Moral decision-making in context: Behavioral and neural processes underlying allocations based on need, merit, and equality

How to fairly allocate goods is a key issue of social decision-making. Extensive research demonstrates that people do not selﬁshly maximize their own beneﬁts, but instead also consider how others are affected. However, most accounts of the psychological processes underlying fairness-related behavior implicitly assume that assessments of fairness are somewhatstable.Inthispaper,wepresentresultsofanoveltask,theRe-AllocationGame,in which two players receive an allocation determined by the computer and, on half of the trials, one player has the subsequent possibility to change this allocation. Importantly, prior to the receipt of the allocation, players were shown either their respective ﬁnancial situations, their respective performance on a previous simple task, or random information, while being scanned using functional neuroimaging. As expected, our results demonstrate when given the opportunity, participants allocated on average almost half the money to anonymous others. However, our ﬁndings further show that participants used the provided information in a dynamic manner, revealing the underlying principle based on which people re-allocate money e namely based on merit, need, or equality e switches dynamically. On the neural level, we identiﬁed activity in the right and left


Introduction
Imagine you are celebrating your birthday with friends and family, and the moment to cut the cake has arrived.How large should each piece be?You count the people in the room and mentally sketch how to cut the cake so that there is a slice for everyone.However, as you are making the first cut, you hear some say they do not want to have too large a piece, whereas others are quite hungry and so want at least two pieces.Moreover, since your best friend spends hours with you preparing the party, you want to give them the first and largest portion to show your appreciation for their help.But is it fair to give out unequal amounts?
While the decision here is obviously not exceptionally consequential, this dilemma does illustrate a core issue in social decision-making: How do we fairly allocate resources and burdens across individuals?A vibrant research tradition, rooted in game theory and behavioral economics, focuses on the perceived fairness of allocations.In contrast to the theoretical notion that humans are inherently selfish and therefore tend to maximize their own personal payoff, this literature shows that people value not only how many resources they receive themselves, but in addition also care about how allocations are distributed across all interaction partners (Fehr & Krajbich, 2013).The canonical tasks demonstrating these social preferences in the lab are the Dictator Game (Kahneman, Knetsch, & Thaler, 1986) and the Ultimatum Game (Gu ¨th, Schmittberger, & Schwarze, 1982).In these simple two-player games, the first player -Dictator or Proposer, respectively -makes an offer of how to split a pot of money (e.g., V10) between themselves and the second player -Receiver or Responder, respectively.In the Dictator Game, this allocation decision is final: if the Dictator decides to keep all V10 for themselves, there is no recourse for the Receiver.In the Ultimatum Game, the Receiver (known as Responder) gets to decide to either accept or reject the offer; importantly, rejecting an offer means that neither player gets anything.
Clearly, the distinction between the Ultimatum and Dictator Games is largely based on the agency of the second players.Due to the lack of agency for the Receiver in the Dictator Game, the giving behavior of the Dictator offers insight into individual preferences for fairness, as weighted against material self-interest.Inversely, in the Ultimatum Game the ability of the Responder to choose between the amount offered by the Proposer and nothing for both players enables researchers to garner insights into how individual perceptions of unfairness are weighted against material selfinterest from Responders' behavior.
Deviating from rational, self-interested accounts of human behavior, research has consistently found that Dictators give away a significant amount of the allocation -approximately 30% (Camerer, 2011).Responders in the Ultimatum Game, on the other hand, reject offers of 20% of the Endowment at roughly a 50% rate, with rejection rates increasing as offers decrease, even though doing so means they will get no money at all (reviewed in Camerer, 2003;Houser & McCabe, 2014).The dominant explanation for both patterns of behavior is inequity aversion (Fehr & Schmidt, 1999) which posits that people consider inequitable allocations unfair and, therefore, results in experienced disutility.An equitable allocation, unlike simply an equal distribution, is an allocation where the benefits match the contributions, that is, where the outputs are proportional to the inputs of the individuals (e.g., giving your friend a larger piece of cake because they helped you prepare the party).Apart from a concern for equity, people also take other information about others into account when making allocations.For example, Responders who believe themselves to be poorer than Proposers are more likely to reject low offers (Bratanova, Loughnan, Klein, Claassen, & Wood, 2016).Though need-based giving is much less studied, this pattern suggests that people may pay attention to the needs of others when making judgments about what is fair (for a review, see Nicklish & Paetzel, 2020).
A crucial, albeit somewhat implicit, aspect of this research line is that fairness norms concerning allocations are static (e.g., inequity aversion as a trait).However, a separate research tradition rooted in social justice proposes two distinct forms of fairness (with the terms justice and fairness being used interchangeably; Lind & Tyler, 1988; for metaanalyses, see Colquitt, Conlon, Wesson, Porter, & Ng, 2001; for a review see Tyler, 2015), namely distributive and procedural justice.Distributive justice refers to our perceptions of the allocations themselves as fair or unfair, and three characteristic principles underlie these perceptions.One is equity, that allocations match the individual contributions of players, a second is equality, that payouts are uniform across players, and a third is need, that allocations match what people need.Deutsch (1982) proposed that these principles promote different social goals: equity promotes economic productivity, equality promotes social harmony, and need promotes social welfare.
Procedural justice, on the other hand, can be roughly defined as the subjective evaluations of the justice of procedures used in determining how competing interests and claims will be resolved (Tyler, 2015), with many researchers arguing that these procedures are more important to perceptions of fairness than the distribution itself is (Thibaut & Walker, 1975;Sweeny & McFarlin, 1993;van den Bos, Lind, & Wilke, 2001;Krawczyk, 2011;Ambrose & Arnaud, 2013).These views are buttressed by studies that show that people regard interpersonal treatment and unfair procedures to be more predictive of unfair evaluations than the outcomes themselves (Huo, 2002;Messick, Bloom, Boldizar, & Samuelson, 1985;Mikula, Petri, & Tanzer, 1990).One reason for this 'primacy' of Procedural Justice is intuitive: in judging the fairness of a given allocation, perceptions of neutrality and impartiality in the process of determining who will benefit from an allocation is the more revealing piece of information about the fairness of a given allocation than the allocation itself.
This axiom entails that a specific allocation can be viewed as fair in one context and as unfair in another: this reality raises the question of how this flexibility is implemented on a computational level.One possibility is that people automatically evaluate the allocation itself (i.e., distributive justice), but then subsequently take the contextual information into account to assess overall fairness (which can be positive despite large allocation differences).An alternative is that the context directly changes the allocation evaluation.That is, in contexts where principles of equity are not relevant (e.g., after flipping a coin to decide who gets the whole cake), inequity is not necessarily evaluated per se.Instead, the fairness of the allocation is directly computed in a contextspecific manner.
Although these two scenarios are difficult to distinguish by behavioral responses alone, the neural activity related to inequity aversion can potentially be used to distinguish between them.Specifically, if the evaluation of allocations is automatic and performed independently of the situated context, one would expect to see activity related to inequityaversion in the same brain areas as is observed when it is the sole basis of the judgment.For example, in the Ultimatum Game, increased neural activity in the right dlPFC and bilateral anterior insulae (see Feng, Luo, & Krueger, 2015;Gabay, Radua, Kempton, & Mehta, 2014) is observed in responders who are given low offers even when playing on behalf of another person (Civai, Crescentini, Rustichini, & Rumiati, 2012).In other words, these regions responded directly to perceived unfairness.Similarly, Hsu, Anen, and Quartz (2008) found that insula activity correlated with trial-by-trial inequity when deciding between different allocations of food for other people.
However, if fairness evaluations are at their core contextdependent, inequity-related activity should not be observed in these brain areas when the distributional context allows for unequal, but fair, allocations.This would comport with earlier work which has shown that value is derived from prosocial behavior and rule-following (Moll et al., 2005(Moll et al., , 2006) ) and that the value derived from different kinds of behaviors results in different neural representations of value which are integrated in the vmPFC and OFC (Bartra, McGuire, & Kable, 2013;Levy & Glimcher, 2012;Ruff & Fehr, 2014) Then, areas such as the temporoparietal junction, a crucial hub for perspective taking which has been observed in both distributive justice decisions (e.g., Gu ¨ro glu, van den Bos, van Dijk, Rombouts, & Crone, 2011) and procedural fairness judgments (Niemi et al., 2018) might be involved in the evaluation of a particular allocation as either fair or unfair in a context-specific manner.
In the present study, we sought to investigate if different kinds of incidental information could influence the preference for equality-versus-equity-versus-need that is, whether allocation amounts and fairness preferences differed as a result of differing contexts.To this end, we employed the novel Reallocation Task in which participants were first shown a computer-generated allocation between themselves and another, anonymous, game partner.In roughly half of the trials, participants could freely adjust the computer-generated allocation, functionally reallocating money between themselves and their partners.Crucially, on each interaction, participants were provided with extra information.This took the form of financial information about themselves and their partner, performance information about themselves and their partner, or a random pair of numbers for themselves and their partner.We hypothesized that participants' preference for equity versus equality versus need would differ depending on what kind of information they were provided, as well as their own score relative to their partner's e the random number would have no bearing on reallocation decisions, while the difference in finance scores between the participant and their partner would be positively associated with giving scores while the inverse would be true of performance scores.Thus, our behavioral results can shed light on the interdependence of distributive justice and procedural justice in the context of interpersonal decision-making.Additionally, maintaining a consistent trial structure allowed us to identify neural mechanisms underlying the evaluation of a given allocation as fair or unfair, given the procedural context in which it is encountered.We hypothesized that the right dlPFC and anterior insula would encode inequity in the allocation generated by the computer.Meanwhile, we expected that deviations in computer generated allocations from the principle of equality in the random condition, the principle of equity in the performance condition, and the principle of need in the finances condition would be encoded in the temporoparietal junction.

Methods
We report how we determined our sample size, all data exclusions, all inclusion/exclusion criteria, whether inclusion/ exclusion criteria were established prior to data analysis, all manipulations, and all measures in the study.No part of the study procedures or analysis plans was preregistered prior to the research being conducted.

Subjects
Thirty-eight participants (mean age ¼ 22.9, female ¼ 63.2%) were recruited via the SONA system at the Radboud University Nijmegen.The study protocol was approved by the local ethics committee (CMO region Arnhem-Nijmegen, The Netherlands) under general ethical approval (CMO 2014/288), and all experimental methods were conducted in accordance with these guidelines.Participants were financially compensated via a flat fee (V30 on weekdays and V36 on weekend days, as per local guidelines) to complete the task.In addition, they also were paid out the mean of three randomly selected rounds of the task based on their actual decisions.Exclusion criteria were self-reported claustrophobia, neurological or cardiovascular diseases, psychiatric disorders, or the presence of metal parts in the body.

Task and procedure
Participants performed three tasks.The first two tasks were used to generate a "financial score", reflecting their actual financial status, and a "performance score", reflecting how well they performed on a simple cognitive task, respectively.These scores were then used in the subsequent task of interest in the MRI session, where participants made monetary allocations, splitting a pot of money between themselves and other people who also purportedly had completed those same tasks.Importantly, the only information participants had about the other person on a given round was either one of these two aforementioned scores or a third "random score", reflecting a number purportedly generated randomly by a computer.
To create a score that participants believed reflected how well off they are, they first filled out a questionnaire about their financial situation (adapted from Conger, Ge, Elder Jr, Lorenz, & Simons, 1994).This included questions about their current job situation, their income, and whether the money available to them is sufficient to cover their monthly expenses or whether they needed to make cutbacks, especially focusing on whether any of these aspects worsened recently.After completing this questionnaire, participants were given a score which was purportedly calculated based on their responses and reflected their overall financial situation (the larger the number, the better this situation was).All participants were in fact shown the same score to avoid any between-subject anchoring effects.To increase the salience of this number and its meaning, participants were asked to write down this number on a personal "score sheet".
To create the "performance score", participants completed a simple card-sorting task on the computer.A standard deck of 52 cards was randomly positioned on a large square on the screen.Participants were asked to sort the cards into four groups based on the card suit (ignoring the rank of the cards) by dragging the cards to the respective decks on the left side of the screen.They had to perform this as quickly as possible.After all of the cards were correctly sorted, a pop-up message informed participants about their time and displayed a score: the faster the task was completed, the higher the score.Again, they were asked to write this score down on the aforementioned score sheet to increase the salience of this number.Participants performed this task three times and their best score was used in the subsequent task in the scanner.
Next, participants performed the task of interest, the Re-Allocation Game, while in the MRI scanner (Fig. 1).On each round of the task, participants were paired with a randomly selected new partner who had purportedly filled out the same financial questionnaire and performed the card-sorting task.Participants were told that since prior research indicates that people want to know this kind of information, on each round they would see one score of their partner.These scores were based on either the financial questionnaire ("finance" condition), the card sorting task ("performance" condition), or a randomly generated number ("random" condition).Within a trial, participants were first shown their own score as well as the score of their partner on that trial.Participants were informed that although their actual score would be entered into the task program, in order to make it simpler for them to compare their score with their respective partners' scores, their own score would be always displayed as "500" and the partners' scores would be shifted accordingly.From a taskdesign perspective, this allowed us to keep the stimuli consistent across the three conditions.The actual partner scores were drawn from three distinct distributions: scores between 200 and 300, between 500 and 600, and between 800 and 900.Therefore, there were three levels of score comparison: either the two scores were roughly equal ("equal score"; note that the partner's score was always slightly higher, e.g., 500 for the participant versus 532 for the partner), the participant scored approximately 300 points lower than the partner ("lower score") or the participant scored approximately 300 points higher ("higher score") than the partner.To ensure the scores and their meaning were as salient as possible, we employed a mini-block design, with nine consecutive trials presented of the same condition.At the beginning of each mini-block, a screen indicated the description of the upcoming scores, either "finance", "performance", or "random".In addition, in each condition an image was displayed in the upper left corner throughout the mini-block as a reminder of the current condition (see Fig. 1).
Participants were scanned in three runs, separated by short breaks, to avoid fatigue and to allow out-of-sample testing for the multivariate pattern analysis (see below).At the beginning of each run, participants saw their actual scores from the two tasks entered into the task program by the experimenter, to further increase the believability and relevance of the scores.
During a single round, participants first were shown the respective scores of themselves and their trial partner, along with the score condition.Next, one of five splits of V10 was randomly selected (either V1, V3, V5, V7, or V9 given to the participant, with the remainder given to the partner) and displayed to the participant ("allocation" screen).On half of the rounds, this computer-generated default allocation would also be the final allocation for that round; on the other half of the trials, participants would then have the opportunity to change this allocation on an additional "reallocation" screen.Importantly, prior to this screen being shown, there was no indication of whether participants would get an opportunity to change the default allocation on the current round or not.
On the reallocation screen, two rows of payouts were displayed, one for themselves and one for their partner, with the payout indicators on each row set to the computer-generated default allocation shown on the previous screen.Participants could move their own square left or right to decrease or increase their own payoff respectively (the partner's square would move accordingly in the opposite direction to ensure a total amount of V10) and then they confirmed their final choice with a button press.They could also simply confirm the existing pre-allocation if they desired.After 4 s, the next trial would start without explicit confirmation -their response being taken to be the final selection in either case.
After finishing the allocation tasks, participants were debriefed and three rounds for the bonus payment were randomly selected and paid out.

Behavioral data analysis
The behavioral analyses focused on the reallocation choices of participants.We used a linear mixed model to estimate the population-level effects of the score, the score conditions, and the computer-generated default allocations.Specifically, the reallocation choice on each round was modeled using a linear mixed model with the participant as the grouping factor.This model included the 3 (finance/performance/random context) x 3 (lower/equal/higher scores) x 5 (V1/V3/V5/V7/V9 default allocation) design, an intercept, and all the interactions as fixed effects.All categorical variables were coded using effects coding, i.e., as the deviation from the grand mean.To get the maximal power possible without increasing the false positive error rate, we employed the procedure proposed by

Neuroimaging data acquisition and preprocessing
Magnetic resonance imaging data were collected at the Donders Centre for Cognitive Neuroimaging, Nijmegen, The Netherlands, using a 3-T head-dedicated MRI system (Skyra; Siemens Medical Systems).Functional MRI (fMRI) images were acquired using a 32-channel head coil, with a standard multi-echo imaging pulse T2*-weighted sequence (field-ofview: 224 mm using a 64 Â 64 matrix; TR ¼ 2250 ms; echo times (TE): 9.4 ms, 20.65 ms, 31.9 ms, 43.15 ms; flip angle 90 ).Using a multi-echo sequence provides a better signal-to-noise ratio for brain areas susceptible to dropout, while allowing for scanning of the whole brain.Thirty-five ascending slices were acquired (thickness of 3.0 mm; voxel size 3.5 Â 3.5 Â .3.0 mm with a .5 mm slice gap) from the whole brain.A highresolution anatomical T1-weighted image (MPRAGE; 192 slices; TR ¼ 2300 ms, voxel size 1 Â 1x1mm) was acquired for Then, the scores for the participant and the other player would be revealed ("score" screen).Next, participants were shown a computer-generated, default allocation ("allocation" screen).On half the trials, participants were then given the opportunity to change the allocation as they saw fit ("choice" screen").
anatomical localization and structural normalization.Participants' heads were lightly restrained with tape, which was loosely placed on their head and the scanner coil in order to limit movement during image acquisition.The task consisted of three runs, between which participants remained in the scanner.
We combined the four read-outs acquired via the multiecho sequence by calculating the mean image.Further preprocessing was performed using SPM12 and consisted of slicetiming to the middle slice, realignment of functional images, and co-registration to the anatomical images.The structural image was segmented and normalized to the Montreal Neurological Institute (MNI) template.The resulting deformation fields were used to normalize the functional images, which were then smoothed with a Gaussian kernel of 8 mm full-width at half maximum (FWHM) for the univariate analyses, but kept unsmoothed for the multivariate pattern analyses.
Finally, we identified volumes with excessive movement by calculating the volume-by-volume changes in translation and rotation based on the realignment parameters.We defined a framewise translation above .75mm and a framewise rotation above 1.5 as excessive movement.This resulted in 4.99 volumes being flagged on average (see Appendix A for the complete distribution).

Neuroimaging data analysis
On a neural level, we focused on the phase in the trial when participants knew both their own and their partner's scores (as well as the relevant condition), and also the default allocation generated by the computer, but did not yet know whether they could change this allocation (i.e., the "allocation" screens, see Fig. 1).We employed two complementary analysis strategies.First, using a univariate approach, we modeled the mismatch between what the computergenerated default allocation was and what it should be, according to the respective scores on that trial if participants followed either a simple inequity-aversion model or if they assessed these allocations in light of context-specific fairness norms (see details below).This analysis enables us to directly compare our results to previous studies that typically employed only these univariate analyses.However, multivariate pattern analysis (MVPA) approaches can uncover additional, and potentially distinct, neural activity (Davis et al., 2014;Kahnt, 2018).Thus, to more comprehensively address the question as to what extent the observed neural computations are related to inequity aversion versus a context-specific fairness norm (and avoid false negatives as much as possible), we also used a somewhat uncommon MVPA approach, namely a searchlight multivariate pattern regression analysis (see Haynes, 2015 for a comparison of different MPVA approaches).Unlike more common classifier approaches which identify neural patterns predictive of categorically different stimuli (e.g., objects vs places), a regression approach allows the estimation of a relationship between a continuous variable and the neural pattern in a searchlight volume e in direct analogy to a parametric modulator in univariate analyses.Using this approach, we sought to identify brain regions related to the actual fairness evaluations participants performed (on the allocation screen), as revealed by the deviation from each participant's subjectively preferred allocation (i.e., their actual behavioral choices on the subsequent "reallocation" screens).

Univariate analyses
The goals of the univariate neuroimaging analyses were to identify brain areas related to two distinct processes, namely 1) the processing of inequity, independent of any contextual information, and 2) brain areas processing a mismatch between the condition scores (finance, performance, random) and the allocations generated by the computer, that is, context-specific unfairness.
To this end, two first-level GLMs were constructed which differed only in the parametric modulators used.The first model assessed the mismatch between the computergenerated default allocations and the fairness norms of the scores, given the specific meaning of the latter.For financial scores, the person with a higher score (i.e., the financially better off one) should get less money than the person with the lower score; for performance scores, the person with a higher score (i.e., the one who had a better performance) should get more money; for the random scores, as well as for financial and performance scores that are equal, both players should get half of the total pot.So, for a given default allocation of, for example, V5/V5, this could be either a fair allocation (when random or equal scores were displayed), or an unfair allocation (e.g., when finance or performance scores differed substantially -see Table 1).Similarly, a V9/V1 allocation would be mostly unfair (value of 2 or 3), except when it matched either an unequal performance or an unequal financial need between the two players.
The second model identified brain activity related to "pure" inequity-aversion by specifying the absolute difference of allocations for the participant and the partner as a parametric modulator at the allocations screen (see Table 2).
Both of the first-level GLMs included predictors for the condition-indication screen, three predictors for the score screen (one per condition), and three for the allocation screen (one per condition) e the parametric modulators were also split into three parts, one per condition e and one for the choice screen.In addition, we included six movement parameters (estimated during the realignment) and dummycoded indicator variables for volumes when participants showed large movements as nuisance regressors.To assess the mean inequity and mismatch activity, contrasts averaging across the three condition-specific predictors were constructed on the first level, and one-sample t-tests were performed on the group level.All univariate analyses were conducted with SPM12 (Wellcome Trust Centre for Neuroimaging, London, UK).

Multivariate analyses
Next, we focused on identifying areas related to the actual, subjective, evaluations of the proposed allocations participants performed (on the allocation screen).We chose a searchlight approach where we performed a multivariate pattern regression examining fair allocations (as measured c o r t e x 1 7 7 ( 2 0 2 4 ) 5 3 e6 7 by the signed deviation between the default allocation and the subsequent reallocation choices).Note that, in principle, these deviations from the subjective preferences could also have been used in a univariate approach as parametric modulators; however, using multivariate pattern regressions on a subject level is expected to have more statistical power, as it discards between-subject variability in mean activations (Davis, et al., 2014) which might be especially important when subjective notions of what is fair differ between individuals.Specifically, we first calculated the individual preferred allocation for each participant by computing the mean final reallocation they chose for each trial type after they had the opportunity to reallocate the amounts (i.e., each cell in Tables 1  and 2).Note that two participants always took V10 for themselves; these participants were removed from this analysis.
Next, we calculated a first-level GLM for each trial (270 in total), by including one regressor for the trial of interest and a second regressor consisting of all other trials (Mumford, Turner, Ashby, & Poldrack, 2012), also using the same nuisance regressors as outlined for the above univariate analyses.We used the ensuing trial-specific beta-maps as input for the multivariate pattern analysis.Using a searchlight approach (radius of 3 voxels), we aimed to identify areas that are reliably related to the degree of the unfairness of the computer-generated allocation.Specifically, for each searchlight, we calculated a regression where the trial-specific betas within the searchlight were the independent variables (regressors) and the deviation from the preferred allocation on each trial was the dependent variable.We estimated the regression coefficients on two out of three runs and checked the correlation between the predicted values and true values in the third run (i.e., a leave-one-out cross-validation approach with three runs, and then calculated the average) for each participant.The group-level analysis consisted of a onesided t-test of the Fisher-transformed correlation coefficient maps.To account for multiple comparisons, we used the Threshold-Free Cluster Enhancement cluster-level correction method (Smith and Nichols, 2009), as implemented in the CosMoMVPA package.All multivariate analyses were conducted using CoSMoMVPA (Oosterhof, Connolly, & Haxby, 2016).

Allocation decisions
On average, participants allocated V4.17 of the V10 pot to their partner, as measured by examining the reallocation choices that occurred on approximately half of the trials.Importantly, participants varied in how much they gave as a function of the Table 1 e Score-Mismatch parametric modulator values coding for how unfair the computer-generated default allocation for participants ("you") and the partner ("other") on each trial were.Note: "Score of Other" refers to the relative relationship of the participant's score to the score of the other player on a given trial.

Score condition
Table 2 e Inequity-aversion parametric modulator values coding for how inequitable the computer-generated default allocation for participants ("you") and the partner ("other") on each trial were.Note: "Score of Other" refers to the relative relationship of the participant's score to the score of the other player on a given trial.scores and their meaning (interaction effect of score by context: c 2 (4) ¼ 67.17, p < .0001;see Fig. 2).Specifically, participants gave more to a partner both when the partner scored higher on the card-sorting task (i.e., performed better; V5.49) or when the partner scored lower on the financial questionnaire (i.e., had a higher financial need; V5.82).Conversely, participants gave less when the partner scored lower on the performance score (i.e., when the partner performed worse; V2.83) or higher on the financial score (i.e., when the partner was better off financially; V2.69).Post-hoc pairwise comparisons revealed that neither the two "giving" nor the two "keeping" behaviors differed significantly from each other (both ps > .13).However, participants gave away more money in the performance context (V4.41) than in the financial context (V4.07) when the scores were roughly equal (difference ¼ V0.34, p ¼ .005).

Score condition
When the scores were randomly generated, participants gave away roughly half of the money to the partner, but anchored their allocation slightly by the scores themselves, such that when the other player had a higher random score the participants gave them more money (lower vs equal score: difference ¼ V0.46, p ¼ .0088;equal vs higher score: difference ¼ V0.44, p ¼ .029),albeit this effect was substantially smaller than the differences in the other two conditions.
We also observed an anchoring effect as a function of the computer-generated default allocation, such that participants kept more money for themselves when the computergenerated default allocation was in their favor (main effect of default allocation: c 2 (4) ¼ 41.63, p < .0001;e.g., default allocation to participants V1 vs V5: difference ¼ V0.25, p ¼ .014;V5 vs V9: difference ¼ V0.33; p ¼ .003); the exception to this was in the low-performance score condition where they gave the same for all default allocations (three-way interaction of default allocation by scores by condition c 2 (16) ¼ 38.91, p ¼ .001).
In sum, on average participants allocated money according to financial and performance information when it was provided, with small biases in their favor related to the default allocation.When only random scores were given, that is, in the absence of any relevant information about their partner, they gave almost half of the money to the partner (though this was not required), with again a small anchoring effect of both the computer-generated default allocation and the random scores.

Univariate activity
On the neural level, we aimed to identify brain areas associated with the degree of unfairness of the computer-generated default allocation.A fair allocation was defined here based on a fairness norm which takes the available context information into account: more money given for better performance (merit-based fairness) and for the financially worse off (need-based fairness), and equal allocation when no information is available about their partner (equality-based Fig. 2 e Individual differences in subjectively preferred allocations.Participants' average reallocation to themselves is plotted as points over the group means in each condition, connected across conditions for each participant.Across all conditions, participants gave more to those who performed better, were ascribed higher random numbers, and who had lower financial scores and less to those who performed worse, were ascribed lower random number numbers, and had higher financial scores.Most participants followed this trend but some deviated e it appears that this trend was followed most closely in the performance condition and least closely in the random condition.fairness).After correction for multiple-comparisons, neural activity in the left dlPFC (p ¼ .015), in the left angular gyrus (p ¼ .001FWE cluster level) and left precuneus (p < .001),significantly corresponded to this context-specific unfairnessrelated activity in a parametric manner (see Fig. 3 and Table 3).
We compared this activity with the activity related to processing the inequity of the computer-generated default allocations.An equitable allocation is one where the allocation (outputs) is proportional to the contributions (inputs) made by the players.Note that since neither player contributed to the creation of the money (no inputs), an equitable allocation would be one where both get half of the pot (equal output) independent of the condition.We found clusters of activation in the precuneus (p < .001)and angular gyrus (p ¼ .020)that positively correlated with the difference between allocations to the participant and the partner (see Fig. 4 and Table 3).However, the activity in the precuneus extended more dorsally for the fairness-related than the inequity-related parametric regressor.In addition, the right dlPFC correlated strongly with the inequity of the allocation (p ¼ .005).Even at a lower statistical threshold (p < .05uncorrected at cluster level), we observed no inequity-related activity in the left dlPFC (see Fig. 5).Instead, there was a small cluster in the right dlPFC related to the context-specific unfairness at this weaker statistical threshold.Notably, we did not find any inequity related activity in the anterior insula, even at this liberal statistical threshold.We also checked for pairwise differences between the conditions-specific parametric modulators, but no differences survived multiple comparison correction.
In order to reveal the extent to which the parametric modulation attributed either Inequity or Mismatch was uniquely caused by either variable, we estimated a new GLM.In this GLM, Inequity and Mismatch were both included as parametric modulators of the Allocation screen and there were no differentiations between conditions on any screens.In this model where orthogonalization was turned off, we found that Inequity was associated with significant activation in the right dlPFC (MNI ¼ [36,24,28]

Multivariate activity
In addition to the aforementioned pattern of responses, we also observed systematic individual differences in how participants chose to reallocate the money (see Fig. 2).For example, one participant allocated money using a combination of the merit norm (giving more money to the other player when they had performed better) and the equality norm (giving roughly half the money otherwise).However, this particular participant largely ignored the financial scores.In contrast, another participant allocated money also utilizing the financial information.To account for these individual differences, we also sought to more exhaustively identify brain activity related to the actual evaluations of the proposed allocation participants performed, as revealed by their subsequent reallocation choices.Specifically, we identified brain areas whose patterns of activity across multiple voxels are related to deviations from the subject's preferred allocation amount.To this end, we conducted a search-light analysis which revealed that the left putamen (peak: t (35) ¼ 4.92; p ¼ .0001), the adjacent left anterior insula (peak: t (35) ¼ 3.14; p ¼ .0017),and the left precuneus (peak: t (35) ¼ 4.47; p ¼ .0004)exhibited activity patterns that correlated with the unfairness of the allocation, where unfairness was quantified by the Table 3 e Univariate results: Activity related to the (a priori) unfairness and inequity of a default allocation, as quantified by the parametric modulators (see Tables 1 and 2).Coordinates and z-score correspond to the peak of the cluster.difference between the subjectively chosen reallocation and the computer-generated default allocation (see Fig. 6).

Mixed effects modeling
In order to assess if the amplitude of BOLD responses to the mismatch variable could predict individual differences in reallocation behavior, we estimated the linear mixed effects model wherein we predicted the change in reallocation, or the difference between the final payout and the initial allocation.Since this value was signed, we included main effects for inequity and mismatch which were also signed.We also included the interaction between inequity and the normalized mean betas for the Inequity parametric modulator in the right dlPFC as well as the interaction between mismatch and the normalized mean betas for the mismatch parametric modulator in the left dlPFC.These betas were extracted on a condition-by-condition basis, and were extracted from spherical ROIs centered at [À20, 32, 38] for the left dlPFC and [29,38,32] in the right dlPFC, each with radii of 10 mm.A random intercept, as well as the random slopes of Inequity and mismatch were also included in the model.Outliers for the left dlPFC and right dlPFC interactions were excluded.
Including the left dlPFC and right dlPFC interactions in the model led to a small increase in model performance (BIC ¼ 6363.656)compared to a purely behavioral version of this model (BIC ¼ 6514.662).This more complex model (Marginal R 2 ¼ .582,Conditional R 2 ¼ .811),reported in Table 4, revealed that the interaction between the left dlPFC and Mismatch was found to predict the difference between Final Payout and Initial Allocation, though the interaction between the right dlPFC and Inequity was not.Thus, interindividual and condition-level differences in the encoding of score mismatch by the left dlPFC activation predicted reallocation which reduced this mismatch.This finding is particularly striking when considering that the association between these two interaction terms was strongly positive (r ¼ .65).
In order to assess whether or not a single condition was driving the parametric activity of the left dlPFC with respect to mismatch or the right dlPFC with respect to inequity, we compared these average modulatory effects across conditions.Uncorrected paired t-tests comparing each conditioncomparison (3 per ROI) and for both ROIs confirmed this interpretation e the largest difference of these 6 tests was highly insignificant (t (37) ¼ .340,p ¼ .736)and had a very small effect (d ¼ .055).6.

Discussion
In this study, we investigated the psychological and neural processes underlying three different possible fairness principles: allocations based on merit, allocations based on need, and allocations based on equality.Our novel task enabled us to examine decisions based on all three allocation principles in a within-subject design by providing participants with specific information about the other player.The primary question of interest was whether participants utilized flexible norms of fairness depending on the type of information they were provided about their game partner, or whether the allocation decisions were static and context-invariant.
Behaviorally, we found that participants gave away, on average, almost half of the money to the other player, despite there being no incentive, or threat of sanction, to do so.This largely replicates typical general patterns of behavior in Dictator Games.On reallocation trials, participants could always have reduced the amount of money to be given to their (anonymous) partner to zero, but did not do so; similarly, on trials where the computer-generated allocation was in their favor, they could have remained inactive, and simply accept the advantageous payoff, but again did not do so (but see discussion below on the small anchoring effect).Together, this provides strong evidence against the notion of people as self-interested, homo economicus.Instead, our results demonstrate that people have clear social preferences e they value fairness.
Importantly, and disproving the notion of contextinvariant fairness, our results show that contextual information is indeed taken into account when deciding on a reallocation of the monetary allotments.Specifically, when no information was available about the other players (random condition), participants (re)allocated almost half of the money to their partner, suggesting that a social norm of equality may form a 'baseline' for fairness in the absence of any other information.However, when contextual information on the other player was provided participants used this information even though it was, strictly speaking, unrelated to the decision situation itself.Specifically, in the financial condition, the only information participants had about the other player was how their respective financial situations compared.When participants were worse off financially than their partners, they chose to keep more money for themselves; conversely, when participants were better off than their fellow players, they gave more money to the otherwise unknown players.This demonstrates a needs-based allocation principle when relevant information for such a decision was available.In the performance condition, participants knew only how well they had performed, in comparison to the other player, on a simple card-sorting task just prior to the scanning session.In this case, participants allocated more money to whoever had a better task performance, demonstrating adherence to a meritbased allocation principle.Importantly, it does not necessarily have to be true that participants view high performers as inherently more "deserving": they simply used the information available to them and applied a merit principle to guide their reallocation decisions.Of course, this pattern of behavior could also be due to participants' attempts to confirm our hypotheses e however in their responses to posteexperiment questionnaires, participants refer to the thoughts, feelings, and expectations of their partners when articulating their game strategy.Thus, these results clearly show that people enact different procedures about fairness in a context-specific manner, based on the available information in the given situation.
Although previous research has shown that people consider both need (e.g., Tricomi, Rangel, Camerer, & O'Doherty, 2010) and merit (e.g., Feng, et al., 2016) when deciding on allocations, our results extend these findings in important ways by showing that average behavior shifts predictably from one fairness norm to another depending on what information they have available in a given situation.This context-sensitive view of fairness raises interesting theoretical questions.For example, are individual differences in fairness-related behavior due to differential attention to contextual information in a given situation, instead of to stable traits?Likewise, debates on whether people base their judgments on utilitarian or deontological fairness principles could consider which aspects participants focus on in a given experiment.Indeed, the observation that people encode both efficiency (a key variable of utilitarian fairness) and equity (an example of deontological fairness; Hsu et al., 2008) suggests concurrent processing of multiple social norms (van Baar, et al., 2019).
The ability to dynamically switch between different fairness principles (like merit, need, and equality) raises the question of how the brain incorporates contextual information into a single coherent fairness judgment.To assess this, we focused our fMRI analyses on the timepoint when participants already had the relevant contextual information and were shown the default allocation, thus being able to form a judgment as to whether this allocation was fair or Table 4 e Mixed Effects Results: Inequity and mismatch were both signed in order to make specific predictions of participants' Reallocation decisions.Parametric activity in the left dlPFC and right dlPFC ROIs attributed to mismatch and inequity respectively (Table 3) was multiplied by these signed effects.Positive values indicate that reallocation benefits the participant while negative values connote that reallocation benefits the other player.unfair.We examined neural activity related to three distinct forms of fairness evaluations: first, context-independent inequity-aversion (inequity); second, context-specific deviation from a fair allocation (unfairness), i.e., one which took into account performance and financial information in an a priori defined manner; and third, the deviation from the subjective notion of a fair allocation.We found inequityrelated activity strongly lateralized to the right dlPFC, with unfairness-related activity in the left dlPFC (and also a smaller cluster in the right dlPFC, at a lower statistical threshold).Relatedly, our data shows that the parametric modulation of inequity on BOLD activity in the right dlPFC did not explain any individual differences in behavior in the task, while the parametric modulation of mismatch on the left dlPFC did.Interestingly, when controlling for the main effects of inequity and mismatch on change in participants' payouts, we find that a stronger parametric response to mismatch in the left dlPFC predicts participants giving more to their partner e regardless of whether this mismatch was advantageous or disadvantageous.Specifically, stronger encoding of mismatch in the left dlPFC predicted stronger behavioral effects for undoing the computer's unfair allocation.A similar lateralization effect has been observed in previous studies related to social norms.For example in the Ultimatum Game, rejecting an unfair offer is associated more with the right dlPFC (Sanfey, Rilling, Aronson, Nystrom, & Cohen, 2003; for a meta-analysis, see Feng, et al., 2015or Gabay, et al., 2014).In addition, interfering with the right, but not left, dlPFC using transcranial magnetic stimulation increased the number of accepted unfair offers (Knoch, Pascual-Leone, Meyer, Treyer, & Fehr, 2006), demonstrating that this lateralization effect is causally relevant to fairnessrelated decisions.Importantly, our data show that people switch between distributive principles depending on available contextual information, but it was not optimized to study the neural mechanisms underlying this rule-switching in the current design due to too few condition switches.Future studies might adapt our Reallocation Task by switching conditions more frequently and thus shed light on how strategies are selected in the brain based on the contextual information which is available.Additionally, such studies may also investigate how people select strategies when there are different types of contextual information available: for instance both a performance and finance score.

Effect
In contrast to the Ultimatum Game studies, the behaviorally more relevant contextual information, that is, how much the default allocation deviated from a fair allocation based on the respective scores, was more strongly encoded in the left dlPFC in the present study.Note that in standard Ultimatum Game studies, inequity is not distinguishable from the unfairness of the offer (as the expectations of what kind of offers will be encountered are usually not manipulated, see Vavra, Chang, & Sanfey, 2018 for detailed discussions).An unexpected possibility raised by the current results is that inequity of a certain allocation is encoded by the right dlPFC independent of whether this information is relevant to one's behavior or not, while the left dlPFC processes additional information (i.e., how unfair or fair an allocation is in the current context) when this information deviates from the equity-related information.The right dlPFC tracking social information independent of whether it will be acted on would potentially also be in line with decreased theory-of-mind abilities in patients with the right, but not left, dlPFC lesions (Cristofori, Cohen-Zimerman, & Grafman, 2019).A fruitful avenue for future work would be to further investigate the causal role of this lateralization in tasks that make distinct contextual information to participants, such as the task presented here.
In addition to this prefrontal activity, we observed activity in the angular gyrus and precuneus related to both inequity and context-specific unfairness, albeit these clusters overlapped only partially and to a different extent in the two regions.The angular gyrus, as part of the temporoparietal junction (TPJ), has been consistently activated by social context (Carter & Huettel, 2013).The TPJ has been involved in a range of processes, for example memory (Wagner, Shannon, Kahn, & Buckner, 2005), attention (Corbetta & Shulman, 2002), language (Binder, Desai, Graves, & Conant, 2009), and social cognition (Saxe & Kanwisher, 2003), and thus its overall function remains under debate.However, an emerging proposal is that the TPJ acts as a hub where distinct processes converge (as the aforementioned processes involve only partially overlapping parts of the TPJ) to create a representation of the social context and thus alter downstream processing and behavior (Carter & Huettel, 2013).In the present study, we identified neural activity in the angular gyrus related to both the inequity and the unfairness of the default allocation.Given that these independent factors had a large neural overlap, one intriguing possibility is that the angular gyrus encodes the default allocation from the perspective of the other player (i.e., theory-of-mind processing), where both the overall (in)equity and context-specific fairness are considered, thus representing the overall current social context.In a similar vein, the left TPJ was found to be more active the more self-serving motivations were detectable in protagonists' reciprocal behavior in a study using scenario vignettes (Niemi et al., 2018).In general, these findings are in line with meta-analytic results which showed that this part of the inferior angular gyrus is most strongly related to the social context (Carter & Huettel, 2013).
In the precuneus, we observed two somewhat distinct spatial patterns: the unfairness-related (and thus contextspecific) activity was confined to the ventral part, while the inequity-related activity extends more dorsally and was overall more widespread.The precuneus has been shown to be involved in self-processing, visuospatial imagery, and episodic memory (for a review, see Cavanna & Trimble, 2006).This broad range of involvement is in line with its anatomical connections: the precuneus does not have any direct input from primary sensory cortices, making it a higher-order association cortex.Intriguingly, its strongest anatomical connections outside the adjacent areas of the parietal lobe are cortically direct to the dlPFC and subcortically to the putamen (and caudate), both regions which were strongly activated in relation to the unfairness of the computer-generated default allocation.In addition, the precuneus and the putamen showed a clear multivariate c o r t e x 1 7 7 ( 2 0 2 4 ) 5 3 e6 7 pattern of activity related to how different the default allocation was to participants' preferred division, as revealed by their subsequent reallocation choices (i.e., subjective notion of fairness).Given the extensive role of the precuneus in episodic memory, it is possible that the activity in the present study, together with the dlPFC activity, represents a working-memory signal, signaling how unfair the default allocation is on the current trial.Such a signal is necessary, as participants were given the opportunity to change the computer-generated default allocations on half the trials.However, to do this, they would need to know how unfair the allocation actually had been on any given trial, that is, to remember the context.Indeed, the dlPFC has been identified as a crucial hub for working memory (for a review D' Esposito, 2007) and cognitive control, in conjunction with the putamen (e.g., Robertson, Hiebert, Seergobin, Owen, & MacDonald, 2015).One possibility is therefore that the precuneus and dlPFC retain the information on the current trial, while the putamen represents the aspects of this information that can be used for reallocation on the choice screen, i.e., that which is more directly related to the subsequent decision output.
Unexpectedly, and in contrast to decision-making in the Ultimatum Game and similar tasks, we did not observe any activity-related inequity aversion or the deviation from the a priori defined context-specific fairness in the anterior insula (even at a liberal statistical threshold) which has been hypothesized to be monitoring (un)fairness (see Vavra, van Baar, & Sanfey, 2017, pp. 9e31 for a review).One potential reason for this is that the source of the default allocation is the computer and not another person.In a similar manner, in Ultimatum Game studies the insula is less strongly activated by offers by a computer (e.g., Sanfey, et al., 2003).However, our multivariate analysis, which took the individual differences in preferred allocations (i.e., the subjectively fair allocations) into account, revealed a multivariate pattern in the left insula related to the differences between the computer-generated and subject-preferred allocation.In line with previous results in the Ultimatum Game (Chang & Sanfey, 2013;Xiang, Lohrenz, & Montague, 2013) where the behaviorally relevant deviation from the mean expected offer correlated with the activity in the insula, this suggests that only subjectively relevant deviations from a fair allocation are represented in the anterior insula.
Although not the focus of the present work, deviations from the overall pattern of behavior elicited by the three different fairness principles revealed that participants had small but reliable biases.Specifically, we observed an anchoring effect as a function of the default allocation, such that when the computer-generated default allocation was high, participants allocated slightly more money to themselves than on trials where the default allocation was low.This is in line with the classic anchoring-and-adjustment heuristic as described by Tversky and Kahneman (1974), with the default allocation playing the role of a reference point.However, as participants adjusted the allocations more in their favor than towards the other player, this reveals that this bias is somewhat self-serving.We also observed a similar effect with the random scores: when the random, meaningless, score was lower for the other player than themselves, participants gave them less money, while when the scores were higher, they gave the other player more money.Importantly, this bias might be more in line with a confirmatory-hypothesis-testing account of the anchoring effect (e.g., Chapman & Johnson, 1999; for a discussion of possible distinct mechanisms underlying the anchoring effect, see Furnham & Boo, 2011) than a pure anchor-and-adjust account, because of the underlying asymmetry of the actual inputs required by the participant: when reallocating money, pressing the left button moved the amount for to the participant to the left (while the selection for the other moved in the opposite direction).This means that the default allocation functioned as a reference point, in that when it was high, participants pressed less often to decrease the allocation to themselves.In contrast, when the score of the other player was lower (participants' scores were always 500), participants pressed more often to increase their amount.An interesting avenue for future research is to use this asymmetry to investigate how different anchoring processes interact.
In conclusion, the present study investigated the psychological and neural processes underlying the evaluation of, and decisions about, monetary allocations based on different principles of fairness.We demonstrated that people use the available information to enact context-specific procedures based on merit, need, and equality e even at a personal financial cost e using brain regions consisting of nodes from the networks associated with cognitive control and theory of mind.Herein, we found an interesting lateralization in the dlPFC: the right dlPFC was found to encode inequity while the left dlPFC was found to encode unfairness.

Open Practices
The study in this article has earned Open Data and Open Materials badges for transparent practices.The data and materials preregistered studies are available at: https://data.ru.nl/collections/di/dccn/DSC_3014018.14_101/2.
, Vasishth, Baayen, andBates (2017) to obtain the maximal random-effects structure supported by the data.For the present dataset, this model-comparison procedure resulted in a random effects structure containing fifteen random slopes and a random intercept, and ten correlations between five of those random slopes and the random intercept.All models were estimated using lme4 (Bates, M€ achler, Bolker, & Walker, 2015) called using the mixed function of the package afex (Singmann, Bolker, Westfall, & Aust, 2016).To determine p values of the fixed effects, we computed Type 3 Likelihood Ratio Tests as implemented in the mixed function.Post-hoc comparisons were performed using the lsmeans package (Lenth, 2016), such that degrees of freedom were approximated using the Satterthwaite algorithm and Tukey-corrected for multiple comparisons.All behavioral analyses were performed using the R statistical package (version 3.4.3;R Core Team; 2022).

Fig. 1 e
Fig. 1 e Task Structure.A mini-block of 9 trials would start by indicating the meaning of the scores on the upcoming rounds.Then, the scores for the participant and the other player would be revealed ("score" screen).Next, participants were shown a computer-generated, default allocation ("allocation" screen).On half the trials, participants were then given the opportunity to change the allocation as they saw fit ("choice" screen").

Fig. 3 e
Fig. 3 e Parametric activity related to the (a priori) unfairness (i.e., taking the context of merit, need, or equality into account) of the computer-generated default allocation.

Fig. 4 e
Fig. 4 e Parametric activity related to the inequity (i.e.,.inequality) of the computer-generated default allocation.

Fig. 6 e
Fig. 6 e Patterns of neural activity related to the deviations from the subjectively preferred allocation of a computergenerated default allocation.Marked voxels are the centers of searchlights with a 3-voxel radius.