General rank-reversal aversion expressed only when self-rank is preserved
The task comprised 6 conditions with combinations of two general rank-reversal conditions and three self-centered rank-reversal conditions. Rejection rates were calculated for each condition to distinguish various motivations underlying the decision-making process.
The 2 (General rank-reversal) \(\times\) 3 (Self-centered rank-reversal) two-way rm ANOVA for rejection rates revealed an almost significant main effect of general rank-reversal \((F\left(\text{1,54}\right)=3.918, p= .053, {{\eta }_{p}}^{2}=0.068)\). When general rank-reversal was present, participants showed a higher tendency to reject the redistribution offer (\({M}_{RR}= 0.238, {SD}_{RR}=0.022)\)compared to when it was absent \(({M}_{NRR}= 0.221, {SD}_{NRR}=0.023)\).
With the Greenhouse-Geisser correction, a significant main effect of self-centered rank was observed on the rejection rate \((F\left(1.427, 77.037\right)=12.002, p <.001 , {{\eta }_{p}}^{2}=0.182)\). A post-hoc analysis with Bonferroni correction revealed higher rejection rates when participants’ self-centered rank decreased (\({M}_{D}= 0.347, {SD}_{D}=0.043)\) compared to when it increased (\({M}_{U}= 0.172, {SD}_{D}=0.025)\) or remained unchanged (\({M}_{M}= 0.169, {SD}_{M}=0.026)\). The interaction effect of general rank-reversal and self-centered rank was also significant \((F\left(\text{2,108}\right)=6.293, p<.001, {{\eta }_{p}}^{2}=0.104)\), showing higher rejection rates when general rank-reversal was present while self-centered rank remained constant.
To explore the effect of general rank-reversal among different self-centered ranks, a paired-sample t-test indicated that general rank-reversal aversion was expressed only when participants' self-centered rank remained constant throughout the redistribution process (\(t\left(54\right)= 3.683, p=.001, Cohe{n}^{{\prime }}s d=0.497\)) (Fig. 2a).
General rank-reversal slows reaction time
For the reaction time, the 2 (General rank-reversal) \(\times\) 3 (Self-centered rank-reversal) two-way rm ANOVA showed a significant main effect of general rank-reversal, \((F\left(\text{1,51}\right)=42.193, p<.001, {{\eta }_{p}}^{2}=0.453)\) and a significant main effect of self-centered rank-reversal \((F\left(\text{2,102}\right)=7.302, p=.001, {{\eta }_{p}}^{2}=0.125)\). Participants exhibited slower reaction times in general rank-reversal conditions (\({M}_{RR}= 0.08, {SD}_{RR}=0.014)\), compared to no general rank-reversal conditions (\({M}_{NRR}=-0.087, {SD}_{NRR}=0.013\)). Post-hoc analysis with Bonferroni correction revealed slower RTs when participants’ self-centered rank decreased (\({M}_{D}= 0.091, {SD}_{D}=0.027)\) compared to when it increased (\({M}_{U}= -0.069, {SD}_{U}=0.026)\) or was maintained (\({M}_{M}= -0.033, {SD}_{M}=0.024)\). No interaction effect was found between general and self-centered rank-reversal.
Furthermore, a paired-sample t-test indicated that general rank-reversal impacted RT for self-centered rank-reversal conditions. Results showed that for all self-centered rank-reversal conditions, RT became slower when general rank-reversal was present (\({t}_{U}\left(51\right)= 3.168, p=.003, Cohe{n}^{{\prime }}s d=0.439; {t}_{M}\left(51\right)= 4.043, p<.001, Cohe{n}^{{\prime }}s d=0.561 ; {t}_{D}\left(51\right)= 5.658, p<.001, Cohe{n}^{{\prime }}s d=0.785)\) (Fig. 2b).
For a closer examination of reaction time, we analyzed the selection process by distinguishing between acceptance and rejection of the redistributed offer. A paired-sample t-test between general rank-reversal and no general rank-reversal condition revealed that only when participants accepted the redistributed offer, the presence of the general rank-reversal made the reaction time slower in all self-centered rank-reversal conditions (\({t}_{U}\left(51\right)= 2.830, p<.01, Cohe{n}^{{\prime }}s d=0.392; {t}_{M}\left(51\right)= 3.794, p<.001, Cohe{n}^{{\prime }}s d=0.526 ; {t}_{D}\left(51\right)= 4.054, p<.001, Cohe{n}^{{\prime }}s d=0.562\))
Individual differences in resource distribution behavior
After discovering that rank-reversal circumstances impact participants' redistribution behavior, we conducted a comparison of rejection tendencies among all individuals using binomial-GLMM. This included fixed effects of conditions (‘U’, ‘D’, interaction parameter of ‘G’ and ‘M’) as well as random effects of ‘U’, ‘D’, and the interaction parameter. The analysis showed significance for fixed effects of downward condition (\(\beta =1.710, SE=0.362, p<.001)\) and the interaction of general rank-reversal and maintain condition (\(\beta =0.898, SE=0.255, p<.001),\) and marginal significance for the upward condition (\(\beta =0.657, SE=0.340, p=.053)\). This suggests that the conditions for general and self-centered rank-reversal affected the choice of rejecting redistributed offers.
Clustering individuals with diverse moral principals
The parameter estimates were utilized to explore variations in different redistribution motives among individuals. The k-means algorithm, a non-model-based method, was employed to define clusters. To estimate the optimal number of clusters k, the elbow method and silhouette score was used where both methods yielded the same result, k = 3 (average silhouette score 0.49). As a result, three clusters were yielded, where the most participants were assigned to Cluster 1 (\({n}_{1 }=\) 28, silhouette score = 0.47), followed by Cluster 2 (\({n}_{2}=\) 15, silhouette score = 0.28) and Cluster 3 (\({n}_{3 }=\) 12, silhouette score = 0.82).
To gain deeper insights into each of the clusters, we conducted comprehensive analyses on both behavior and reaction time for individual clusters.
Cluster 1: Context-dependent rank-reversal aversion
In Cluster 1, a 2 (General rank-reversal) \(\times\) 3 (Self-centered rank-reversal) two-way rm ANOVA on rejection rates revealed a significant interaction between general and self-centered rank-reversal \((F\left(\text{2,54}\right)=7.652, p= .001, {{\eta }_{p}}^{2}=0.221)\). A more detailed analysis through a non-parametric paired-sample t-test showed that the rejection rate increased significantly during general rank-reversal only when the self-rank was maintained (\(Z=3.437, p<.01, {M}_{NRRM}=0.186, {SD}_{NRRM}=0.136 ; {M}_{RRM}= 0.277, {SD}_{2}=0.142)\) (Fig. 3a).
Examining reaction time in the same manner, the two-way rm ANVOA indicated only the main effect of general rank-reversal (\(F\left(\text{1,24}\right)=16.817, p< .001, {{\eta }_{p}}^{2}=0.412).\) Further, a paired-sample t-test revealed the general rank-reversal significantly slowed down reaction time in the maintain and downward conditions, and marginally in the upward condition \(\left({t}_{U}\left(24\right)= 1.890, p=.071, Cohe{n}^{{\prime }}s d=0.289; {t}_{M}\left(24\right)= 2.900, p=.008, Cohe{n}^{{\prime }}s d=0.321 ; {t}_{D}\left(24\right)= 3.573, p=.002, Cohe{n}^{{\prime }}s d=0.220\right)\) (Fig. 4a).
Participants in Cluster 1 displayed a higher rejection rate and slower reaction times when general rank was reversed, indicating a clear aversion to rank-reversal within this group.
Cluster 2: Prioritizing self-interest
In Cluster 2, a 2 (General rank-reversal) \(\times\) 3 (Self-centered rank-reversal) two-way rm ANOVA on rejection rates showed a significant main effect only for self-centered rank (\(F\left(\text{2,28}\right)=58.993, p< .001, {{\eta }_{p}}^{2}=0.808).\) Post-hoc analysis with Bonferroni correction revealed higher rejection rates for downward conditions (\({M}_{D}= 0.753, {SD}_{D}=0.055)\), compared to upward (\({M}_{U}= 0.057, {SD}_{U}=0.017)\) and maintain (\({M}_{M}= 0.187, {SD}_{M}=0.072)\) conditions. However, the Wilcoxon test did not show any significant effect of general rank-reversal among self-centered rank conditions, indicating that general rank-reversal did not impact participants' behavior in any of the self-centered conditions (Fig. 3b).
For reaction time, a two-way rm ANOVA showed main effects for both general \((F\left(\text{1,14}\right)=13.533, p=.002, {{\eta }_{p}}^{2}=0.492)\) and self-centered rank (\(F\left(\text{2,28}\right)=7.712, p=.002, {{\eta }_{p}}^{2}=0.355)\), with an almost significant interaction effect (\(F\left(\text{2,28}\right)=2.776, p=.079, {{\eta }_{p}}^{2}=0.165)\). Post-hoc analysis with Bonferroni correction showed faster RTs when participants’ self-centered rank increased (\({M}_{U}= -0.196, {SD}_{U}=0.047)\) compared to when it decreased (\({M}_{D}=0.157, {SD}_{D}=0.060)\) or was maintained (\({M}_{M}= 0.026, {SD}_{M}=0.051)\). According to paired sample t-tests, general rank-reversal affected reaction time only in the downward condition (\({t}_{D}\left(14\right)= 3.828, p=.002, Cohe{n}^{{\prime }}s d=0.269)\) (Fig. 4b).
Although Cluster 2 appeared to follow a specific decision-making process, prioritizing their own rank, the general rank-reversal did cause a delay in their reaction time, indicating the presence of general rank-reversal aversion, albeit not to a significant extent.
Cluster 3: Prioritizing inequality aversion
For participants in Cluster 3, rejection rates were close to zero, preventing a statistical analysis on these rates (Fig. 3c). However, the two-way rm ANVOA on reaction time revealed that general rank-reversal was a factor, with significant main effects for both general (\({F}_{general}\left(\text{1,11}\right)=13.708, p=.003, {{\eta }_{p}}^{2}=0.555)\)and self-centered rank \(({F}_{self}\left(\text{2,22}\right)=4.187, p=.029, {{\eta }_{p}}^{2}=0.276)\).
Furthermore, paired sample t-tests on all self-centered ranks demonstrated a significant effect of general rank conditions, indicating a slower reaction when general rank-reversal was present (\({t}_{U}\left(11\right)= 3.867, p=.003, Cohe{n}^{{\prime }}s d=0.283; {t}_{M}\left(11\right)= 2.276, p=.044, Cohe{n}^{{\prime }}s d=0.342 ; {t}_{D}\left(11\right)= 2.302, p=.042, Cohe{n}^{{\prime }}s d=0.287)\) (Fig. 4c).
Despite the low rejection rate for the more equitable offer under all conditions, suggesting a strong aversion to inequality, the reaction time results indicate that general rank-reversal among choices is also considered by participants in this group.
Differences among clusters
To assess the validity of clustering, nonparametric tests were conducted on rejection rates in each condition. The Kruskal-Wallis test revealed significant differences in rejection rates for conditions involving general rank-reversal with upward (‘RRU’) or downward (‘RRD’) self-rank, and for conditions with no general rank-reversal with downward self-rank (‘NRRD’) (\({H}_{RRU}\left(2,N=55\right)=36.874, p<.001;{H}_{RRD}\left(2,N=55\right)=38.298, p<.001;{H}_{NRRD}\left(2,N=55\right)=38.261, p<.001)\).
For conditions with no general rank-reversal but with upward (‘NRRU’), maintained (‘NRRM’) self-rank, or with general rank-reversal and maintained self-rank (‘RRM’), only Cluster 1 and 2 were compared, excluding Cluster 3 with 0 rejection rate. The Mann-Whiteny U test revealed significant difference in NRRU (\(Mann-Whitney U=39, N=43, p<.001)\) and RRM conditions (\(Mann-Whitney U=118.5 , N=43, p=.019)\)but not under NRRM conditions, indicating that that Cluster 1 and 2 showed difference in rejection rates when ranks were not preserved.
A one-way ANOVA for normalized reaction times revealed significant differences among clusters only for the RRU condition (\(F\left(\text{2,49}\right)=7.536, p=.001, {{\eta }_{p}}^{2}=0.235)\). Post-hoc analysis using the Bonferroni correction showed that Cluster 2 (\({M}_{2}= 0.-0.184, {SD}_{2}=0.263)\) reacted faster than Cluster 1 and 3 (\({M}_{1}= 0.030, {SD}_{1}=0.235;{M}_{3}= 0.156, {SD}_{3}=0.187 )\).
A one-way ANOVA examining potential age differences between clusters did not reveal any significant differences (\(F\left(\text{2,52}\right)=0.703, p=.5)\). A Chi-Square test to determine gender composition differences among the groups showed no significant association between gender and clusters (\({\chi }^{2}\left(2,N=55\right)=1.569, p=.456)\).
Significant differences in SVO were found among clusters (\(F\left(\text{2,52}\right)=3.264, p=.046, {{\eta }_{p}}^{2}=0.112)\). Post-hoc analysis using the Bonferroni correction indicated that Cluster 1 (\({M}_{1}= 31.147, {SD}_{1}=10.623)\)exhibited higher SVO scores than Cluster 2 (\({M}_{2}= 23.241, {SD}_{2}=7.095)\), suggesting a higher prosocial tendency.