at least 0.80 (Cohen, 2013), study 1 could be used to detect effect size of 0.09 or higher, with power of 0.83. With this sample, effect sizes of 0.08 would only have power of 0.77. With study 2's larger sample, effect sizes of 0.04 could still be detected with power of 0.80. As a result, we decided to use study 1's data as a pilot study to give indicative findings and we gave more credence to study 2's data with its greater power.

Personal Belief in a Just World (PBJW) Scale
The PBJW (Dalbert, 1999) scale was used to measure how just and fair the participants viewed their personal worlds to be. It had 7 items and was scored on a Likert scale from 1 "strongly disagree" to 6 "strongly agree". Items included "I am usually treated fairly" and "In my life, injustice is the exception rather than the rule". The PBJW scale has been found to have good internal reliability (Cronbach's Alpha = 0.82, sample: German university students) in addition to having good factorial validity (Dalbert, 1999). It is also one of the most frequently used scales for measuring PBJW, which aids comparison with other studies (Bartholomaeus & Strelan, 2019).

General Belief in a Just World (GBJW) Scale
The GBJW scale (Dalbert et al., 1987) (Cronbach's Alpha = 0.82, sample: aged 18-64 years) was used to measure how just and fair individuals perceive the world in general to be. It had 6 items scored on a Likert scale from 1 "strongly disagree" to 6 "strongly agree". Items included "I believe that, by and large, people get what they deserve". This scale was found to have good concurrent validity when correlated with another respected Just World beliefs scale (Loo, 2002). (Tennant et al., 2007). We used the WEMWBS (Cronbach's Alpha = 0.89, sample: UK respondents aged 16 years or older) to assess mental wellbeing. It aimed to measure both the functional and feeling aspects of wellbeing. Permission to use the scale was granted by Warwick University. The 14-item scale was scored on a Likert scale from 1 "none of the time" to 5 "all of the time". Items included "I've been feeling good about myself". Numerous forms of validity have been tested as being satisfactory with this scale, including construct validity and cross-cultural validity (Tennant et al., 2007).

Depression
We used the Depression scale (Lovibond & Lovibond, 1995) (Cronbach's Alpha = 0.97, sample: Canadians aged from young adulthood to old age), which is a subscale of the Depression Anxiety Stress Scales (DASS-21). It measures depressive symptoms in clinical and nonclinical samples. It comprised 7 items measured on a 4-point Likert scale. Items included "I felt that I wasn't worth much as a person" and "I felt down-hearted and blue". A higher score was indicative of greater depressive symptom expression. Good construct validity has been found for all three scales in the DASS-21 (Randall et al., 2017).

Gratitude Questionnaire-6 (GQ-6)
We used the GQ-6 (McCullough et al., 2002) (Cronbach's Alpha = 0.82, sample: USA undergraduate students) to measure how grateful individuals are in their life. It had 6 items scored on a Likert scale from 1 "strongly disagree" to 7 "strongly agree" and included some reverse-scored items. Items included "If I had to list everything that I felt grateful for, it would be a very long list". The scale has been shown to have good construct and cross-cultural validity (Sumi, 2017).

Optimism (Revised Life Orientation Test)
The LOT-R (Scheier et al., 1994) (Cronbach's Alpha = 0.78, sample: USA undergraduate students) was used to assess people's general tendencies towards optimism and pessimism. A higher score indicated higher levels of optimism. It had 10 items and was scored on a Likert scale from 1 "strongly disagree" to 5 "strongly agree", including filler and reverse-scored items. Items included "I'm always optimistic about the future". Good concurrent validity was found via its relationship with psychosocial adjustment and wellbeing (Monzani et al., 2014). It could be argued that the measure of optimism might correlate substantially with one of the items from the WEMWBS ("I've been feeling optimistic about the future") and the LOT-R total score, but the correlation was not strong enough (e.g. r = 0.58) to merit concern (Dormann et al., 2013). In a like manner, removal of that one WEMWBS item from the total composite score would hinder comparisons with other studies measuring wellbeing in this way.

Perceived Control (Environmental Mastery)
The Environmental Mastery scale was used and is a subscale of Ryff's (1989) Psychological Wellbeing Scales (Cronbach's Alpha = 0.90, sample: young, middleaged, and older adults from the USA). It was used to measure the sense of control and competence in one's environment, including responsibilities, relationships, and lifestyle. It had 7 items scored on a Likert scale from 1 "strongly disagree" to 6 "strongly agree". Some items were reverse scored. Items included "I am quite good at managing the many responsibilities of my daily life". It could be argued that this subscale-as part of a wellbeing scale-might overlap substantially with the content of one of the items being measured by the WEMWBS (e.g. "I've been dealing with problems well"), but the correlation strength between this item and the perceived control total score (r = 0.50) was not sufficiently strong to merit concern (Dormann et al., 2013). In addition, removal of the one item from the WEMWBS would then mean we could not compare like-with-like if aiming to compare our WEMWBS scores with other studies. Moreover, this scale has been used by Fischer and Holz (2010) as a measure of perceived control in their study of BJW and its role in women's experiences of sexism.

Checking for Empirical Overlap between Items and Scale Scores
For both the WEMWBS and Perceived Control analysis and the WEMWBS and Optimism analysis, respectively, we checked to see if removal of the potential biasing item from the WEMWBS (i.e. see above for each respective scale) could mean different results, but we found the difference between the analyses before and after the removal of the item as being negligible. As a result, it made sense to leave the scales intact to enable comparisons between our research and other similar studies.

Control Factors
In line with similar research (Jiang et al., 2016(Jiang et al., , 2017, we connected the control variables to all the endogenous variables (i.e. mediators being predicted or outcome variables) in the path models. The following two variables were used as control factors:

Ethnicity
Participants were asked: "What is your ethnic group?" They were given 7 options, which included "other", for them to self-specify. These options were informed by the British government census data on ethnicity. Ethnicity was coded as '0' for white and '1' for minority status. Previous research has found that white people can have a higher PBJW than black or mixed-race people (Thomas & Rodrigues, 2020). As a result, we would expect those from a minority ethnic group to have lower PBJW, GBJW, gratitude, optimism, perceived control, and wellbeing scores, along with higher depression scores.

Gender
Participants were asked: "What is your gender?" They could choose "male", "female" or "other", where they could self-specify. Gender was coded as '0' for male and '1' for female/other in Study 1 and '1' for female in Study 2. Past research has found that being female has been associated with a lower PBJW than being male (Dalbert & Stoeber, 2006). We hypothesised that participants who were female/ other would perceive lower levels of PBJW and GBJW, which would, in turn, lead to lower levels of gratitude, perceived control and optimism, and, in so doing, lower levels of wellbeing and higher levels of depression.
It could be argued that as we measured age in our survey, age could also be used as a control variable in our analyses. However, from our review of studies into BJW, the potential mediators of perceived control, optimism and gratitude, and wellbeing/depression, we could not find much support for age as a potential confounding variable. For example, Jiang et al.'s (2016) study with age as a predictor of subjective wellbeing, depression, optimism, and gratitude did not show it as a significant predictor with the first step of their hierarchical regression analyses. Likewise, Strelan and Callisto (2020) did not find age as being a significant correlate with PBJW, GBJW and all other variables in their study. Spector and Brannick (2011) warn against the automatic and blind inclusion of control variables; without a strong theoretical or empirical rationale for its inclusion, we therefore chose not to use age as a control variable. 1

Procedure
Ethical approval for the study was granted by the researchers' School Research Ethics Committee. Participants voluntarily took part in the study and were directed to the study on Qualtrics. Recruitment for Study 1 took place between November 2019 and February 2020. Study 2 took place between December 2020 and July 2021. Participants were presented with an information screen, which involved giving consent for the researchers to use their data. If a participant did not give consent, they were directed to the end of the study and could not take part. After completing the survey, participants were thanked and debriefed.

Data Screening and Preliminary Analyses
Regarding missing data, when responses for at least 80% of the scale items had been obtained, mean imputation was used for any remaining missing items. Research has shown this is an adequate way to treat missing data to preserve an appropriate sample size while still producing favourable results (Shrive et al., 2006). Mean imputation was used for 14 and 26 empty data points in Study 1 and Study 2, respectively. When analysing non-responses to each item, there were no discernible items that were characterised by sizable non-completion rates. In Study 1, the fourth item of the Depression scale was omitted three times. In Study 2, only one of the items of the PBJW scale (item #5) was omitted four times and only one of the items from the Depression scale (item #3) was omitted three times, but any other item was only omitted once or twice as a maximum. Any responses not meeting the 80% completion criterion were excluded from the final analyses. All variables in the present study fell within the acceptable range of normality for path analysis (i.e. skewness < 3, and kurtosis < 10, as recommended by Kline, 2005;Weston & Gore, 2006). See Tables 1 and 2 for descriptive statistics relating to the variables measured in Study 1 and Study 2, including means, standard deviations, ranges, Cronbach's Alphas, and Pearson's correlation coefficients. Table 1 shows no evidence of multi-collinearity among the variables as they were all below 0.80 (Vatcheva et al., 2016). Table 2 shows that all the means were within the expected ranges and did not differ substantially between the two studies. Cronbach's Alphas ranged from 0.77 to 0.92.

Model Testing
Firstly, four models were analysed, with the three mediating variables connecting a single exogenous variable to a single outcome variable (e.g. PBJW predicting wellbeing directly and indirectly via three mediators). Models 1 and 3 had excellent fit in Study 2, with Models 2 and 4 receiving less support. See Table 3 for details of these models, across both Study 1 and Study 2.
With data from both studies, the fit statistics supported both Models 1 and 3 with the role of PBJW predicting wellbeing and depression, respectively, via the three mediators. With Models 2 and 4, Study 1 also showed support, although Study 2 was less supportive. Considering Study 2 had a larger sample size and thus, more Table 1 Pearson's correlation coefficients for the study variables (including control variables) Ethnicity was coded as 0 = white and 1 = ethnic minority; Gender was coded as 0 = male and 1 = female/other (Study 1)    statistical power, it can be concluded that the models with PBJW as the key predictor had more empirical support than the models with GBJW predicting wellbeing and depression via the three mediators. Secondly, a larger, singular model (i.e. Model 5), with all the variables included, was also tested (GBJW and PBJW as exogenous variables; perceived control, optimism, and gratitude as mediators; and wellbeing and depression as outcome variables). Paths were estimated from each exogenous variable to each endogenous variable directly and then, indirectly through each mediating variable. Model 5 did not have as much empirical support, when examining the fit statistics for study 1 and compared with Models 2 and 4. Likewise, it underperformed in relation to Models 1 and 3 in study 2 (see Table 3).
Thirdly, with further exploratory analyses, we tested if both GBJW and PBJW could predict wellbeing directly and via the three mediators (Model 6) and could do likewise to predict depression (Model 7). These models were not that well supported in study 2, with relatively low TLI values, a significant Chi-squared statistic, and relatively high RMSEA values.
Fourthly, we conducted exploratory tests to see if gratitude could moderate the relationship between PBJW and wellbeing (Model 8), GBJW and wellbeing (Model 9), PBJW and depression (Model 10), and GBJW and depression (Model 11), while accommodating for perceived control and optimism as mediators to these relationships. These models had poor statistical fit.
Fifthly, and finally, we explored if double mediation could exist in which GBJW predicted perceived control, which then predicted optimism, and in turn predicted wellbeing, while also having gratitude as a parallel mediator (Model 12). We tested for double mediation with a similar pattern of relationships for the link between PBJW and depression (Model 13). Neither of these models had satisfactory fit. The fit statistics for these exploratory tests can be seen in the supplementary information.

Model 1
Model 1 was fully supported across both studies as PBJW was positively associated with wellbeing via the indirect effects of gratitude, perceived control, and optimism. Across both studies, significant effects were all consistent, except for the direct effect of PBJW onto wellbeing after controlling for the mediated effects. This direct effect was only significant in Study 2, and the effect sizes were slightly attenuated in Study 2, relative to Study 1, with an overall beta of 0.38 in Study 1 compared with 0.31 in Study 2. See Table 4 for more details. The standardised effect sizes for this model are in Fig. 1. Table 5 shows that Model 2 was partially supported in both studies: in Study 1, GBJW was positively associated with wellbeing via the indirect effect of perceived control, but not optimism and gratitude. In Study 2, GBJW was positively associated with wellbeing via the indirect effects of perceived control and optimism, but not gratitude. Compared with Study 1, Study 2 data showed that GBJW had an increased total effect on wellbeing (0.20 versus 0.12, respectively). The direct effect from GBJW to gratitude was largely attenuated in Study 2, although this did not change the lack of an overall significant indirect effect of gratitude across both studies. Additionally, Study 2 showed a larger and statistically significant direct effect of GBJW on wellbeing, after controlling for mediated effects. Finally, the indirect effect of optimism in Study 1 was not statistically significant, but it was found to be statistically significant in Study 2. The standardised effect sizes for this model are in Fig. 2. Table 6 shows that Model 3 was fully supported across both studies, as PBJW was negatively associated with depression via the indirect effects of gratitude, optimism, and perceived control. Significant pathways were identical between studies, and the overall effect sizes were similar too (Study 1: − 0.29, Study 2: − 0.26). A direct effect between PBJW and depression was not statistically significant in either study once the mediating effects were included. In both studies, perceived control accounted for the largest indirect effect, followed by optimism, then gratitude. The standardised effect sizes for this model are in Fig. 3.

Model 4
Model 4 was partially supported by Study 2 data, but not with Study 1. Study 1 had only perceived control as a significant indirect effect between GBJW and depression; however, the total effects of GBJW on depression in Study 1 fell short of statistical significance. This was likely owing to the potential for reduced statistical power in Study 1, since the overall betas were very similar (Study 1: − 0.11, Study 2: − 0.11). In Study 2, by contrast, GBJW was negatively associated with depression via the indirect effects of optimism and perceived control, but not gratitude. In both studies, neither direct effect from GBJW to depression (after including mediating effects) was significant. See Table 7 for details. The standardised effect sizes for this model are in Fig. 4. Table 8 shows the direct and indirect effects between the exogenous variables of PBJW and GBJW on the mediators and on the endogenous variables of wellbeing and depression. The combination of PBJW and GBJW as joint predictors had sizable effects in predicting wellbeing (i.e. effect sizes of 0.40 and 0.35 in studies 1 and 2) and depression (i.e. effect sizes of −0.32 and −0.26 in studies 1 and 2), and this was more so when compared with Models 1 and 2 in predicting wellbeing (i.e. effect sizes of 0.38, 0.31 and 0.12, 0.20 for only PBJW or GBJW as single predictors, respectively, in studies 1 and 2). Likewise, this model was able to directly predict depression to a greater extent by combining PBJW and GBJW as joint predictors, when compared with only having them as single predictors in Models 3 and 4 (i.e. effect sizes of − 0.29 and − 0.26 with only PBJW predicting depression in studies 1 and 2, respectively, and effect sizes of − 0.11 and − 0.11 with only GBJW predicting depression in studies 1 and 2, respectively). The indirect effects in Model 5 were more complex. Significant indirect effects were found with PBJW predicting wellbeing and depression via all three mediators in both studies, but the same could not be demonstrated with GBJW predicting wellbeing or depression, with only a significant indirect effect being obtained with perceived control as the only mediator in study 2, but not in study 1.

Discussion
The aim of this research was to test a range of models explaining how PBJW or GBJW might directly predict wellbeing and depression or indirectly predict these outcomes via three mediators of gratitude, optimism, and perceived control (i.e. Models 1 to 4). We also tested whether PBJW and GBJW could simultaneously predict wellbeing and depression via the three mediators (Model 5), or only predict either wellbeing or depression (Models 6 and 7). We also examined if gratitude could act as a moderator with PBJW/GBJW to predict wellbeing/depression, while allowing for mediating relationships with perceived control and optimism (Models 8 to 11). We also tested for multiple mediation with perceived control being the first mediator and optimism being the second mediator. Models 6-11 did not  achieve statistical fit at similar levels with Models 1-5. The first four models had very good or excellent model fit across both studies. Of the total effects obtained in each model, Model 1 had the most support, followed by Model 3. Model 2 had even less support, and Model 4 showed mixed trends, with non-significant total effects obtained in Study 1 and, in Study 2, the weakest, albeit significant, total effects were obtained out of all of four models.

Direct and Mediating Mechanisms of PBJW Predicting Wellbeing/Depression (Models 1 and 3)
Given that Model 1 was the best supported in Study 2, it is noteworthy how and why this might be the case. Of interest is the trend that PBJW significantly predicted gratitude, optimism, and perceived control across both studies and that these mediators also significantly predicted wellbeing. However, it was only in the larger sample in Study 2 that a significant predictive direct effect was also detected between PBJW and wellbeing. As the direct effects, indirect effects, and total effects from Study 1 were largely replicated in Study 2, we can presume that there is tentative support for a direct relationship between PBJW and wellbeing, but this still needs to be confirmed in subsequent studies. It should be noted that although PBJW has occasionally had direct links with wellbeing (e.g. Sutton & Douglas, 2005), most of the literature (e.g. Fischer & Holz, 2010) points to there being indirect paths from PBJW to wellbeing via mediation processes. In the case of both our studies, perceived control was the strongest mediator, followed by optimism; gratitude was the weakest mediator. Although PBJW has been found to have had positive associations with wellbeing ( Bartholomaeus & Strelan, 2019;Dalbert, 2001;Donat et al., 2016;Fischer & Holz, 2010;Lerner, 1980;Ucar et al., 2019), our findings point to PBJW mainly doing so via dynamics of heightened perceived control, optimism, and gratitude as parallel pathways through which better states of wellbeing can be attained.
A key implication of the personal contract in the BJW phenomenon is that it affords people a sense of control (Dalbert, 1999;Lerner, 1980); if people see their personal worlds as just, then they are often willing to delay gratification for the pursuit of future-oriented goals and expect their hard work to be rewarded. The link between perceived control and feelings of wellbeing has been well established (Peterson, 1999) and is reaffirmed with results from Model 1 testing. Our finding of the salient role of perceived control as mediating the relationship between PBJW and wellbeing resonates with findings obtained in other samples (Donat et al., 2016;Fischer & Holz, 2010).
The role that optimism plays in mediating between PBJW and wellbeing also adds to the explanatory mechanism underpinning PBJW and its impacts. The direct effect of PBJW on optimism in the path analysis was the strongest of all three mediators in Study 1 and was the second strongest in Study 2. The processes of seeing oneself personally benefit from one's efforts are likely to lead to positive feelings about future good outcomes and to then predict better wellbeing states, as we found when testing Model 1. This is in line with Dalbert's (2001) argument that optimism plays a pivotal role in the link between BJW experiences and wellbeing; this dynamic has been explained by Dalbert (2001) as going through a process of meaning-making, including: making sense of events that happen as either adverse or beneficial, expecting fair treatment (and looking out for instances of this in past and future events), and trusting in a positive outcome (Dalbert & Donat, 2015;Nudelman et al., 2016).
When testing Model 3, PBJW did not directly predict depression in either Study 1 or Study 2, but, instead, this relationship was mediated by perceived control, optimism and gratitude. Yet again, as with Model 1, perceived control was the strongest mediator, followed by optimism, and then gratitude. The present research corroborates results from other studies that have found mediating relationships to explain the links between PBJW and depression (Fischer & Holz, 2010;Jiang et al., 2016;Ucar et al., 2019). Additionally, the strength of PBJW's relationship with depression appears to be slightly smaller than its relationship to wellbeing. This corroborates notions of wellbeing and depression as being inversely related, but still distinct, experiences (Henry & Crawford, 2005;Kercher, 1992); if depression and wellbeing were at either ends of a continuum, we would expect depression to be associated with BJW to a similar magnitude as wellbeing, but this was not the case. It also suggests that PBJW is more strongly connected to positive psychological phenomena, such as wellbeing, than it is to mental ill-health, such as depression.

Direct and Mediating Mechanisms of GBJW Predicting Wellbeing/Depression (Models 2 and 4)
The present research has shown that GBJW is directly associated with wellbeing, but this was only confirmed with Study 2. The GBJW-wellbeing relationship was mediated by two out of the three mediators, with perceived control mediating the relationship in both studies and optimism being a mediator in Study 2. In both studies, gratitude did not mediate GBJW-wellbeing and GBJW-depression relationships. Perceived control was pivotal for mediating the link between GBJW and wellbeing, and this is consonant with previous studies (e.g. Yu et al., 2018). With Model 4, however, the trends overall were less clear-cut across both studies. For instance, optimism was a significant mediator of the link between GBJW and depression, but only in Study 2. Perceived control was the only mediating variable that consistently affected the relationship between GBJW and depression across both studies. This trend can be used to emphasise the importance of perceived control in BJW-related psychological mechanisms (e.g. Strelan & Callisto, 2020) that could influence wellbeing and mental health, since it is a stable pattern across all four models.
Theoretically, these findings could be explained in the following ways. Firstly, believing the wider world to be a fair place is a belief system that is vulnerable when learning of injustices through a range of media, including the consumption of news and social media messaging. The myriad reference points for witnessing injustice and misery are likely to elicit the need to make sense of such situations and cope with the cognitive dissonance of being in a world that is meant to be fair, but may not appear to be so on the face of it. Secondly, by believing that this global lens of a fair/just world is controllable-after all, the viewer of such misery could contribute to a worthwhile charity to feel like they are making a difference-the experience of cognitive dissonance could be lessened, and the person's wellbeing could still be maintained. Thirdly, and finally, by being able to exert influence over one's global lens by helping those in need, the belief that the world continues to be a fair place persists and reduces the risk of depressive feelings resulting from perceptions of powerlessness. Although optimism only mediated the link between GBJW and wellbeing/depression in the larger sample in Study 2, the trend is sufficiently noteworthy to analyse in depth. Having an optimistic explanatory style can help to affirm one's perceptions of the wider world being a fair and meaningful place; possession of an optimistic explanatory style has been found to inoculate oneself from depression (Seligman, 2007) and can also promote wellbeing in the face of stressors (Genç et al., 2021) by viewing these stressors as 'challenges' that can be surmounted (Baumgartner et al., 2018).
The lack of a role for gratitude in mediating the link between GBJW and wellbeing and depression merits further discussion since this appears counterintuitive and the opposite to what was hypothesised. Gratitude is an important component of Justice Motive Theory (Dalbert, 2001). It has also tended to be a strong predictor of wellbeing and has helped to filter out depressive feelings (Disabato et al., 2017). Directly, gratitude was still found to be a product of GBJW in study 1, and gratitude also predicted lowered depressive feelings in both studies and predicted increases in wellbeing. However, the indirect pathways from GBJW to wellbeing/depression via gratitude were not confirmed in either of the samples. In our further tests of the role of gratitude as a potential moderator, we also did not find support for this possibility in studies 1 and 2.

Direct and Mediating Mechanisms of PBJW and GBJW Predicting Wellbeing and Depression (Model 5)
We tested whether GBJW and PBJW could simultaneously predict wellbeing and depression both directly and indirectly via the presence of the three mediators. Model 5 was tested to evaluate its statistical fit in studies 1 and 2, and we examined the direct effects, indirect effects, and total effects for this model. It is noteworthy that, with study 1, Model 5 did not achieve as good statistical fit when compared with Models 2 and 4, which were models focused on how GBJW could predict wellbeing or depression. In a similar manner, Model 5 was not as well supported in study 2 when compared with Models 1 and 3, which were models focused on the PBJW-wellbeing/depression relationship. Despite these lower levels of statistical fit, there were some noteworthy trends obtained in Model 5. Firstly, the direct effects in predicting wellbeing or depression were stronger in this model when compared with the other four models. There are not many studies we could find that simultaneously measured the direct effects of GBJW and PBJW in predicting wellbeing and depression, but we were able to locate some analogous findings with which to compare with our studies. In our research, we found the combination of PBJW and GBJW had a stronger direct effect in predicting wellbeing when compared with PBJW and GBJW combined when predicting depression. The capabilities of being able to predict wellbeing versus depression are more pronounced when PBJW is introduced into any BJW-related analyses. For instance, Sutton et al. (2017) measured PBJW and GBJW with the extent to which each variable could predict various elements of wellbeing and they found that PBJW could directly predict flourishing and overall wellbeing to a much greater extent than GBJW. In Model 5, the dynamics present in the model whereby PBJW appeared to be more influential might also be explained more by the indirect effects that were obtained that showed PBJW predicting wellbeing or depression via the three mediators. Conversely, there were no such trends that could be found with indirect effects for GBJW predicting wellbeing or depression through the indirect routes of the three mediators. With GBJW, only perceived control was a mediating variable with a significant indirect effect, and this was only in study 2 for GBJW-wellbeing and depression relationships. Clearly, perceived control appears to have the most salient role in any simultaneous testing of PBJW and GBJW as direct or indirect relationships with wellbeing and depression. This finding-of the integral importance of perceived control-synchronises with studies such as those by Ucar et al. (2019) and Xiong et al. (2022).

Comparing the Differential Impacts of PBJW and GBJW
Our findings suggest that PBJW is more strongly related to wellbeing and depression than GBJW, as shown by model fit statistics and regression coefficients.
These differential effects were most stark when looking at the indirect effects for optimism, perceived control, and gratitude as mediators. Across both studies, PBJW had stronger associations with optimism, perceived control, and gratitude, when compared with GBJW's associations to these variables. The most salient of these differences is that GBJW did not have a significant indirect effect through gratitude to either wellbeing or depression, but PBJW did. In Study 2, when comparing PBJW's and GBJW's direct relationships with wellbeing, PBJW had a stronger relationship. Dalbert's (2001) theory about the relationship between PBJW and mental health explains why PBJW, in the present work and in other research, is more strongly related to wellbeing and depression than GBJW. People's beliefs that their personal worlds should be fair appear to be more integral to their wellbeing and in having a lower propensity towards depression when compared with needing to have a general view of the broader world needing to be fair and just. Evidence for this relates back to Justice Motive Theory, as studies have found people are more likely to deny injustices that concern them personally, rather than those injustices that concern others (Dalbert, 2001). Moreover, self-serving biases in the form of positive illusions seem to be ubiquitous, as people tend to believe they have above-average chances of experiencing positive events and below-average chances of experiencing negative events (Taylor & Brown, 1988;Weinstein, 1980). The salience of it being their personal world, and therefore, it is more likely to affect them, is what makes PBJW more important to people's wellbeing and levels of depression. Lerner (1980) posited that this need to view one's world as fair is adaptive and essential; it appears that this innate need can be broken down further into a hierarchy with personal justice being most important to one's wellbeing, followed by justice for others in the wider world. Perceived control, optimism, and gratitude are states of mind that people may experience while believing the world is generally just, but when people truly believe that their personal worlds are just, feelings of control and optimism appear accentuated, in line with self-interest. Gratitude is also more likely to occur in relation to good things happening to oneself, rather than to others, since people are more likely to look to find ways of meeting their own interests, instead of focusing on meeting the needs of others (Berman & Small, 2012).
Present results concur with previous research with differential impacts of PBJW and GBJW via mediating relationships. Model 1 corroborates Fischer and Holz (2010), who found that perceived control partially mediated the relationship between PBJW and wellbeing, and it confirms Ucar et al.'s (2019) study, which found perceived control mediated the relationship between PBJW and life satisfaction. Similarly, our research is in line with Donat et al.'s (2016) research, which found that having an internal locus of control correlated strongly with PBJW. Regarding optimism, much past research has focused on GBJW correlating with optimism (Correia & Vala, 2004;Jiang et al., 2016;Littrell & Beck, 1999) and the present research confirms this, but also shows that PBJW is correlated with optimism more strongly; these differential relationships support the need to regularly make the distinction between PBJW and GBJW when conducting research into BJW and its correlates. In the present research, PBJW had a much stronger effect on gratitude than GBJW had done so in Jiang et al.'s (2016) study.

Strengths, Limitations and Future Research
This article is a modest addition to the literature regarding the role of BJW in relation to wellbeing and depression. We acknowledge that there are other studies that have tested gratitude, perceived control, and/or optimism as mediators of the BJWwellbeing/depression dynamic, but there were no studies we could find that have simultaneously examined the roles of all three mediators. For example, although it could be argued our studies have shared features with Jiang et al.'s (2016) study, since they researched gratitude and optimism as mediators for wellbeing and depression, but they did not differentiate between PBJW and GBJW and did not look at the role of perceived control. Like some previous research, we have found that PBJW and GBJW have differential impacts on wellbeing and depression, and this is further evidence for these two BJW components needing to be studied separately, rather than grouping them into a composite score. We have unpacked the relative strengths of each of the mediating variables of gratitude, optimism, and perceived control in the PBJW/GBJW relationships with wellbeing and depression, and we have shown that perceived control was the strongest mediator, followed by optimism, and then gratitude. In these analyses, we showed that the first four models had substantial empirical support and were superior to models incorporating multiple mediation mechanisms, or one that encompassed both GBJW and PBJW predicting wellbeing and depression either singly or simultaneously, or by having gratitude as a possible moderator of GBJW/PBJW-depression/wellbeing relationships.
There are some potential limitations to the present research. Firstly, as both studies involved analyses of cross-sectional data, we cannot assume causal relationships. It is therefore recommended that future studies employ longitudinal and experimental methodologies while testing the same constructs to discern causal directions. This could be done by testing if increases in perceived control, optimism, and gratitude cause PBJW to increase. Dalbert (2001) explained how it is likely that GBJW and PBJW have adaptive qualities in relation to mental health, and from the studies that have tested causality, one longitudinally and the other experimentally, a reciprocal relationship appears to be present (Correia et al., 2009;Dalbert & Stoeber, 2006). Secondly, the samples obtained were self-selecting and only included people who had access to the Internet, so there was a potential for sampling bias, although it should be noted that the samples were drawn from many different countries. It is also noteworthy that the sample for Study 2 appeared to provide a wider cross section than the sample for Study 1 might have done. Thirdly, the use of self-reporting measures might result in socially desirable responding. However, McCullough et al. (2002) found that the GQ-6, which we used to measure gratitude, was not confounded by social desirability, along with Sutton and Douglas (2005) who found that PBJW's association with life satisfaction was not confounded by social desirability. Moreover, the present study preserved participants' anonymity, which may have helped to reduce social desirability. Fourthly, and finally, the models tested only encompassed a limited number of mediating variables while still obtaining sufficient responses by not overloading the participants with too many items to complete; this meant that other potentially important constructs, such as conscientiousness (Nudelman & Otto, 2021), could not be assessed, but they could merit further investigation to understand the processes underpinning PJBW/GBJW-wellbeing/ depression relationships.

Conclusion
This research has demonstrated that people's levels of PBJW can directly influence their wellbeing and depression levels, but it also achieves this indirectly via perceived control, optimism, and gratitude. We have also provided strong evidence for the PBJW and GBJW distinction as needing to be separately analysed for their processes and impacts, rather than using composite measures of BJW, as some researchers have done. Perceived control appears to be the strongest mediator of PBJW/GBJW-wellbeing/depression relationships. As a result, we would argue that supporting people to enhance their levels of perceived control may help them with their perceptions of their immediate social worlds and the wider world and, in turn, lead to better knock-on effects with their overall wellbeing and mental health.