Human pursuance of equality hinges on mental processes of projecting oneself into the perspectives of others and into future situations

In the pursuance of equality, behavioural scientists disagree about distinct motivators, that is, consideration of others and prospective calculation for oneself. However, accumulating data suggest that these motivators may share a common process in the brain whereby perspectives and events that did not arise in the immediate environment are conceived. To examine this, we devised a game imitating a real decision-making situation regarding redistribution among income classes in a welfare state. The neural correlates of redistributive decisions were examined under contrasting conditions, with and without uncertainty, which affects support for equality in society. The dorsal anterior cingulate cortex (dACC) and the caudate nucleus were activated by equality decisions with uncertainty but by selfless decisions without uncertainty. Activation was also correlated with subjective values. Activation in both the dACC and the caudate nucleus was associated with the attitude to prefer accordance with others, whereas activation in the caudate nucleus reflected that the expected reward involved the prospective calculation of relative income. The neural correlates suggest that consideration of others and prospective calculation for oneself may underlie the support for equality. Projecting oneself into the perspective of others and into prospective future situations may underpin the pursuance of equality.


Supplementary Information
[1] Task inside fMRI An experimental framework of redistribution games was devised, based on the result of behavioral experiments (3 players x 45 groups = 135 subjects) in which we compared two different sets of redistribution rules and two different proportions of costs. If we compared the level of (in)equality of three redistribution rules by using the Gini coefficients that represent absolute equality by 0 and absolute inequality by 1, Rules 1, 2, and 3 have the value of 0.36, 0.19, and 0, respectively. The level of equality of Rule 1 was set close to 0.32, the average of thirty-four member countries of the Organisation for Economic Co-operation and Development, as well as 0.34, the value assigned to the Japanese society as of 2012. The level of equality of Rule 2 was the same as the level of Sweden in the early 1980s when the country achieved its highest level of equality. We devised the experimental framework to examine brain activity when participants were sensitively responding to redistribution rules from absolute equality to a moderate level of inequality.
Participants played four separate sessions in a randomized order. The redistribution game was repeated so that a participant played in all (high/middle/low) classes that were randomly assigned and, in each class assignment, experienced all society-level outcomes (inequality / intermediate / equality) in a random order except when she decided it as a dictator. Therefore, the number of rounds varied across sessions, from 12 to 40, i.e., from the VoI to informed sessions, respectively.
[2] Decomposition of ANOVA effects One important methodological challenge of the fMRI data was the analysis of the interaction effects in the high-dimensional data. The estimation of the effects depends on the baseline activity level; thus the interpretation of the empirical findings was also influenced by the choice of the baseline. 58 To solve this problem, we have used the method developed by Imai and Egami 59 and examined the invariant effect of each factor, especially the VoI and Equality decision, on brain activation. Imai and Egami define the concept of the marginal treatment interaction effect, whose relative magnitude does not depend on the choice of a baseline condition for higher-order interaction. Then, they developed a method by which we can calculate the effect of the interaction in the high-dimensional data so as to be invariant to the choice of a baseline category. The details about the methodological information and the software for the analysis are found at http://imai.princeton.edu/research/int.html.
[3] Categorization of the attitudes with accordance and non-accordance with others Among one hundred and thirty-two cases (132 cases = 33 participants x 4 sessions x 2 partners) we found seventy-eight cases when participants earned higher income than partners' in the sessions that observed an equality/selfless decisions (and thus included in the neural analysis), we excluded twenty-four cases when participants did not change the affective rating after income disclosure (0 = Affective Feeling III -Affective Feeling II) and four contradictory cases when two participants revealed accordance attitude to one partner but non-accordance attitude to other partner in the same session.
In resulting fifty cases, we found nineteen cases with the accordance attitude and thirty-one cases with non-accordance attitude. Note that the same participants' data were included more than once if they revealed the same attitude in different sessions.
When they showed the same attitude to different partners in the same session we averaged the changes between different partners. Since the data of seven participants were included twice in accordance and fourteen in non-accordance, we counted twelve participants (female = 4) who ever revealed the accordance attitude and seventeen participants (female = 2) who ever revealed the non-accordance attitude. Six participants (female =1) ever revealed the both attitude and thus twenty-three participants' data were included in the analysis.  When participants chose the inequality rule more than 60% of the time we define they were more risk seeking. A riskaverse tendency was observed among 15% of those who chose the equality rule more than 60% of the time. Overall, 27% were found in between. In the risk-seeking group, 26% (in dictatorship) to 47% (in voting) shifted away from risk-seeking in the redistributive decision behind the VoI, whereas the risk-averse groups in the lottery also avoided risk in the redistributive decision. .41 sub-maxima within in a cluster º FWE corrected p < 0.1 for multiple comparisons across the whole brain for main effect/interaction : the number of k on uncorrected F-map FWE corrected p < 0.05 for for multiple comparisons across the whole brain positive effect/positive interaction : the number of k on FWE corrected p < 0.05 t-map Selfless = High(Intermediate/Equality) : Low(Equality/Intermediate) Selfish = High(Inequality) : Low(Equality) The BA9 and anterior insular were excluded from the further analysis since activation behind the VoI was not differentiated by equality and non-equality decision.

Supplementary Figure 1
The BA9 and anterior insular also revealed an interaction (see Supplementary Table 3) but were excluded from the main result since activation behind the VoI was not significantly differentiated by equality and non-equality decision. A. The coordinates in BA9 and anterior insult were included in the ANOVA result but were not included in the analysis. Both equality and inequality rules activated these regions in the VoI conditions. B. anterior insular (-32, 26, 4) The base line is set at activation level associated with High Inequality. Compared with activation associated with the lottery decision, the VoI condition specifically reduced activation in the dACC as well as in the caudate nucleus but neither high-nor lowincome class conditions.