Explaining inequality tolerance in the lab: effects of political efficacy and prospects of mobility on collective demand for redistribution

The low public demand for redistribution despite growing economic inequality has been characterized as a paradox especially for disadvantaged individuals. One prominent explanation for people’s tolerance to growing inequality posits that increased optimism about prospects of upward mobility undermines support for redistribution. A less explored explanation postulates that low political efficacy of disadvantaged individuals to enact meaningful change erodes collective demand for redistribution. In two preregistered experiments, we create a dynamic environment where low-income individuals collectively demand income redistribution by contributing to a public pool (collective action strategy), compete with each other for high-income group positions (individual mobility strategy), or avoid risks and disengage from both strategies (social inaction strategy). Lack of political efficacy, operationalized as high redistribution thresholds, gradually curtailed collective action, while exposure to high prospects of mobility did not influence collective action even when income group boundaries were highly permeable. Across participants, we identified three behavioral types (i.e., “mobility seekers”, “egalitarians”, and “disillusioned”) whose prevalence was affected by political efficacy but not by prospects of mobility or actual group permeability. These results cast doubt on the universality of the prospects of mobility hypothesis and highlight the prominent role of political inequality in the perpetuation of economic inequality.


Social identity theory and reactions to inequality
Both the ideological and the political explanation of the tolerance to growing inequality are consistent with social identity models that consider group efficacy beliefs and perceived permeability of group boundaries as determinants of disadvantaged group members' responses to social inequality 8,32 .Surveys and experimental studies have shown that permeable or semi-permeable (compared to strictly impermeable) group boundaries, and perceptions thereof, increase the willingness of low-status members (e.g., ethnic minorities, women, national groups) to engage in individual strategies [33][34][35][36] .On the other hand, perceived group efficacy is associated with collective action against inequality 37,38 .

Current research
Our research builds upon and extends this work by examining whether sociostructural characteristics (i.e., lack of political efficacy and permeability of income group boundaries) and perceptions thereof (i.e., high prospects of mobility) undermine collective reactions to economic inequality.Unlike previous studies that employed selfreport measures, we develop a novel economic experiment where low-income individuals make costly decisions in the face of large and unfair economic inequality.In modern meritocratic societies, access to high-status groups is restricted and individuals compete against each other to achieve upward mobility.In this competitive setting, demanding income redistribution through various forms of collective action may entail financial, reputational, or opportunity costs 39 .Even voting for political parties that advocate for redistribution can be costly when these parties' agenda conflicts with voters' preferences in other social or economic issues.
Based on this insight, we conceptualize individual mobility and collective demand for redistribution as competing costly strategies.We use a repeated threshold public goods game where low-income individuals can collectively reduce intergroup inequality by reaching predetermined redistribution thresholds.At the same time, they compete with each other for upward mobility after being exposed to information about their prospects of moving to a high-income position.Given that both collective action against inequality and striving for individual mobility entail risks, individuals may opt for a risk-free strategy (social inaction), especially when they perceive low political efficacy and no prospects of mobility.We thus introduce a third social inaction strategy which accounts for the possibility of political passivity 26 and eliminates the strict negative interdependence between income redistribution and individual mobility strategies.In other words, the presence of a third risk-free strategy allows us to exclude the possibility that investment in one strategy (e.g., individual mobility) merely reflects disbelief in the other strategy (e.g., collective action).
In light of the discrepancy between optimistic prospects of mobility and low actual social mobility rates that characterize many societies 13,14 , we also investigate how repeated frustration of high prospects of mobility influences the strategies that people adopt to navigate economic inequalities.Lastly, we explore the dynamic evolution of public demand for redistribution in the presence of previous successful or failed attempts to collectively reduce inequality.Our dynamic setting allows the identification of different behavioral types based on how disadvantaged individuals' reactions to inequality evolve over time.

Study 1
In Study 1, we assessed to what extent lack of political efficacy and exposure to high prospects of mobility undermine low-income individuals' demand for redistribution over time.In this study, income group boundaries were strictly impermeable and thus personal mobility prospects were repeatedly frustrated.To emulate the real-life ambiguity regarding the permeability of group boundaries 43 , disadvantaged individuals received ambiguous feedback about the reasons for the absence of upward mobility (i.e., insufficient personal investment in this strategy or impermeable group boundaries).
Consistent with aforementioned social identity models 32 and the well-documented gradual erosion of the public good 44 , we hypothesized that lack of political efficacy gradually undermines collective action against inequality as disadvantaged individuals cease demanding redistribution after repeated failure to achieve it (H1).Given that people update their prospects of mobility based on evidence about actual mobility rates 9,20 , we hypothesized that exposure to high prospects of mobility increases investment in individual mobility (H2) but this prospects-ofmobility effect gradually declines as group boundaries are actually impermeable (H3a).

Methods
Participants and general procedure Participants were UK residents and were recruited through the online platform Prolific Academic.We recruited 232 participants (Μ age = 31.1,SD = 10.7,149 females).We used a 2 × 2x10 mixed design whereby participants were randomly assigned to a high or a low efficacy condition and a high or a low prospects-of-mobility condition (see Table S1 for demographics).Participants played the threshold public goods game for ten rounds.Experimental sessions were conducted online using the software o-Tree 45 .Four participants took part simultaneously in each session and they interacted anonymously online.Upon entering the session, participants read detailed instructions about the threshold public goods game, and then answered four comprehension questions (see Supporting Information S1 for instructions).The experiment lasted around 25 min.At the end of the session, one round was randomly selected to determine participants' bonus payment.We obtained informed consent from all participants prior to taking part in the experiment and after debriefing at the end of the session.No observations were excluded from the analysis.
Study design, sample sizes, hypotheses, and statistical analyses were preregistered and are available at https:// osf.io/ zv34k (Study 1), https:// osf.io/ zsudy/, and https:// osf.io/ sg3rn (Study 2).Some preregistered hypotheses are not presented here to increase clarity and focus on the main objectives of the present work.All preregistered hypotheses are reported and tested in the Supporting Information S1.We conducted a priori power analysis to obtain 0.80 power for main effects and two-way interactions to detect a medium effect size of η p 2 = 0.06 at α = 0.05 after correcting for the number of hypotheses (Bonferroni correction).The analyses regarding the behavioral types were not preregistered.Both studies were carried out in accordance with relevant guidelines and regulations and were approved by the Ethical Review Committee Inner City Faculties of Maastricht University.

Experimental paradigm
At the beginning of each session, participants performed a Counting Zeros Task 46 to produce their income.This task consisted of counting, within two minutes, the number of zeros that are contained in 5 × 5 tables of numbers.Participants who correctly counted the zeros in a predetermined (but unknown to them) number of tables, successfully produced their income and participated in the next experimental phase.Subsequently, we instructed participants that they will be randomly assigned to a low-income (£1) or a high-income group (£5).In reality, the four participants of each session were assigned to the low-income group (i.e., deception), which is the group whose reactions to inequality we aim to investigate.After group assignment, the four low-income members were given ten independent opportunities (i.e., ten rounds) to increase their income by playing the threshold public goods game.In each round, they were endowed with ten Action Points (APs) which they could invest in three different strategies (i.e., three main dependent variables): (1) Collective action strategy (Fig. 1A): low-income members could collectively demand income redistribution by contributing their APs to the public pool.In each round, if the total contributions to the public pool exceeded certain thresholds, income was redistributed from the high-income to the low-income group.We imposed a "reduced inequality" and an "absolute equality" redistribution threshold.When contributions exceeded only the former threshold, income redistribution led to reduced intergroup inequality (low-income: £2 and high-income: £4).When contributions exceeded both thresholds, income redistribution led to equal incomes between the two groups (low-income: £3 and high-income: £3).(2) Individual mobility strategy (Fig. 1B): lowincome members could increase their chances of moving to the high-income group by allocating their APs to a personal account.Participants were informed that with some probability each of the ten rounds could be a "mobility round".In a "mobility round", two out of the four low-income members, those who allocated the most APs to their personal account, move to the high-income group and thus earn a high income for this specific round.(3) Social inaction strategy (Fig. 1C): low-income members could avoid risks related to collective action or individual mobility by exchanging their APs for money (1AP = £0.05).
To operationalize political efficacy, we changed the redistribution thresholds.In the low efficacy condition, the redistribution thresholds were higher than the high efficacy condition and thus participants needed to contribute more APs to the public pool to reach these thresholds.To manipulate prospects of mobility, we informed participants and we reminded them at the end of each round, that low-income members of previous sessions stated that each round is a "mobility round" with 10% (low prospects of mobility) or 50% (high prospects of mobility) probability.This information was truthful in both conditions as there were indeed participants that indicated probabilities close to 10% and 50%, respectively.
Participants were informed that the outcome of one round (i.e., successful collective action or upward mobility) affects their income and their group membership in this round but not in subsequent rounds.At the start of each round, participants are members of the low-income group and are endowed with £1.Thus, each round is independent.At the end of each round, participants received real feedback about whether collective action was successful and how this affected the group's income in this specific round.In both high and low prospectsof-mobility conditions, participants were also informed that they failed to move to the high-income group (i.e., impermeable system) for one of the following reasons: (1) boundaries between income groups were impermeable (i.e., no mobility round) or (2) participant exerted insufficient personal effort/investment (i.e., few APs in personal account).
At the end of the first and last round and before they receive any feedback, we elicited participants' beliefs regarding the fairness of the initial income gap, the permeability of group boundaries, and the efficacy of the low-income group.At the end of the experiment, we also assessed the extent to which participants identify with the low-income group.All aforementioned beliefs were measured on 7-point Likert scales.At the end of the experimental session, participants were debriefed about the purpose of the study and the fact that all participants were assigned to the low-income group (i.e., no random group assignment).

Data analyses
To test the effect of efficacy and prospects of mobility on the time evolution of investment in the three strategies, we sequentially fitted fixed-effect models and linear mixed effect models.The random intercept and random slope model provided the best model fit.Hence, all reported results are based on this model.We performed separate three-way mixed ANOVAs to quantify how investment in each of the three strategies differs across conditions and over time (Tables 1 and S10 for robustness tests).Thus, we adjusted statistical significance for three comparisons (Bonferroni correction: α = 0.017).Similar analysis was performed to quantify how perceptions of fairness, permeability, and efficacy differ across efficacy and prospects-of-mobility conditions and over time (Fig. S1 and Table S4).www.nature.com/scientificreports/

Results
As depicted in Table 1, we did not observe any significant interaction between efficacy and prospects of mobility on investment in any of the three strategies indicating that efficacy and prospects of mobility exert independent effects.

Efficacy effects
Consistent with H1, low (vs high) efficacy of disadvantaged individuals gradually curtailed collective demand for redistribution (F(1, 228) = 35.34,p < 0.001, η 2 = 0.130).This efficacy by time interaction effect was driven by the declining popularity of the collective action strategy in the low efficacy condition (F(1, 113) = 52.40,p < 0.001, η 2 = 0.320).In both efficacy conditions, participants invested around half of their APs in redistribution in the first round.However, by the last round, the share of APs invested in redistribution had fallen to 17% in the low efficacy condition, while it remained stable around 50% in the high efficacy condition (Fig. 2A).We also observed weaker efficacy by time interaction effects on investment in individual mobility (F(1, 228) = 10.94,p = 0.001, η 2 = 0.050) and social inaction (F(1, 228) = 5.79, p = 0.017, η 2 = 0.020).Overall, the low efficacy-driven decline in collective action was associated with growing popularity of individual mobility (59%) and social inaction (41%) strategies (Fig. 2C).

Prospects-of-mobility effects
Contrary to the prospects of mobility hypothesis, exposure to high (vs low) prospects of mobility had no impact on collective action against inequality, but, as hypothesized (H2), it led to increased investment in individual mobility (F(1, 228) = 6.93, p = 0.009, η 2 = 0.030).Contrary to H3a, the prospects-of-mobility effect on individual mobility did not decline over time as investment in this strategy remained stable in both prospects-of-mobility conditions (Fig. 2B).The persistent pursuit of individual mobility across the ten rounds indicates that participants were not discouraged by the repeated frustration of their mobility prospects.Exposure to high (vs low) prospects of mobility did not affect investment in social inaction.Overall, the prospects-of-mobility-driven rise in the popularity of individual mobility was associated with reduced investment in both social inaction (60%) and collective action (40%) (Fig. 2D).

Study 2
In Study 1, access to the high-income group was systematically blocked.However, in real life, group boundaries are rarely strictly impermeable.Thus, in Study 2, disadvantaged individuals were again exposed to high or low prospects of mobility but now they personally experienced or witnessed upward mobility in the first round (low group permeability condition).Study 2 aims to replicate the efficacy by time interaction effect on collective action (H1) and the main prospects-of-mobility effect on individual mobility (H2) that we observed in Study 1.However, unlike Study 1 where participants never experienced upward mobility, we hypothesized that the prospects-of-mobility effect on individual mobility increases over time (H3b) after an early (i.e., first round) experience of upward mobility.Specifically, exposure to high prospects of mobility in this context may lead to sustained investment in individual mobility despite the absence of upward mobility in subsequent rounds.On the other hand, exposure to low prospects of mobility after an early experience of upward mobility may lead to disengagement from this strategy in subsequent rounds.In Study 2, we also assessed disadvantaged individuals' reactions to inequality when income group boundaries were indeed highly permeable.Thus, we also introduced a high group permeability condition where prospects of mobility were frequently realized.We hypothesized that high, compared to low, permeability of group boundaries gradually undermines collective action against inequality (H4) and increases investment in individual mobility (H5).

Methods
Participants and general procedure Participants were UK residents and were recruited through the online platform Prolific Academic.We recruited 664 participants (Μ age = 32.0,SD = 10.0, 265 females).We used a 2 × 3x10 mixed design whereby participants were randomly assigned to a low or a high efficacy condition and a low prospects-of-mobility & low permeability, a high prospects-of-mobility and low permeability or a high prospects-of-mobility & high permeability condition (see Table S1 for demographics).We analyzed participants' investment behavior across ten rounds.The experimental procedure was identical to Study 1.

Experimental paradigm
Similar to Study 1, we used a repeated threshold public goods game.Study 2 differed from Study 1 in that we introduced one or multiple "mobility rounds" and we eliminated the ambiguity regarding the permeability of www.nature.com/scientificreports/ group boundaries.Participants received explicit feedback about mobility outcomes.Participants who kept track of the mobility outcome in each round could thus infer that group boundaries were permeable only in the first round.We introduced two low permeability conditions where participants were exposed to either low or high prospects of mobility.In both low permeability conditions, upward mobility took place only in the first round.
In subsequent rounds, group boundaries were impermeable.In a third condition (high prospects-of-mobility & high permeability), mobility took place in the first round and in four of the nine subsequent rounds.In "mobility rounds", two out of the four low-income members personally experienced upward mobility while the other two low-income members witnessed it (i.e., vicarious experience).In the remaining rounds, participants received explicit feedback that no low-income member achieved upward mobility.We did not differentiate between personal and vicarious experiences of upward mobility as both groups displayed similar patterns of investment (see Table S14).As in Study 1, we elicited participants' beliefs regarding the fairness of the income gap, the group permeability, and the group efficacy.

Data analyses
Similar to Study 1, we used the random intercept and random slope model, which provided the best fit to the behavioral data.We performed separate three-way mixed ANOVAs to quantify the effect of efficacy, prospects of mobility, and group permeability on the time evolution of investment in the three strategies (Tables 2 and S11 for robustness tests).To test H2 and H3b, we compared exposure to low vs high prospects of mobility in a low group permeability context (Test 1).To test H4 and H5, we compared high vs low group permeability after exposure to high prospects of mobility (Test 2).Since two separate tests were performed for each of the three strategies, we adjusted statistical significance for six comparisons (Bonferroni correction: α = 0.008).Similar analyses were performed to quantify efficacy, prospects-of-mobility, and group permeability effects on perceptions of fairness, group permeability and group efficacy (Fig. S1 and Table S5).

Results
As shown in Table 2, Test 1 and Test 2 yielded similar efficacy effects and revealed no interaction between efficacy and prospects of mobility (Test 1) or efficacy and group permeability (Test 2).This pattern suggests that efficacy effects are robust and independent from prospects-of-mobility and group permeability manipulations.Thus, in the text below, we describe efficacy effects in the entire sample (i.e., all three prospects-of-mobility & group permeability conditions).

Efficacy effects
Similar to Study 1 and consistent with H1, low (vs high) efficacy gradually undermined collective demand for redistribution (F(1, 662) = 53.92,p < 0.001, η 2 = 0.080).In both efficacy conditions, low-income individuals invested half of their APs in collective action in the first round, but investment in collective action declined over time (Fig. 3A).Although this gradual decline was steeper when efficacy was low, it was significant in both low (F(1, 331) = 216.22,p < 0.001, η 2 = 0.400) and high (F(1, 331) = 36.22,p < 0.001, η 2 = 0.100) efficacy conditions.By the last round, investment in redistribution had declined to 20% in the low efficacy condition and to 37% in the high efficacy condition.In both efficacy conditions, participants gradually shifted away from collective action mostly to social inaction, which gradually became the most popular strategy.However, this shift was more prominent in the low (compared to high) efficacy condition (F(1, 662) = 50.17,p < 0.001, η 2 = 0.070).In fact, 76% of the low efficacydriven decline in collective action was associated with increased investment in social inaction (Fig. 3C).Notably, efficacy had only a marginal main effect on individual mobility (F(1, 662) = 6.36, p = 0.009, η 2 = 0.010).

Prospects-of-mobility effects in low group permeability context
Contrary to the prospects of mobility hypothesis but similar to Study 1, exposure to high (vs low) prospects of mobility when group permeability was low did not influence collective action against inequality.Consistent with H2, exposure to high (vs low) prospects of mobility increased investment in individual mobility (F(1, 439) = 24.57,p < 0.001, η 2 = 0.050).Contrary to H3b, we observed no prospects of mobility by time interaction effect.However, unlike Study 1 where investment in individual mobility remained stable across rounds, here we observed drastic changes in the popularity of this strategy over time (Fig. 3B).Following the experience of upward mobility in the www.nature.com/scientificreports/first round, exposure to low prospects of mobility led to a steep decline in the popularity of individual mobility in the next three rounds, which remained low in the remaining seven rounds.On the other hand, exposure to high prospects of mobility slightly increased investment in individual mobility in the first four rounds but the popularity of this strategy gradually declined in subsequent rounds as repeated failure to achieve upward mobility was explicitly attributed to impermeable group boundaries.
We conducted an exploratory analysis to assess whether these different short-term and long-term trends are significant.Consistent with H3b, the prospects-of-mobility effect on investment in individual mobility gradually increased in the first four rounds (F(1, 439) = 23.70,p < 0.001, η 2 = 0.050).However, consistent with H3a, the prospects-of-mobility effect on individual mobility gradually declined in the subsequent six rounds (F(1, 439) = 9.35, p = 0.002, η 2 = 0.020).Overall, the prospects-of-mobility-driven increase in individual mobility was associated with both reduced investment in social inaction (52%) and reduced collective action (48%; Fig. 3D).This shift is also reflected in the lower popularity of the social inaction strategy after exposure to high prospects of mobility (F(1, 439) = 9.59, p = 0.002, η 2 = 0.020).
Group permeability effects after exposure to high prospects of mobility Contrary to H4, high (vs low) group permeability had no impact on collective action (Fig. 3B) but, consistent with H5, it led to a slow (after the fifth round) and gradual increase in the popularity of individual mobility (F(1, 437) = 21.76,p < 0.001, η 2 = 0.050).Post hoc tests revealed that this effect was driven by both growing popularity of this strategy in the high group permeability condition (F(1, 220) = 11.81,p = 0.001, η 2 = 0.050) and declining popularity in the low group permeability condition (F(1, 219) = 10.10,p = 0.002, η 2 = 0.040).Low (vs high) group permeability also led to a steeper rise in the popularity of social inaction (F(1, 437) = 22.31, p < 0.001, η 2 = 0.050).As shown in Fig. 3E, the permeability-driven decline in social inaction was predominantly associated with increased investment in individual mobility (75%).

Behavioral types
Apart from average investment in the three strategies at the population level, we tried to gain further insights into how individual reactions to income inequality evolve over time.In each study, we fitted latent class linear mixed models (LCLMM) 47 to classify low-income individuals into distinct behavioral types based on the evolution of their investment in the three strategies (see Supporting Information S1 and Tables S6 and S7 for detailed analysis and results).The LCLMM tries to explain between-subject heterogeneity in growth on an outcome by assuming that the population is divided into a finite number of latent subpopulations.Each latent group of participants is characterized by a different growth trajectory (i.e., behavioral type) which is modelled by a classspecific linear mixed model.

Results
The analyses revealed four behavioral types in Study 1 and five behavioral types in Study 2 (Fig. 4).In both studies, we identified three generic behavioral types.The most populated behavioral type was the "mobility seekers" (47% of the sample in Study 1 and 37% of the sample in Study 2) who predominantly strived for individual mobility throughout the ten rounds by consistently investing 37-50% of their APs in this strategy.These individuals gradually shifted away from the redistribution strategy to the two individualistic strategies.The second generic type was the "egalitarians" (42% of the sample in Study 1 and 31% of the sample in Study 2) who persistently engaged in collective action throughout the ten rounds.In both studies, we identified a moderate and an extreme version of "egalitarians".The moderate "egalitarians" (34% of the sample in Study 1 and 24% of the sample in Study 2) invested 50-63% of their APs in collective action, 25-37% in individual mobility, and only 9-19% in social inaction across the ten rounds.The extreme "egalitarians" (8% of the sample in Study 1 and 7% of the sample in Study 2) overwhelmingly engaged in collective action by investing 80-100% of their resources in this strategy throughout the ten rounds.The third generic type, the "disillusioned" (11% of the sample in Study 1 and 33% of the sample in Study 2), gradually disengaged from both risky strategies (mostly from redistribution) and opted for the risk-free and low-profit social inaction strategy.In Study 2, two versions of "disillusioned" individuals were identified, a moderate (21% of the sample) and an extreme version (12% of the sample).Their main differences lie in the starting point and the final degree of investment in social inaction (Fig. 4).The high prevalence of "disillusioned" individuals in Study 2 corroborates the view that explicit feedback about impermeable group boundaries renders social inaction an attractive alternative strategy for a considerable segment of low-income individuals despite being a low-profit strategy.

Discussion
Our work examined how two relevant sociostructural characteristics and perceptions thereof affect disadvantaged individuals' willingness to collectively redress economic inequality in the presence of two competing individualistic strategies.We showed that low political efficacy of disadvantaged individuals, but not exposure to high prospects of mobility or even high group permeability, undermines public demand for income redistribution.Importantly, the observed differences between the efficacy-based and the mobility-based explanations of www.nature.com/scientificreports/tolerance to inequality are not only statistically significant (see comparison of effect sizes in Supporting Information S1 and Tables S2 and S3) but also quantitatively relevant and persistent over time.
Exposure to high prospects of mobility, even when combined with highly permeable income group boundaries, did not undermine collective action against inequality as low-income individuals predominantly shifted from one individualistic strategy (social inaction) to the other (individual mobility).Τhis finding contradicts the prospects of mobility hypothesis 6 but resonates with prior evidence that permeability of group boundaries and perceptions thereof mainly affect the willingness to engage in individual rather than collective strategies 33 .
One plausible explanation for the lack of mobility-driven effects on collective demand for redistribution is that disadvantaged individuals strive to accomplish two different goals: (1) increase their low personal income and (2) reduce high and unfair intergroup inequality.When income group boundaries are (perceived as) permeable, individual mobility offers an attractive solution to the problem of low personal income without necessarily affecting motivations to reduce high and unfair inequality.Based on this view, previous economic experiments that imposed a negative interdependence between income redistribution and individual mobility [40][41][42] , were not able to distinguish the two aforementioned goals.Unlike these attempts, we introduced a third risk-free social inaction strategy, which allowed both motivations to be expressed.Nevertheless, the absence of mobility-related effects on collective action may be specific to contexts where inequality is overwhelmingly perceived as unfair.In our setting, this strong sense of unfairness probably contributed to the persistent presence of "egalitarians" across all prospects of mobility & group permeability conditions.
Nonetheless, exposure to high prospects of mobility increased the popularity of individual mobility even in the absence of upward mobility experiences.We initially hypothesized that an early experience of upward mobility (low group permeability in Study 2) combined with exposure to high prospects of mobility would lead to persistent engagement in individual mobility.However, this context failed to produce a long-term prospectsof-mobility effect on individual mobility.Instead, explicit feedback about impermeable group boundaries undermined the longevity of this prospects-of-mobility effect.
This finding suggests that when the absence of upward mobility can be attributed to either impermeable group boundaries or insufficient personal investment (ambiguous feedback of Study 1), exposure to high prospects of mobility exerts a sustained effect on investment in individual mobility and group permeability perceptions.In contrast, when the absence of upward mobility is solely attributed to impermeable group boundaries (explicit feedback of Study 2 after the first round), exposure to high prospects of mobility has a short-lived effect on individual mobility as disadvantaged individuals gradually shift away from individual mobility and adjust downwards their permeability perceptions.The explicitly negative feedback may also explain the substantially higher www.nature.com/scientificreports/prevalence of "disillusioned" individuals in this study.However, when group permeability was actually high, the popularity of individual mobility and group permeability perceptions increased over time.Taken together, these results suggest that people incorporate information about actual group permeability, when these are available, and adjust their beliefs and behavior accordingly 9,20 .At the same time, these findings highlight the crucial role of ambiguity regarding group permeability in explaining the persistent optimism about prospects of mobility and preference for individual rather than collective action observed in token systems 16 .Consistent with the gradual erosion of the public good 44 , collective demand for redistribution started off as the most popular strategy across all conditions, but it gradually declined when disadvantaged individuals lacked political efficacy.This trend probably reflects the presence of conditional cooperators who stopped contributing after failed attempts to collectively reduce inequality (see Supporting Information S1 and Tables S12 and S13 for feedback effects on collective action).Despite the declining collective action, the income gap was persistently deemed unfair and even more so in the low efficacy condition.This discrepancy between beliefs and behavior disproves a system-justifying account whereby powerless individuals legitimize the inequality they tolerate 29 .Instead, it is consistent with evidence that powerless and low-status individuals are more likely to recognize the unfairness of the existing economic system 30,31,48 .A question that remains unaddressed and perhaps an avenue for future research is whether prolonged lack of political efficacy could shape people's ideology by rendering egalitarianism a utopian ideal rather than a cognitive alternative to a highly unequal system.
Our work builds upon a recent series of public good experiments where individuals could solve shared problems collectively or individually 49,50 .In these studies, people displayed a strong tendency to opt for the individual solution, which resonates with our finding that "mobility seekers" was the most populated behavioral type.These studies also showed that as the collective solution becomes more efficient, people engage more in collective action and vote to abolish individual solutions.Similarly, we found that when disadvantaged individuals have the means to collectively reduce inequality, public demand for redistribution rises.This shift is also reflected at the individual level, as there were three times more "egalitarians" and half as many "disillusioned" individuals when political efficacy was high.In this respect, our results contradict classic instrumental accounts according to which people free-ride when a collective goal becomes feasible without personal contribution 39 .Instead, our results corroborate evidence from the social identity tradition showing that group efficacy beliefs are important predictors of collective action against inequalities 8,32,38 .In fact, the present work goes beyond the existing social identity models of collective responses to inequality by testing some of their assumptions using incentivized behavioral measures rather than group efficacy and group permeability beliefs.
The robust efficacy effect on collective action has profound political implications in light of the changes that characterize many countries in the last three decades.Growing economic inequality is concurrent with a general crisis of democratic institutions, which has resulted in growing disparities between high and low socioeconomic status individuals in political participation [21][22][23][24][25][26] .To date, the low political efficacy of disadvantaged individuals has been mostly considered as a consequence of economic inequality 27,[51][52][53] .The present work reverses this argument in an attempt to understand how political inequality contributes to the consolidation and perpetuation of economic inequality.The potential self-reinforcing link between economic and political inequality 25 provides a plausible explanation as to why low public demand for the growing wealth and income gap is more prevalent in highly unequal countries 3 .Consistent with this view, median voter models that take into account the wealth bias in political participation outperform the standard model 5 in predicting the dynamics of income redistribution 54 .
One important limitation of the present findings is that political efficacy was operationalized as a structural manipulation, while exposure to different mobility prospects is an ideological manipulation given that actual group permeability was the same across conditions.As explained in the introduction, we opted for these two manipulations to increase ecological validity.Nonetheless, the different nature of the two manipulations (i.e., structural vs ideological) may account for the stronger efficacy effects on collective action.To counteract this argument, in Study 2, we manipulated actual group permeability.Interestingly, even this structural manipulation had no effect on collective action.
To conclude, the present work highlights the lack of political efficacy as a plausible explanation of the disadvantaged individuals' tolerance to growing inequality and casts doubt on the prominent mobility-based explanations especially in contexts where social inaction is an alternative strategy to costly collective action and individual mobility.These results call for more attention on how broader political factors affect motivations of disadvantaged individuals to address economic inequality.

Figure 1 .
Figure 1.Hypothetical example of how the four low-income members invest their APs in the three strategies in a given round.Depending on contributions to the public pool, three different redistribution outcomes are possible: no inequality reduction, reduced inequality, absolute equality (A).In this example, the four lowincome members contributed 15 APs to the public pool, which results in no inequality reduction in the low efficacy condition and reduced inequality in the high efficacy condition.Low-income members can also pursue an individual mobility strategy by allocating their APs to a personal account (B).In this example, participants B and C allocated the most APs to their personal account.In a "mobility round", these two participants would move to the high-income group.Low-income members can also opt for a risk-free social inaction strategy by exchanging their APs for money (C).

Figure 2 .
Figure 2. Time evolution of average investment in three strategies across efficacy (A) and prospects of mobility (B) conditions.Bands around the averages in A and B indicate the 95% confidence interval of the mean.Action Points shifted from individual mobility (blue) or from social inaction (orange) to collective action in the high vs low efficacy condition (C).Action Points shifted from collective action (blue) or from social inaction (orange) to individual mobility in the high vs low prospects-of-mobility condition (D).

Figure 3 .
Figure 3.Time evolution of average investment in three strategies across efficacy (A), prospects of mobility (B), and group permeability (B) conditions.Bands around the averages in A and B indicate the 95% confidence interval of the mean.Action Points shifted from individual mobility (blue) or from social inaction (orange) to collective action in the high vs low efficacy condition (C).Action Points shifted from collective action (blue) or from social inaction (orange) to individual mobility in the high vs low prospects-of-mobility condition (D).Action Points shifted from social inaction to collective action (blue) or individual mobility (orange) in the high vs low group permeability condition (E).

Figure 4 .
Figure 4. Behavioral types across the two studies.In both Study 1 (left) and Study 2 (right), low-income individuals were classified into three generic behavioral types.Bands around the averages in (A) and (B) indicate the 95% confidence interval of the mean."Mobility seekers" persistently pursued an individual mobility strategy and gradually disengaged from collective action.Moderate and extreme "egalitarians" predominantly engaged in collective action.The "disillusioned" gradually disengaged from both risky strategies (mostly redistribution) and opted for social inaction.In Study 2, the "disillusioned' type was represented more prominently and was divided into a moderate and an extreme version.

Table 1 .
Three-way mixed ANOVA testing the effects of efficacy, prospects of mobility, and time on investment in three strategies.*p < 0.017 (p value adjusted for multiple testing).

Table 2 .
Three 2way mixed ANOVA testing the effects of efficacy, prospects of mobility, group permeability, and time on investment in three strategies.1Test1:ANOVAtesting the effects of efficacy and prospects of mobility (only low permeability conditions were included).2Test2: ANOVA testing the effects of efficacy and group permeability (only high prospects-of-mobility conditions were included).*p < 0.008 (p value adjusted for multiple testing). )