Measuring the impact of inequality on subjective well-being

Our experimental design involved testing subjects in groups of four. Subjects (n=47) were first introduced to each other, then seated in separate rooms and asked to complete three different tasks (Fig. 1a). The first task was a non-social decision task15,22,23, in which subjects chose between safe and risky options. Subjects faced Gain trials (certain gain versus a gamble to gain a larger amount or zero), Mixed trials (zero versus a gamble to gain an amount or lose an amount) and Loss trials (certain loss versus a gamble to lose a larger amount or zero). Chosen gambles were resolved after a brief delay and the outcomes of all trials counted towards earnings. The second task was a standard economic task, the dictator game, in which a subject decided how to split an endowment (either £2 or £3, see the Methods for details) with one of the other players24. Importantly, these allocations were private and subjects were told that the monetary split would never be revealed to the other player. At the end of the experiment, subjects learned their total earnings for completing all tasks and were not told if, or how much, any other player had contributed to that total. The design feature whereby allocations were private is important because generosity might otherwise reflect primarily a reputational concern for what other players will think of them25. Generosity was estimated based on behaviour in the dictator game as the percentage of the endowment that subjects allocated to their social partner. This quantity varied between 0 and 50%, consistent with previous research26. The third and final task involved social and non-social decision trials, where subjects were again presented with safe and risky options (Fig. 1b). In the non-social trials, subjects made choices as in the first task. In the social trials, subjects were shown two sets of identical safe and risky options and informed that one set was allocated to them, and the other set corresponded to a trial the partner had previously experienced in the non-social decision task. Subjects were informed that on these trials they could not make a decision for themselves, but observed, and were subject to the outcomes of the choices that the partner had previously made. In reality, choices on social trials were generated using a standard decision model based on prospect theory, using parameters for a typical subject (see the Methods for details). This procedure ensured that all participants had a similar experience in social trials.

Figure 1: Experimental design. (a) Four participants were introduced to each other and seated in separate rooms to perform three tasks: a non-social decision task, a dictator game, and a social decision task. In the non-social decision task, subjects (n=47) chose between safe options and risky gambles with equal probabilities of two outcomes. In the dictator game, subjects decided how to split an endowment between themselves and another player. (b) The social decision task consisted of non-social and social trials. In non-social trials, choice outcomes (here £0) did not affect partner earnings. In social trials, subjects were told that they were observing choices made by their partner in the non-social decision task. When their partner chose to gamble, the subject received an equivalent but independent gamble. The subject’s outcome was revealed first (here gaining £0.95), followed by the partner’s outcome (here £0). After every 2–3 trials, subjects were asked to report their current level of happiness. Full size image

When the partner chose the safe option, both players received the same outcome; when the partner chose the risky option, both players received the gamble. The critical manipulation centred on the independence of the two gambles for the subject and the partner. This meant that for any single gamble chosen by the partner, the outcomes experienced by the subject and their partner could be identical or different (Fig. 1b), providing the potential for inequality. In all trials, the outcomes for the subject counted towards overall earnings. To investigate the relationship between subjective emotional state and the outcomes of choices, including choices made by others, we used experience sampling15,27,28, repeatedly asking subjects, ‘How happy are you at this moment?’ after every 2–3 trials. Subjects were tested using two slightly different procedures (see the Methods for details) with an identical trial structure, and were informed of total earnings only after completion of all tasks. Although happiness due to inequality could potentially be measured without any choice on the subject’s part, not being able to make any choices would reduce engagement, and the results of our previous studies show that outcomes resulting from a subject’s choices substantially impact happiness15,18. Thus, we interleaved social and non-social trials, and outcomes for the two types of trials were independent, allowing us to dissociate these influences.

We first examined the determinants of subjective well-being, and found, consistent with our previous research15, that subjects reported greater average happiness at the subsequent rating after winning compared with losing gambles in both social and non-social trials (Wilcoxon signed-rank test, n=47, both Z>4, P<0.001). In social trials, we tested whether there was an impact of partner outcomes on well-being by z-scoring ratings for each subject and computing average happiness at the subsequent rating across the following four contexts: both participants win, both participants lose, subject wins and partner loses and subject loses and partner wins. The last two conditions are associated with advantageous (subject has more) and disadvantageous (subject has less) inequality, respectively. These two contexts are ones that might engender the social emotions of guilt and envy, respectively, emotions that have parallels with terms in models of altruistic behaviour12.

Inequality reduces subjective well-being

We found that, regardless of whether subjects themselves won or lost, average subjective well-being was attenuated for unequal compared with equal outcomes. Well-being was reduced both when subjects were better off (Z=−2.2, P=0.028) and when they were worse off (Z=−2.8, P=0.005) than the other person (Fig. 2a). We tested the possibility that the sensitivity of subjective well-being to advantageous and disadvantageous inequality (referred to here as guilt and envy) is equivalent, as might be expected if it reflected a unified concept of inequality aversion. However, we found no correlation between the change in well-being when subjects were better compared with worse off than their partner (Spearman’s ρ=−0.04, P=0.78; Fig. 2b), suggesting independent variation in the degrees of guilt and envy, a result inconsistent with a unified concept of inequality aversion.

Figure 2: Descriptive analysis. (a) Subjects (n=47) reported being happier at the subsequent rating after winning compared with losing gambles, and happiness ratings were lower on average when the partner received a different outcome, regardless of whether that outcome was better or worse. (b) The amount that happiness was affected by advantageous inequality (guilt is when subject wins and partner loses minus subject wins and partner wins) and disadvantageous inequality (envy is when subject loses partner wins minus subject loses and partner loses) was uncorrelated across subjects (Spearman’s ρ=−0.04, P=0.78). (c) Subjects completed a dictator game in which they could anonymously give a fraction of an endowment to their partner; the bar farthest to the right indicates that 10 subjects gave half of the endowment and the bar farthest to the left indicates that 16 subjects gave nothing. (d) Subjects were more generous in the dictator game if their happiness in the separate social decision task was higher when the partner won than lost gambles. The difference between guilt and envy measures was correlated with generosity in the dictator game (Spearman’s ρ=−0.48, P<0.001). Subjects who were happier after the partner lost than won gambles included only 2 of 10 subjects who gave half but 12 of 16 subjects who gave nothing. Error bars, s.e.m. *P<0.05. Full size image

Emotional impacts of inequality relate to generosity

We next determined whether a social influence on well-being was related to generosity in the entirely separate dictator game. For each subject, we computed the difference in happiness between when the partner loses and when the partner wins, equivalent to taking the difference between guilt and envy measures. Against a backdrop of a 20% average allocation in the dictator game (Fig. 2c), consistent with previous studies26,29, subjects who were more happy on average when the partner wins than when they lose were also more generous in the dictator game, compared with subjects who were less happy when the partner wins than when they lose (Wilcoxon rank-sum test, Z=3.4, P<0.001; Fig. 2d). Strikingly, the first group of subjects gave three times as much of their endowment on average than the second group (30% versus 10%). Generosity in the dictator game was highly correlated with the difference between guilt and envy measures derived from happiness ratings (Spearman’s ρ=−0.48, P<0.001). Although generosity might be thought to depend on the guilt of receiving an unexpected endowment, we found that generosity was not significantly correlated with guilt measures alone (Spearman’s ρ=−0.18, P=0.22) but was correlated with envy measures (Spearman’s ρ=0.30, P=0.042) such that subjects exhibiting greater envy were less generous, a pattern of results inconsistent with any plausible demand characteristics of the experimental design.

Modelling the impact of inequality aversion on well-being

Our next goal was to apply our previously established methodology for measuring determinants of momentary subjective well-being to quantify individual dispositions in the social domain that impact emotional reactivity. Our starting point was our pre-existing non-social happiness model15, in which chosen certain rewards (CR), the expected value (EV) of chosen gambles and RPEs resulting from those expectations, all exert separate influences that decay exponentially with time:

where t is trial number, w 0 is a constant term, other weights w capture the influence of different event types, 0≤γ≤1 is a forgetting factor that makes events in more recent trials more influential than those in earlier trials, CR j is the certain reward if chosen instead of a gamble on trial j, EV j is the average reward for the gamble if chosen on trial j and RPE j is the RPE on trial j contingent on choice of the gamble. Terms for unchosen options were set to zero. We z-scored happiness ratings to prevent subjects with greater variability in their ratings from having a disproportionate effect on results. The constant term is omitted when ratings are z-scored. We fitted parameters to the happiness ratings of individual subjects in the social decision task and found, as expected, that CR, EV and RPE weights were on average positive (all Z>4, P<0.001). The forgetting factor γ was 0.67±0.25 (mean±s.d.) indicating that ratings on average depended on the cumulative impact of five to ten past events. Despite having no way to account for any social effect, this model explained momentary happiness well, with r2=0.39±0.19 (mean±s.d.), comparable to fits for a non-social task in a previous study15.

We next expanded the model by including additional terms to account for influences related to advantageous and disadvantageous inequality12. These influences might be considered as related to guilt and envy, respectively:

where w 4 relates to advantageous inequality (guilt) when the reward received by the subject R j exceeds the reward received by the other player O j , and w 5 relates to disadvantageous inequality (envy) when O j exceeds R j . This guilt-envy model explained momentary happiness better than its non-social variant with r2=0.44±0.18 (mean±s.d.; Fig. 3a). This model was preferred to the simpler non-social model in a Bayesian model comparison, which penalizes for the number of parameters30,31 (see Table 1 for details), demonstrating that social comparison significantly impacts subjective well-being in our task. Model parameters for guilt and envy were negative on average (both Z<−2, P<0.05; Fig. 3b), consistent with both advantageous and disadvantageous inequality reducing momentary happiness.

Figure 3: Model-based analysis. (a) Happiness ratings of an example subject over the course of the experiment plotted with the predictions of the guilt–envy model. (b) Happiness was affected by model parameters (n=47) related to the subject’s rewards. Two additional model parameters related to inequality aversion were both negative, indicating that both advantageous inequality (guilt parameter) and disadvantageous inequality (envy parameter) negatively impact happiness on average. (c) Subjects with stronger (more negative) guilt parameters were more generous in the separate dictator game than subjects with stronger (more negative) envy parameters. The difference between guilt and envy parameters was correlated with generosity in the dictator game (Spearman’s ρ=−0.48, P<0.001). (d) Guilt and envy parameters estimated by the model for subjects with different levels of generosity in the dictator game. Subjects who gave nothing had significant envy parameters. Subjects who gave something had significant guilt parameters. Error bars, s.e.m. *P<0.05. Full size image

Table 1 Bayesian model comparison analysis. Full size table

Envy and guilt parameters predict generosity

When we tested how model parameters related to individual social preferences, we found subjects with stronger (more negative) guilt parameters were more generous in the dictator game than subjects with stronger (more negative) envy parameters (Z=2.8, P=0.006; Fig. 3c). Consistent with the descriptive analysis, the difference between guilt and envy parameters estimated from happiness ratings was highly correlated with generosity in the dictator game (Spearman’s ρ=−0.48, P<0.001). Guilt but not envy parameters were significantly negative for subjects that altruistically gave either half or some of the endowment (guilt, both Z<−2.3, P<0.05; envy, both |Z|<0.5, P>0.5; Fig. 3d), whereas the opposite was true for those subjects that gave nothing (guilt, Z=−0.2, P=0.88; envy, Z=−2.9, P=0.003).

One concern is whether demand characteristics might contribute to any of our results. Some subjects might have noticed that inequality was one feature of the experiment and hypothesized that well-being should reflect a unitary concept of inequality (‘inequality is bad’). To test whether this possibility could explain our results, we fitted an additional model with a term for the magnitude of the difference in rewards between players. The inequality parameter in this simple-inequality model was significantly negative on average (Z=−5.13, P<0.001), capturing lower well-being with greater inequality (see the Methods for details). However, this inequality parameter was uncorrelated with generosity in the dictator game (Spearman’s ρ=−0.036, P=0.81), which might theoretically have responded to the same demand characteristic, and the guilt–envy model outperformed the simple-inequality model according to Bayesian model comparison (Table 1).