Fair and unfair punishers coexist in the Ultimatum Game

In the Ultimatum Game, a proposer suggests how to split a sum of money with a responder. If the responder rejects the proposal, both players get nothing. Rejection of unfair offers is regarded as a form of punishment implemented by fair-minded individuals, who are willing to impose the cooperation norm at a personal cost. However, recent research using other experimental frameworks has observed non-negligible levels of antisocial punishment by competitive, spiteful individuals, which can eventually undermine cooperation. Using two large-scale experiments, this note explores the nature of Ultimatum Game punishers by analyzing their behavior in a Dictator Game. In both studies, the coexistence of two entirely different sub-populations is confirmed: prosocial punishers on the one hand, who behave fairly as dictators, and spiteful (antisocial) punishers on the other, who are totally unfair. The finding has important implications regarding the evolution of cooperation and the behavioral underpinnings of stable social systems.

Therefore, the rejection of unequal but positive offers combined with zero-transfers in the DG is an unequivocal symptom of competitive spite.
We report data from two large-scale experimental studies. Study 1 (n 5 754) is a survey-experiment employing a representative sample of a city's adult population which was carried out at the participants' households. The pie to be split was J20 in each game. For UG responses, the strategy method was used in which the responder states whether she accepts/rejects any possible offer beforehand. Study 2 (n 5 623) is a replication of Study 1 in the laboratory employing university students (freshmen) as subjects (see Methods). Figure 1 breaks down the sample into three groups according to participants' decisions in the DG: ''unfair'' refers to participants who offer zero in the DG, ''fair'' refers to those who make an equal split, while those who make an offer in between the two are labeled ''remaining''. For each group, the figure displays the percentage of responders who reject offers below the equal split in the UG. Study 1 [2] is captured by the left [right] panel.

Results
The data clearly demonstrate that it is not only the ''fair'' but also the (totally) ''unfair'' dictators who reject unequal offers significantly more often than the ''remaining'' group (Probit model controlling for order effects in decisions; fair vs. remaining: p , 0.001 in Study 1 and 2; unfair vs. remaining: p 5 0.005 in Study 1, p , 0.001 in Study 2; see model 1 in Table S1 for Study 1 and Table S2 for Study 2 in the Supplementary Information (SI)). What is more, both groups are similarly likely to reject an unequal offer (p 5 0.123 in Study 1, p 5 0.356 in Study 2). As analyzed in more detail in the SI (see Figure  S3), there is a statistically significant U-shaped, non-linear relationship between the two variables in both samples (all ps , 0.001) when using the offers in the DG as a continuous explanatory variable (rather than comparing between the three DG groups). Furthermore, having decided first as dictator or as responder does not affect the reported relationship (no significant main or interaction order effects are observed in any study: all ps . 0.16; see SI).
Thus, fair and unfair punishers coexist in the UG. In addition, in both samples fair dictators are more numerous than unfair ones (see the numbers on the top of the bars in Figure 1; the percentage of fair dictators is significantly higher than the percentage of unfair dictators according to a two-tailed binomial test: p , 0.001 in both studies). This implies that fairness-based punishment is more frequent in both samples -which, nevertheless, should not necessarily be the case in samples taken from other populations/societies 30 (also, as discussed in the SI, methodological factors might influence these proportions). Indeed, among the UG responders who reject unequal offers in Study 1 [2], 17% [15%] are unfair dictators while 70% [72%] are fair dictators (these percentages are also significantly different according to a two-tailed binomial test: p , 0.001 in both studies). Importantly, note that the relationship between DG offers and UG rejections holds even in the presence of differences between the two samples. In particular, in Study 1 the proportion of unfair dictators as well as the likelihood of rejecting unequal UG offers is higher compared to Study 2 (in both cases, two-tailed Fisher's exact test yields p , 0.001).

Discussion
The results show that punishment decisions in the UG are indistinguishably ''prosocial'' and ''antisocial''; it is not one or the other, but both kinds of human behavior that shape the outcomes of the UG. Such a finding has important implications in interpreting previous results and designing future research.
One prominent example lies in the realm of behavioral and social neuroscience, where data from rejections in the UG have been extensively used to investigate the neurobiological basis of costly punishment. This research has implicated the brain areas responsible both for negative emotional processes (e.g., the anterior insula) and for executive control (e.g., the dorsolateral prefrontal cortex) in rejection behavior. Yet, there is much debate on the exact role of executive control. Some studies appear to indicate that executive control must be exerted to override the emotional impulse to punish unfairness at personal cost 5,37 whereas others suggest that it is the selfish impulse to accept an unfair offer which must be overridden in order to impose fairness through rejection, thus implying that punishment is an act of self-control 8,38 . Recently, more studies have shed light on these apparently contradictory observations [13][14][15][16] but the debate is far from closed. The results presented in this note indicate that there is a nonnegligible fraction of rejections that are rooted not in normative, fairness-based judgments but instead in competitive, spiteful desires. It would in fact be hard to claim that a common neural mechanism underlies these extremely different natures of rejection behavior. Instead, one of the two might be overrepresented in some databases -which might have been due to the small sample sizes typically featured in brain studies -and, as suggested in 29 , this could explain part of the above controversy. Note also that the proportion of prosocial and antisocial punishers may vary dramatically across societies 30,35,39 .
Thus, in order to unravel the neurobiological basis of costly punishment, researchers should carefully investigate not only which behavior gets punished but also who is the punishing individual.  [2]. The horizontal axis depicts behavior in the DG: unfair (offer 0%), remaining (offer between 0 and 50%), fair (offer 50%). The numbers on top of the bars denote the total number of observations in each group. The vertical axis represents the percentage of individuals (6 SE) who reject offers below 50% in the UG, i.e. whose minimum acceptable offer is the equal split (mean percentage: 45 However, this cannot be addressed using the standard UG as the only information researchers obtain from responders is whether they accept or reject a given proposal (or a number of them). Other experimental settings, or the combination of UG rejections with subjects' behavior in other frameworks, should be employed.
Additionally, the results are also important from the viewpoint of evolutionary biology and the social sciences. Costly punishment has been shown to be crucial in promoting cooperation [40][41][42][43] . Nevertheless, in the presence of spiteful punishers, social efficiency becomes difficult to sustain since spiteful behavior often leads to escalating conflict rather than to lasting cooperation. When sanctions are not used as norm-enforcement devices but instead at the service of dominance-or conflict-seeking behavior, their effects over social stability can be perverse [30][31][32]44 . If the punisher lacks the legitimacy to teach a moral lesson -because she does not comply with the social norm herself -the punished individual can view punishment as unjustified coercion. This might activate the mechanisms involved in competition with conspecifics instead of those involved in norm compliance, thus paving the way to inefficient, corrupt societies 45,46 rather than to efficient, cooperative ones 47 . In fact, corruption among the responsible for the enforcement of rules is recognized as a major source for the failure of social institutions 48 .
Therefore, special care has to be taken in the interpretation of rejection behavior as a mechanism to enforce the norms implicated in the maintenance of stable social systems. Extending the argument to the field of institutional design, failing to recognize the possible duality of motives behind punishment behavior in bilateral bargaining interactions can lead to less-than-optimal, or even countereffective incentive mechanisms.

Methods
The details of the survey-experiment have been reported elsewhere 49 . In both studies, subjects made their decisions in the UG (both roles) and the DG in random order. Subjects' decisions as proposers in the UG are not being used here as a measure of fairness since generous offers might equally be motivated by strategic self-interest (avoidance of rejection) and by other-regarding concerns, thus making them difficult to interpret 50 (indeed, zero offers in the UG are extremely rare). In contrast, the interpretation of subjects' offers in the DG is straightforward because they are not influenced by strategic concerns.
In the DG, subjects had to split a pie of J20 between themselves and another anonymous participant. Subjects decided which share of the J20 (in J2 increments) they wanted to transfer to the other subject. For the role of responder in the UG the strategy method was used 51 . That is, subjects had to state their willingness to accept or reject each of the following proposals (proposer's payoff [J], responder's payoff [J]): (20, 0); (18,2); (16,4); (14,6); (12,8); (10,10). After making their decisions, participants in each study were randomly matched and one of every ten was selected for real payment (see Supplementary Information).
For the statistical analyses, we use Probit regressions with the likelihood that a subject rejects any unequal offer (i.e. whether her minimum acceptable offer is the equal split) in the UG as the dependent variable and DG behavior as the explanatory variable. Using the same database, a similar approach was employed in Staffiero et al. 52 for the study of the motivational drives behind the acceptance of zero offers in the UG.
All participants in the experiments reported in the manuscript were informed about the content of the experiment prior to participating. Verbal informed consent was obtained from participants in the city experiment (Study 1) since literacy was not a requirement to participate (this was necessary to obtain a representative sample), and all the instructions were read aloud by the interviewers. Written informed consent was obtained from participants in the lab experiment (Study 2). Anonymity was always preserved (in agreement with Spanish Law 15/1999 on Personal Data Protection) by randomly assigning a numerical code to identify the participants in the system. No association was ever made between their real names/addresses and the results. As is standard in socio-economic experiments, no ethic concerns are involved other than preserving the anonymity of participants. This procedure was checked and approved by the Vice-dean of Research of the School of Economics of the University of Granada; the institution hosting the experiments.