Contractualist tendencies and reasoning in moral judgment and decision making ☆

The social-contract tradition of Hobbes, Rousseau, Kant, and Rawls has been widely influential in moral philosophy but has until recently received relatively little attention in moral psychology. For contractualist moral theories, ethics is a matter of forming, adhering to, and enforcing (hypothetical) agreements, and morality is fundamentally about acting according to what would be agreed by rational agents. A recent psychological theory, virtual bargaining, models social interactions in contractualist terms, suggesting that we often act as we would agree to do if we were to negotiate explicitly. However, whether such contractualist tendencies (a propensity to make typically contractualist choices) and forms of reasoning (agreement-based cognitive processes) play a role in moral cognition is still unclear. Drawing upon virtual bargaining, we develop two novel experimental paradigms designed to elicit incentivized decisions and moral judgments. We then test the descriptive relevance of contractualism in moral judgment and decision making in five preregistered online experiments ( n = 4103; English-speaking Prolific participants). In the first task, we find evidence that many participants show con-tractualist tendencies: their choices are “ characteristically ” contractualist. In the second task, we find evidence consistent with contractualist reasoning influencing some participants' judgments and incentivized decisions. Our findings suggest that a propensity to act as prescribed by tacit agreements may be particularly important in understanding the moral psychology of fleeting social interactions and coordination problems. By complementing the rich literature on deontology and consequentialism in moral psychology, empirical approaches inspired by contractualism may prove fruitful to better understand moral cognition. The social-contract

The social-contract tradition, which traces back to Plato (375 BCE/ Plato, 2007), Hobbes (1651/Hobbes, 2018), Locke (1689/Locke, 1988), Rousseau (1762/Rousseau, 2004), and Kant (1785/Kant & Korsgaard, 1998), has been widely influential in moral and political philosophy and in the social sciences in general.As a family of moral theories, contractualism holds that morality is primarily about acting according to what would be agreed by rational agents. 1 Common to the main contractualist approaches (Gauthier, 1986;Rawls, 1971;Scanlon, 1998) is the idea that acting morally is about acting in mutually advantageous ways (Baumard, 2016), and that the morality of an action depends on whether relevantly affected parties could reasonably agree to it, or not reasonably reject it (Levine, Kleiman-Weiner, Chater, Cushman, & Tenenbaum, 2022).Interestingly, contractualist theories have so far received relatively little attention in empirical studies of moral cognition.
But recent advances suggest that contractualism can also provide a fruitful framework to better understand morality's "ultimate" evolutionary logic and "proximate" cognitive mechanisms.Regarding morality's ultimate logic, Baumard, André, and Sperber (2013) and André, Fitouchi, Debove, and Baumard (2022) advocate an evolutionary account of cooperation in which the emergence of a contractualist morality in humans is explained by partner choice mechanisms-contending that selective pressures led to the evolution of a moral cognitive "organ" designed to help us respect relational contracts and thereby appear as good cooperative partners.Their account finds some preliminary empirical support in studies involving hypothetical moral dilemmas (Everett, Pizarro, & Crockett, 2016), suggesting that agents who make contractualist judgments are seen as more trustworthy, and thus more likely to be included in cooperative exchanges, which increases their evolutionary fitness.Recently, Levine, Chater, Tenenbaum, and Cushman (2024) have proposed that moral cognition is fundamentally organized around the logic of agreement, negotiation, and bargaining.In this view, the aim of moral cognition is to approximate the outcome of contractualist reasoning in a resource-rational (i.e., cognitively efficient) manner.
Regarding morality's "proximate" cognitive mechanisms, Levine, Kleiman-Weiner, Schulz, Tenenbaum, and Cushman (2020) show that adults and children sometimes make moral judgments consistent with the logic of universalization (asking themselves "what if everybody did that?"), a specific form of reasoning that has a contractualist flavor.Furthermore, Levine et al. (2022) use hypothetical scenarios to investigate when it is acceptable to break rules and present preliminary evidence of contractualist moral intuitions.Recent experimental studies also show the relevance of contractualism in the context of vaccination: a social contract between vaccinated individuals leads to less generosity toward non-vaccinated individuals, especially for those who regard vaccination as a moral obligation (Korn, Böhm, Meier, & Betsch, 2020).Nonetheless, direct empirical tests of contractualist moral cognition are still scant, and whether and to what extent contractualist tendencies (i.e., to act in typically contractualist ways or make characteristically contractualist choices, such as moral judgments or incentivized decisions, whether or not such choices result from contractualist reasoning processes) and forms of reasoning (i.e., agreement-based cognitive processes that can influence subsequent judgments or decisions) are involved in moral judgment and decision making is not well understood. 2  Basing descriptive models of morality on normative ethical theories has considerable appeal: after all, the most influential moral theories have been constructed to be intuitively compelling and consistent with many of our moral judgments, at least in simple cases.This strategy has proven to be very fruitful in moral psychology where the opposition between two normative ethical perspectives, consequentialism and deontology, has deeply shaped the field (Malle, 2021).Consequentialism bases the morality of an action on its consequences.For deontology, the morality of an action depends on whether it conforms with, or violates, specific moral rules, which often represent prohibitions, permissions, or obligations.Viewing morality in terms of psychological rules (e.g., Mikhail, 2007;Nichols, 2004), calculations of consequences (e.g., Baron, 1994;Gray, Young, & Waytz, 2012), or both (e.g., Crockett, 2013;Cushman, 2013;Greene, 2014b), has led to sophisticated descriptive theories of moral cognition.Importantly, what could be reasonably agreed will often depend on the consequences of our choices, and on whether they violate moral rules.Hence, rather than attempting to decisively adjudicate between the psychological validity of various ethical perspectives (see also the burgeoning literature on virtue ethics (Uhlmann, Pizarro, & Diermeier, 2015)), we develop two novel experimental paradigms aimed at testing the descriptive relevance of contractualism, alongside established deontological and consequentialist factors.
Contractualist reasoning seems crucial to creating the flexible and spontaneous agreements that help us manage social interactions outside the moral domain.Indeed, social interactions require intricate coordination of thought and behavior, which raises a fundamental cognitive challenge: how are different individuals able to formulate and play their part in the same plan, so that their thoughts and actions cohere smoothly?Imagine one person, A, moving to one side to allow another, B, to pass down the aisle of a crowded train carriage.This coordination problem could be resolved in several ways.Instead of moving aside, A might temporarily sit in an empty seat.B might move past cautiously, at speed, with or without thanks.A and B might play opposite roles.How do both parties align on the same plan, often without communicating?A could attempt to second-guess B's action and choose an action that coordinates with it.But this leads to an infinite regress, as B would simultaneously be attempting to second-guess A's action.Breaking out of this "paradox of social interaction" (Chater, Zeitoun, & Melkonyan, 2022) seems to require joint reasoning about what should be the "agreed" plan.But without explicit communication, how can such an agreement be reached?
A recent proposal is that such joint reasoning involves a process of "virtual bargaining" (Misyak, Melkonyan, Zeitoun, & Chater, 2014).Each person figures out what would happen if both parties were able to reach an agreement through discussion and negotiation.They then follow their part in the hypothetical virtual bargain.Suppose that B is pushing a drinks trolley.If A and B were to discuss explicitly, they might conclude that A should move aside.If the conclusion of this hypothetical bargaining process is "obvious", then A may immediately do thisand the interaction is managed successfully.Crucially, the hypothetical agreement to follow this plan has normative force.If A violates the "obvious" agreement and barges ahead, B may complain, likely backed up by bystanders.Notice that the bargain is created "in the moment" to best meet the needs of the immediate circumstances, and its normative force comes from its status as the natural tacit agreement (Melkonyan, Zeitoun, & Chater, 2022) between rational or reasonable people. 3ollowing the virtual bargain is, in a sense, the "appropriate" or "right" course of action; violating it is reprehensible.This line of argument suggests that at least some of our actions in morally relevant contexts might arise from the creation and enforcement of such ephemeral "social contracts in miniature" (Zeitoun, Melkonyan and Chater, 2023).Thus, even the simplest and most fleeting social interactions can have an ethical flavor.
Such virtual bargaining processes are fundamentally contractualist: the prescribed course of action corresponds to what rational or reasonable agents would agree to do.While they can sometimes be conscious and explicit, they need not be.Most often, parties must simply recognize that they share mutual interests, and figure out their respective roles to achieve a common goal.Engaging in such forms of shared intentionality (Tomasello & Carpenter, 2007), collective reasoning (Gallotti & Frith, 2013), or team reasoning (Colman & Gold, 2018) about what "we" should do instead of simply what "I" should dodoes not always require conscious, explicit, or verbalized thinking.Rather, agents behave as if they had been able to negotiate.
Are such contractualist tendencies and reasoning processes involved in moral judgment and decision making, alongside deontological and consequentialist considerations?Most empirical studies of virtual bargaining (Misyak et al., 2014; Misyak, Noguchi, & Chater, 2016; Misyak   2 By contractualist reasoning we mean an agreement-based cognitive process that can influence a subsequent decision or judgment.We are careful to distinguish between contractualist reasoning and contractualist tendencies to emphasize that choices (decisions and judgments) can be characteristically or typically contractualist without necessarily resulting (or being influenced by) a contractualist reasoning process.The lottery ticket game (Studies 1 to 3) primarily looks at contractualist tendencies while the dice game (Studies 4 and 5) primarily looks at contractualist reasoning.& Chater, 2022) are based on coordination games but do not consider moral judgments.By contrast, on-going work that does consider virtual bargaining and moral judgment (in the context of rule-breaking, Levine et al., 2022) has a different and complementary focus from the studies presented here, moving away from incentivized coordination tasks and instead probing moral judgments concerning hypothetical vignettes.To assess the descriptive relevance of contractualism in moral judgment and decision making, we therefore develop two novel experimental paradigms: a moral dilemma ("the lottery ticket game" (Studies 1-3)) and a coordination game with a clear moral component ("the dice game" (Studies 4-5)).Both elicit incentivized decisions alongside moral judgments and are designed to test different aspects of cognitive contractualism.We predict that, in both settings, some participants' moral acceptability judgments and incentivized decisions will reflect a propensity to follow tacit agreements.We find evidence in support of this prediction in five preregistered online experiments (n = 4103), suggesting that contractualist tendencies (Studies 1-3) and forms of reasoning (Studies 4-5) may play a key role in moral cognition.

Transparency and Openness
We report how we determined sample sizes, all data exclusions (if any), all manipulations, and all measures in the studies.The design, sample size, hypotheses, and analysis plan for all five studies were preregistered.Study materials, preregistration forms, raw data, and analysis scripts for all studies are available on an Open Science Framework (OSF) repository, which also includes an additional preregistered study (n = 121), at this link: https://osf.io/ufhvd.

The lottery ticket game
Studies 1-3 were based on a new incentivized game with a clear moral component inspired by the "blue house dilemma" (Levine et al., 2022).While recognizing the potentially intertwined nature of the three ethical theories, these experiments are designed to split apart characteristically contractualist from characteristically deontological and consequentialist choices, and a nonmoral stance characteristic of egoism (Rachels, 2013).Following Greene (2014a), we define "characteristically deontological" choices as most naturally justified in deontological terms i.e., in terms of rules, rights and duties. 4Similarly, "characteristically consequentialist" choices are those that are naturally justified in consequentialist terms i.e., in terms of impartial aggregate utility maximization (Everett & Kahane, 2020) (utilitarianism is the most prominent consequentialist theory)."Characteristically contractualist" choices are naturally justified as mutually advantageous arrangements that rational or reasonable agents would create if they negotiated explicitly.They coincide with the outcome of a hypothetical bargaining process between the affected partiesthose included in a potential tacit agreement about what to do.Finally, we model nonmoral "characteristically egoist" choices using rational choice theory narrowly understood as individual payoff maximization.
Participants played a lottery game, beginning with an allocation of lottery tickets.The game consisted in a single decision in which player (P1) selected their preferred way (henceforth Decision) of allocating extra lottery tickets not yet distributed.Crucially, in order for additional tickets to be distributed (increasing players' probability of winning), P1 had to destroy one of player 2's (P2) tickets without his permission.
This action is perceived as highly morally relevant for some participants.This is illustrated by free-response data collected during pilot studies, which, while anecdotal, are quite telling in this regard.Thus, one participant explains that "Destroying someone's ticket without their permission isn't morally acceptable" while another one claims that "I personally wouldn't do something as unfair as tearing up other people's tickets".This feeling is shared by other players who declare that "Destroying someone else's tickets isn't the right thing to do, even if it gives me an advantage in a lottery" or explain that it is "Not appropriate to destroy someone's ticketswhether you want to win or not, it has to be fair and moral -I would not be happy if I destroyed someone's tickets just to improve my chancesit would be selfish.Being moral is above winning for me." For each lottery, there were ten lottery tickets in total; each of which had the same probability (10%) of being the unique winning ticket.At the start of the game, five tickets had already been allocated: player (P1) had received three tickets and player 2 (P2) had received two tickets.At the end of the study, ten participants were selected at random, and their lotteries were played for real according to their allocation decisions.Winners received the lottery prize (£10) as a bonus payment via Prolific.

Design
To investigate contractualist tendencies experimentally, participants were randomly assigned to one of three conditions, described below.

Main condition.
In the Main condition, the various possible decisions were designed to correspond to characteristically deontological, consequentialist, contractualist or egoist choices.In order for the last five tickets to be distributed, P1 had to destroy one of P2's tickets without their permission.P1 could Refuse to this, thus respecting P2's property rightsa characteristically deontological moveand as a result, the last five tickets were not allocated.P1 could also Donate, i.e., destroying one of P2's tickets and distributing the last five tickets to a third player (P3), selected at random to enter the game.P1 was also informed that, if P3 won, then the prize of the lottery would be doubled to £20.This decision was characteristically consequentialist as it impartially maximized the total expected payoffs of all players.In contrast, P1 could Split the last five tickets with P2 (i.e., by giving them at least one ticket), a characteristically contractualist choice: it was mutually advantageous for both players (no player was worse off in expectation and at least one of them was better off compared to their starting balance) and could not be reasonably rejected by P2.Split was thus the natural or "obvious" solution of a hypothetical bargaining process between the players.Finally, P1 could Keep the five tickets received by destroying P2's ticket, a characteristically egoist choice which maximized P1's expected payoff.A diagram (also presented to participants) describing the different options ("scenarios") for the Main condition is shown in Fig. 1.Diagrams for the other conditions (see below) as well as complete testing materials are available in the Supplemental Material.

Control conditions.
For contractualist theories, the permissibility of an action depends on whether it would be accepted by relevantly affected parties: parties that would be included in the hypothetical agreement about what to do.Thus, we predicted that incentivized decisions and moral judgments would be less including Scanlon's, are closely related to deontology (e.g., Everett et al., 2016).Similarly, the boundaries between consequentialism and deontology are sometimes blurry (as exemplified by rule-utilitarianism, in which rules are justified by the consequences of their being followed).This is not problematic here: following standard practice in moral psychology (Greene, 2014a), our descriptive approach is concerned with what is representative of each tradition rather than on specific theoretical formulations (often incompatible with one another, even within the same tradition) defended in the philosophical literature.In particular we are not arguing that non-philosophers consciously apply sophisticated moral theories (which, in any case, they are not familiar with) when making choices in our games.
A. Le Pargneux et al. characteristically contractualist when the second player was less likely to be identified as an affected party by the first player, making a potential tacit agreement between P1 and P2 less salient.We therefore compared our Main condition with two control conditions in which we reduced the extent to which P2 was likely to be identified as an affected party by P1.In the first control condition (Self-destruction), P1 had to destroy one of their own tickets ("Someone destroys one of P1's tickets without his permission") in order for the last five tickets to be allocated.In this condition, P2 was not harmed and was therefore unlikely to be identified as an affected party.In the second control condition (Thirdparty destruction), someone else destroyed one of P2's tickets, independently of P1's preferred allocation.As a result, P1 was not responsible for the harm done to P2 and was therefore less likely to view P2 as an affected party of P1's actions.Differences between conditions and scenarios are summarized in Table 1 and Table 2.

Participants
The preregistration site is https://osf.io/pkstz.1205 participants (age range: 18-64 years; M = 26.6;SD = 8; 49.6% female; 49.6% male; 0.8% other) were recruited from Prolific and were paid a small amount for their participation; 181 participants were excluded for failing an attention check, as preregistered.The sample size was determined using power analysis as described in the preregistration form.

Procedure
Participants played an economic game in which they chose how to allocate lottery tickets between players.They were randomly assigned to one of three conditions designed to manipulate the extent to which the second player was an affected party of their decision.They were first presented with the rules of the game alongside an illustrative diagram and asked to answer a set of understanding questions.Then, they made their preferred choice (henceforth Decision) and also selected the option that they found most morally acceptable (henceforth Judgment; the order of these two questions was randomized).Finally, participants answered an attention check and supplied their age and gender.As explained in the rules, ten players were selected at random at the end of the study and their lotteries were played for real according to their allocation decisions.Winners received bonus payments via Prolific.The procedures and materials for all studies presented in this paper were approved by the Humanities & Social Sciences Ethics Committee of the  University of Warwick (E-323-01-21).All analyses were conducted using R statistical software (R Core Team, 2022).All participants provided informed consent.Participants from previous studies could not participate in subsequent studies.For details, see Supplemental Material.

Results
For Studies 1 and 2, unless specified, we report analyses conducted on subsets of participants having answered the Judgment or Decision question first, respectively.This is to avoid bias from potential order effects.All statistical tests are two-sided. 5

Judgments
Which scenario was perceived as most morally acceptable?As predicted, in the Main condition, Split (the contractualist scenario) was judged to be the most morally acceptable option, being endorsed by the majority of participants (53% [95% CI: 45%, 61%]), see Fig. 2A.Importantly, 39% ([95% CI: 32%, 47%]) of participants viewed Refuse as the most morally acceptable option and this proportion dropped to 5% ([95% CI: 1%, 8%]) in the Third-party destruction condition (Fig. 2C), in which the deontological concern was no longer present because someone else had destroyed P2's ticket.This suggests that there was indeed some kind of (characteristically deontological) perceived moral prohibition against destroying the other player's ticket without their permission (all other things being equal) in the Main condition.Strikingly, Donate (2% [95% CI: 0%, 4%]) -the characteristically consequentialist scenariowas almost never perceived as most morally acceptable, being selected even less often than Keep (6% [95% CI: 2%, 10%]), the egoistic scenario.Split was also perceived as most morally acceptable in the Self-destruction (56% [95% CI: 49%, 64%]) and Thirdparty destruction (83% [95% CI: 77%, 88%]) conditions, in which Refuse does not serve deontological purposes (i.e., P1 does not violate P2's property rights: either because P1 refuses to destroy one of his own tickets or because P2's ticket has already been destroyed by someone else) and is therefore much less often viewed as most morally acceptable, see Fig. 2B and C.
Were judgments more characteristically contractualist in the Main condition than in the other two conditions?We posit that, for participants selecting Split, the higher the number of tickets they give to the second player, the more characteristically contractualist their decision or judgment is.This is because the higher this number, the more likely it is that the action would be accepted by the affected party (P2).As predicted, we found evidence that judgments were more characteristically contractualist in the Main condition than in the Self-destruction and Third-party destruction conditions according to this measure.
Were incentivized decisions more characteristically contractualist in the Main condition than in the other two conditions?Again, we had hypothesized that decisions would be more characteristically contractualist in the Main condition than in the other conditions, as measured by the number of tickets given to P2 by participants selecting Split.And indeed, participants selecting Split as their preferred scenario gave on average more tickets to P2 in the Main condition (M = 2.27; SD = 0.90) than in the Self-destruction condition (M = 1.82;SD = 0.89) and this difference is statistically significant (Wilcoxon-Mann-Whitney test: W(n 1 = 74, n 2 = 60) = 1517, p < .001,effect size r = 0.287).However, the evidence was more mixed for our comparison with the Third-party destruction condition: we did not find evidence that decisions were * Each scenario is only characteristic of a specific theory for the Main condition.
5 For conciseness we report some of our secondary pre-registered statistical tests (all of them consistent with our predictions) in the Supplemental Material instead of the main text.These relate to distributions of choices being different from what would be expected if participants made their choice at random.
Split which could introduce some potential selection concerns.This issue is difficult to avoid due to the sensitivity of the average number of tickets to the proportion of participants selecting each scenario, which varies substantially with the specifics of each condition (e.g., Refuse is not helpful in Third-party destruction because P2's ticket has already been destroyed by someone else).
We acknowledge this limit of our experimental design.We discuss this issue and provide complementary analyses in the Supplemental Material.
more characteristically contractualist in the Main condition (M = 2.27; SD = 0.90) than in the Third-party destruction condition (M = 2.16; SD = 1.00;W(n 1 = 74, n 2 = 97) = 3322, p = .379,r = 0.0674).We suggest the following potential explanation: determining who counts as an affected party in the Third-party destruction condition (in which it is not P1 but someone else who destroys one of P2's tickets) is not straightforward.Indeed, P2 is likely to be identified as an affected party due to the mere fact of being harmed, even though the harming is not done by P1.In contrast to the Self-destruction condition (in which P2 is not harmed since P1 must destroy one of their own tickets), the status of P2 is ambiguous and it is plausible that the difference between the Main and Third-party destruction conditions was sufficient to influence moral judgments but not incentivized decisions.Overall, we find mixed evidence that incentivized decisions depend on the identification of affected parties, our results being consistent with predictions only for the first (Main vs Self-destruction condition) but not the second (Main vs Third-party destruction condition) comparison.

Study 2
In Study 1 we find that choices reflect contractualist tendencies: many participants make moral judgments and incentivized decisions that correspond to characteristically contractualist choices.Such choices also violate key properties of characteristically deontological (i.e., they do not respect P2's property rights) and consequentialist (i.e., they do not impartially maximize aggregate utility) choices.Moral judgments are also less characteristically contractualist when P2 is less likely to be identified as an affected party by P1, consistent with predictions.In Study 1, payoffs depend on the outcome of a lottery and are therefore uncertain, and this element of chance could influence participants' choices.In Study 2 we test whether the above results also hold when payoffs for each player are certain, and all players receive bonus payments.

Design
Study 2 was a conceptual replication of Study 1: participants played a different version of the same game based on tokens (with a fixed monetary value) instead of lottery tickets.It served two main purposes: replicating our findings with a different sample of Prolific participants (previous participants could not participate) in which all players received bonus payments, and ensuring that the uncertainty of payoffs associated with the lottery design did not drive our findings.

Participants
The preregistration site is https://osf.io/b25m8.1204 participants (age range: 18-80 years; M = 25.7;SD = 8; 48.8% female; 49.0% male; 2.2% other) were recruited from Prolific and were paid a small amount for their participation; 205 participants were excluded for failing an attention check, as preregistered.The sample size was determined using power analysis as described in the preregistration form.

Procedure
The procedure was nearly identical to the procedure described in Study 1. Instead of lottery tickets, participants had to decide how to allocate tokens (with a fixed monetary value) between players.Note that if Donate was selected, P3 received "special tokens" with a higher value (£0.10), ensuring that Donate maximized the total expected payoffs of all players.Otherwise, both study designs were identical.At the end of the study, all participants received bonus payments via Prolific corresponding to the number of tokens in their possession.For details, see Supplemental Material.

Judgments
Which scenario was perceived as most morally acceptable?As predicted, in the Main condition, Split (the contractualist scenario) was judged to be the most morally acceptable option, being endorsed by the majority of participants (75% [95% CI: 69%, 82%]), see Fig. 4A.Importantly, 19% ([95% CI: 13%, 25%]) of participants viewed Refuse as the most morally acceptable option and this proportion dropped to 2% ([95% CI: 1%, 3%]) in the Third-party destruction condition (Fig. 4C), in which the deontological concern was no longer present because someone else had destroyed P2's ticket.Given that, in this version of the experiment, outcomes are certain and tokens are perfectly fungible from a monetary perspective, this observation is consistent with destroying the other player's token being perceived by some participants as violating some sort of (characteristically deontological) moral prohibition in the Main condition.Strikingly, Donate (3% [95% CI: 0%, 5%]) -the characteristically consequentialist scenariowas almost never perceived as most morally acceptable, being selected as often as Keep (3% [95% CI: 0%, 5%]), the egoistic scenario.Split was also perceived as most morally acceptable in the Self-destruction (76% [95% CI: 69%, 82%]) and Third-party destruction (93% [95% CI: 89%, 96%]) conditions, in which Refuse does not serve deontological purposes (i.e., P1 does not violate P2's property rights: either because P1 refuses to destroy one of his own tokens or because P2's token has already been destroyed by someone else) and is therefore much less often viewed as most morally acceptable, see Fig. 4B and C.
Were judgments more characteristically contractualist in the Main condition than in the other two conditions?As predicted, we found evidence that judgments were more characteristically contractualist in the Main condition than in the Self-destruction and Third-party destruction conditions.Participants selecting Split as the most morally acceptable scenario "gave" on average more tickets to P2 in the Main condition (M = 2.99, SD = 0.86) than in the Self-destruction condition (M = 2.12; SD = 0.59; W(n 1 = 128, n 2 = 115) = 2868, p < .001,r = 0.565) and the Third-party destruction condition (M = 2.78, SD = 0.84; W(n 1 = 128, n 2 = 162) = 9082.5,p = .0366,r = 0.123), see Fig. 5A.Overall, consistent with predictions, moral acceptability judgments seem to depend on the identification of affected parties.
Were incentivized decisions more characteristically contractualist in the Main condition than in the other two conditions?Again, we had hypothesized that decisions would be more characteristically contractualist in the Main condition than in the other conditions, as measured by the number of tickets given to P2 by participants selecting Split.And indeed, participants selecting Split as their preferred scenario gave on average more tickets to P2 in the Main condition (M = 2.43; SD = 0.94) than in the Self-destruction condition (M = 1.79;SD = 0.69) and this difference is statistically significant (Wilcoxon-Mann-Whitney test: W(n 1 = 114, n 2 = 97) = 3299, p < .001,effect size r = 0.369).However, as in Study 1, the evidence was more mixed for our comparison with the Third-party destruction condition: we did not find evidence that decisions were more characteristically contractualist in the Main condition (M = 2.43; SD = 0.94) than in the Third-party destruction condition (M = 2.45; SD = 0.82; P2 (W(n 1 = 114, n 2 = 106) = 6168.5,p = .775,r = 0.0194).
Overall, we successfully replicated all the main findings from Study 1 in Study 2 with one key difference: in the Main condition, the proportion of participants selecting the contractualist choice (P(Split) = 69% [95% CI: 62%, 76%]) was higher than in Study 1.We speculate that one explanation for this observation is that splitting tickets was riskier in Study 1: any additional ticket given to the other player could be the winning ticket, increasing P1's probability of not receiving any bonus payment.By contrast, in Study 2, players were certain to win bonus payments and thus Split did not involve a risk of receiving no bonus payment at all.

Study 3
In Studies 1 and 2 many participants' choices reflect contractualist tendencies: they are characteristically contractualist and violate key properties of characteristically deontological (i.e., they do not respect P2's property rights) and consequentialist (i.e., they do not impartially maximize aggregate utility) choices.In Study 3, we test whether asking participants to engage in explicit virtual bargaining reasoninga typically contractualist form of reasoningmakes incentivized decisions more characteristically contractualist.

Design
The primary purpose of Study 3 (n = 355) was to test whether asking participants to engage in explicit virtual bargaining (VB) reasoning before making their Decision (as in Study 1) would lead to more characteristically contractualist decisions.Thus, we asked some participants to mentally simulate a conversation between the players before making their decision.The rules of the game were identical to those of Study 1. Wording was slightly altered such that participants could not know at first if they were about to play the game as P1 or as P2.They were then randomly assigned to one of three conditions.In the control condition, they were directly asked to make their allocation decision (as P1).In the VB-reasoning condition, they were first asked "Imagine that P1 and P2 are allowed to communicate with each other and to decide together about what to do.Please select the option that you think they would choose."Then they had to make their allocation decision (as P1).In the player 2 condition, they were first asked two questions: "Imagine that you are P2.Please select the option that you would want P1 to choose" and "Imagine that you are P2.Please rank (click and drag) each option in order of preference for you from 1 (best) to 8 (worst)."Then they had to make their allocation decision (as P1).

Participants
The preregistration site is https://osf.io/3ydsq.355 participants (age range: 18-55 years; M = 25.6;SD = 8; 49.5% female; 47.4% male; 3.1% other) were recruited from Prolific and were paid a small amount for their participation; 68 participants were excluded for failing an attention check, as preregistered.The sample size was determined using power analysis as described in the preregistration form.

Procedure
Participants played an economic game in which they chose how to allocate lottery tickets between players.The rules of the game were identical to those of Study 1. Wording was slightly altered such that participants could not know at first if they were about to play the game (A) Consistent with predictions, participants selecting Split as the most morally acceptable choice gave more tickets to the second player in the Main condition than in the Self-destruction and Third-party destruction conditions, in which the second player was less likely to be identified as an affected party by the first player.(B) In the Main condition, judgments of moral acceptability were more characteristically contractualist than incentivized decisions as measured by the number of tickets given to the second player by participants selecting Split.(C) In the Main condition, incentivized decisions were more characteristically contractualist when participants answered the Decision question after the Judgment question (After) than when they directly answered the Decision question (Before).Pvalues from Wilcoxon-Mann-Whitney tests (two-sided).Error bars are SEM.
A. Le Pargneux et al. as P1 or as P2.As in Study 1, all participants were presented with the rules of the game alongside an illustrative diagram and asked to answer a set of understanding questions.They were then randomly assigned to one of three conditions as explained in the Design section.Finally, all participants answered an attention check and supplied their age and gender.As explained in the rules, three players were selected at random at the end of the study and their lotteries were played for real according to their allocation decisions.Winners received bonus payments via Prolific.For details, see Supplemental Material.

Results
The primary purpose of Study 3 was to test whether asking participants to engage in explicit virtual bargaining (VB) reasoninga typically contractualist form of reasoningbefore making their Decision (as in Study 1) would lead to more characteristically contractualist decisions.Thus, we asked some participants to mentally simulate a conversation between the players before selecting their preferred scenario.

Exploratory Analyses
We also used this study to learn more about players' preferences.Exploratory analyses revealed that Split was indeed the natural outcome of a hypothetical bargaining process between the players (71% of responses) and that most participants (54%) viewed the option in which P1 gives 3 tickets to P2 as the virtual bargaining solution that the players would agree on.In a third condition ("Player 2"), participants answered two questions about P2's preferences before making their allocation decision.This allowed us to confirm that Split was indeed P2's preferred choice and that Keep (mean rank M = 6.65) and Donate (M = 6.4) were least preferred (see Supplemental Material).Note also that Refuse (M = 5.01, median rank Md = 5) was preferred to Split if P1 gives 1 ticket to P2 (M = 5.58, Md = 5) which is consistent with some participants construing destroying P2's ticket without his permission as morally prohibited, and perceiving the lottery tickets as not completely fungible.Finally, we found that participants selecting Split in the P2-condition (P (Split) = 30% [95% CI: 21%, 39%]; M = 2.83; SD = 1.14) also gave more tickets to P2 on average than in the control condition (W(n 1 = 37, n 2 = 29) = 372, p = .0274,effect size r = 0.272) suggesting that asking players to take P2's perspective before deciding can also lead to more characteristically contractualist decisions.

Study 4
In the lottery ticket game, each scenario was designed to correspond to characteristically deontological, consequentialist, contractualist, or egoistic choices, respectively.We found that many participants show contractualist tendencies in this task: they select the characteristically contractualist scenario to determine the outcome of the game and perceive it as most morally acceptable.In addition, moral judgments are more characteristically contractualist when P2 is less likely to be identified as an affected party by P1.Finally, incentivized decisions are more characteristically contractualist when participants are asked to engage in explicit virtual bargaining reasoning before deciding.But the experimental design of the lottery ticket game does not allow us to go beyond contractualist tendencies and directly test contractualist reasoning.In Studies 4 and 5, we therefore design a different taskthe dice gameto test for the potential influence of contractualist reasoning in moral judgments and incentivized decisions in a morally relevant setting.The dice game is a repeated binary choice task: taken in isolation, neither option (pressing or not pressing, see below) is characteristically deontological, consequentialist, contractualist, or egoistic.But through the introduction of a random device (a colored dice roll) we can test the influence of one form of contractualist reasoning on choices.Specifically, the dicewhich does not affect the payoff matrixcan be used by players to strike a tacit agreement about what to do.Contractualist reasoning makes distinct predictions about what should happen depending on the dice's color, even though, in the absence of communication and feedback, the game is "identical" in all rounds.

The dice game
In this two-player game, players are in symmetrical positions (see Fig. 7) and face a coordination problem.Coordination problems are inherently moral tasks: by involving opportunities for mutually beneficial cooperation, they should be central for morality (Curry, Mullins, & Whitehouse, 2019), and as such have been used to study phenomena such as moral condemnation and attributions of charitability (De Freitas, Thomas, DeScioli, & Pinker, 2019).Under a consequentialist framework, failure to coordinate also brings about clear negative welfare consequences and should thus be reprehensible and straightforwardly discouraged.
In the dice game, players start each round with three credits (credits determine bonus payments).Each player independently decides whether or not to press a button.Pressing the button is a morally debatable action for two reasons.First, because by pressing the button each player steals two credits from the other player.Second, because if neither player presses the button, both earn one additional credit (ending with 4 credits) so pressing prevents each player from earning a small bonus.If both players press, they each steal two credits from each other and none of them earns additional credits.If only one of them presses, each player earns a large bonus of five additional credits (see Fig. 7 for payoff matrix) and the player who pressed steals two credits from the player who did not press.Therefore, the bestbut unequaloutcome (10 and 6 credits) is achieved if only one button is pressed, but the players cannot communicate to coordinate.
Crucially, in certain rounds, there is a relatively obvious tacit agreement available to the players about what to do.Indeed, at the start of each round, each player is (randomly) assigned a color (red or blue)which is common knowledge to both playersand a virtual colored dice is rolled, its outcome (red, blue, or yellow) being shown to both players.Thus, players can use the color of the dice to infer a possible tacit agreement or virtual bargain: "if the outcome of the dice is red or blue, only the player of the corresponding color should press."If the dice roll is neutral (yellow) no such tacit agreement is available.As such, it is possible to manipulate the presence or absence of a potential tacit agreement between the players simply by varying the outcome of the dice roll, while keeping the nature of the action (pressing the button/ stealing credits) and its consequences (the payoff matrix) constant across types of rounds.
Consistent with some players engaging in contractualist reasoning, we predicted that participants would be more likely to press in "same" rounds (the dice roll matches their color) -as prescribed by the virtual bargainthan in "neutral" rounds (the dice roll is yellow) -in which there is no virtual bargain.Similarly, we predicted that participants would be less likely to press in "opposite" rounds (the dice roll matches their opponent's color) -in which pressing is discouraged by the virtual bargainthan in neutral rounds.In addition, we predicted that pressing would be perceived as more morally acceptable in same rounds (when it is prescribed by the virtual bargain) than in neutral rounds; and less morally acceptable in opposite rounds (when it is discouraged by the virtual bargain) than in neutral rounds.

Participants
The preregistration site is https://osf.io/kx39c.1007 participants (age range: 18-80 years; M = 40.5;SD = 14; 48.6% female; 50.1% male; 1.3% other; approval rate greater than 95%, first language: English) were recruited from Prolific and were paid a small amount for their participation; 28 participants were excluded for failing understanding checks, as preregistered.The sample size was determined using power analysis as described in the preregistration form.

Procedure
All participants were informed that they were about to play a game with another randomly selected participant from the same study and that they would register their decisions for six rounds of the game.They were informed that at the end of the study, one of the rounds would be selected at random and played for real with each participant receiving bonus payments according to the number of credits in their possession by the end of that round, which was determined by the registered decisions of the players.Participants read the rules of the game and were also provided with a diagram (see Fig. 7 and Supplemental Material) illustrating the rules of the game and the payoff matrix.They were informed that they had two attempts to correctly answer all seven questions, and that they would be redirected to the end of the study if they failed on both attempts.Then, they registered their decisions for six rounds, which corresponded to all six possible combinations of colors (blue player, blue dice; blue player, yellow dice; blue player, red dice; red player, red dice; red player, yellow dice; red player, blue dice) and were presented in a random order for each participant.For each round, participants were provided with the diagram of the rules of the game, their color, the color of the other player, and the outcome of the virtual dice roll.Each player also received three credits.They answered the following question: "Do you press the button?"(Yes/No).Finally, each participant answered an attention check and supplied their age, gender, and any comments they had about the study.For details, see Supplemental Material.

Pre-registered Analyses
As predicted, we found that participants were more likely to press the button where the dice roll matched their own color ("same" rounds: 63.5% [95% CI: 60.5%, 66.3%]; logistic regression with random intercepts per participant p < .001)than where the dice roll was neutral ("neutral" rounds: 48.3% [95% CI: 45.2%, 51.4%]).Similarly, participants were more likely to press where the dice roll was neutral than where it was of the color of their opponent ("opposite" rounds: 41.4% [95% CI: 38.4%, 44.4%]; logistic regression with random intercepts per participant p < .001),see Fig. 8A.We confirm the same pattern of results with a variety of robustness checks, which include restricting analyses to the first decision of each participant (equivalent to a between-subjects design, see Fig. 8B), and decisions made by the blue or red player only (see Supplemental Material).

Exploratory Analyses
Exploratory analyses revealed that this pattern was driven by 36.7% of participants which acted as typical "virtual bargainers" (pressed the button more in "same" than in "opposite" rounds on average).These participants consistently followed the virtual bargaining strategy: they were substantially more likely to press the button in "same" (90.7%) than in "neutral" (44.2%) and "opposite" (15.2%) rounds (see Fig. 8C).

Study 5
Study 4 presents evidence that contractualist reasoning can influence incentivized decisions in the dice game.In Study 5, we test whether this is also the case for third-party moral judgments.

Participants
Preregistration site is https://osf.io/7ysmz.332 participants (age range: 18-84 years; M = 39.9;SD = 14; 49.7% female; 50.0%male; 0.3% other; approval rate greater than 95%, first language: English) were recruited from Prolific and were paid a small amount for their participation; 16 participants were excluded for failing understanding checks, as preregistered.The sample size was determined using power analysis as described in the preregistration form.

Procedure
All participants were informed that they were about to read about a game and that they would not play the game but answer questions about it.They were also told that if they correctly answered all understanding checks and all attention checks presented in the study, they would receive a small bonus payment.Then, they were informed that the game had already been played by other participants from a different study and that those participants could earn bonus payments based on their decisions.They were told that each participant had played the game once (i.e., one round) with another randomly selected participant.Next, they read about the rules of the game which were as described and identical to those of Study 4. Participants were also provided with a diagram (see Fig. 7 and Supplemental Material) illustrating the rules of the game and the payoff matrix.Next, participants answered a series of seven questions designed to check and improve their understanding of the rules of the game.They were informed that they would have two attempts to correctly answer all seven questions, and that they would be redirected to the end of the study if they failed on both attempts.Then, they were told that they would be presented with 12 different examples of games actually played by participants and that they would answer questions about each of those.For each game, participants were provided with the diagram of the rules of the game and a description of what happened in that game (i.e., the result of the virtual dice roll, whether or not each player pressed the button, and how many credits each player had at the end of that game) and answered the following question using a slider: "To what extent was it morally acceptable for the red/blue player to press the button in this game?Please indicate one number: (0 = Completely unacceptable, 100 = Completely acceptable)."All games were presented in a random order for each participant.Participants saw all twelve (2 player colors * 3 dice colors * 2 buttons) possible combinations of rounds for which either one player or both players pressed their button.Then, each participant answered an attention check.Next, participants were asked the following question (open-ended): "Imagine that two participants (the blue player and the red player) are about to play a different version of the game.Before the dice is rolled, they are allowed to communicate with each other and decide together about what to do.After the dice roll, they can no longer communicate and must decide independently whether or not to press the button.Please describe the strategy that you think they would be most likely to agree on."and wrote their answers in a text box.Then, they answered a different version of the same question (closed-ended format) (last sentence replaced with "Which of the following strategies do you think they would be most likely to agree on?") in which they could select one out of six strategies, one of them corresponding to the virtual bargaining strategy.Finally, each participant supplied their age, gender, and any comments they had about the study.For details, see Supplemental Material.

Virtual bargainers C
Fig. 8. (A) Consistent with contractualist reasoning influencing incentivized decisions, participants were more likely to press their button where the dice roll matched their color ("same") than where it was "neutral."Participants were also less likely to press their button where the dice roll matched the color of the other player ("opposite") than where it was "neutral."P-values from logistic regression with random intercepts per participant.(B) The same pattern was already present when restricting the analysis to the first decision made by each participant (equivalent to a between-subjects design).P-values from logistic regression.(C) 36.7% of participants behaved as "virtual bargainers" and drive the observed pattern at the aggregate level.P-values from logistic regressions with random intercepts per participant.All error bars are SEM.
A. Le Pargneux et al.

Pre-registered Analyses
As predicted, we found that moral acceptability ratings were higher where the dice roll matched the color of the player being judged ("same": M = 79.3 [95% CI: 76.9, 81.7]; linear regression with random intercepts per participant p < .001)than where it was neutral ("neutral": M = 73.0[95% CI: 70.6, 75.4]).Similarly, they were also higher where the dice roll was neutral than where it matched the opponent's color ("opposite": M = 66.8 [95% CI: 64.5, 69.2]; linear regression with random intercepts per participant p < .001),see Fig. 9A.Again, we obtained the same pattern of results when restricting analyses to the first decision of each participant (equivalent to a between-subjects design, see Fig. 9B), and to decisions made by blue or red players only (see Supplemental Material).

Exploratory Analyses
Exploratory analyses revealed that this pattern was driven by 48.7% of participants which acted as typical "virtual bargainers" (individual mean moral acceptability judgments are higher in "same" than in "opposite" games).These participants made moral judgments consistent with contractualism: they found it more morally acceptable to press the button in "same" games (M = 80.2 [95% CI: 78.2, 82.3]) (where doing so is prescribed by the virtual bargain) than in "neutral" games (M = 66.5 [95% CI: 64.4,68.5]) (where there is no obvious tacit agreement about what to do); and less morally acceptable where doing so violates the virtual bargain (M = 51.8[95% CI: 49.7, 53.8]), see Fig. 9C.
Next, when asked to describe the strategy that the players would be most likely to agree on if they could communicate (open-ended question), 26.9% of participants spontaneously mentioned a strategy akin to virtual bargaining (e.g., "if the dice roll is red or blue, only the player of the corresponding color should press").In addition, this strategy was selected by 52% of participants (closed-ended question) as the one that the players would be most likely to agree on if they could communicate (among six strategies, all others being selected by 4% to 18% of participants).
Finally, we also found a significant association between being categorized as a "virtual bargainer" (based on ratings) and spontaneously mentioning the virtual bargaining strategy in the open-ended format question (χ 2 (1, n = 316) = 13.8, p < .001).A similar association is also found between being categorized as a "virtual bargainer" and selecting the virtual bargaining strategy in the closed-ended format question (χ 2 (1, n = 316) = 11.5, p < .001).This constitutes supporting evidence that this strategy is indeed the natural outcome of a hypothetical bargaining process between the players and that some aspects of the virtual bargaining reasoning could perhaps be explicit.

Constraints on Generality
As with most experiments in moral psychology, caution is advised when assessing the generalizability of our findings.First, there are clear limits to the external validity of behavior in economic games (Galizzi & Navarro-Martinez, 2019), and the extent to which our laboratory experiments relate to real-life behavior is largely unknown.Second, our tasks involved brief, anonymous, and low-stakes interactions between strangers without shared history, which only constitute a fraction of morally relevant situations.Third, our studies were conducted using online samples of English-speaking participants which are not representative of the general population and likely to be substantially WEIRD (Henrich, Heine, & Norenzayan, 2010).Such controlled studies have the potential to isolate key cognitive mechanisms underpinning moral cognition, which can most easily be done under rather idealized conditions.But further work is required to establish whether such proposed mechanisms apply to moral cognition more broadly.

General Discussion
We present five preregistered experiments (n = 4103) involving two new experimental games designed to elicit both moral judgments and incentivized decisions in morally relevant settings.In Studies 1, 2, and 3, we present evidence consistent with many participants exhibiting contractualist tendencies (i.e., a propensity to make typically contractualist judgments and decisions).In Studies 4 and 5, we present evidence consistent with contractualist reasoning (i.e., agreement-based cognitive processes) influencing some of our participants' judgments and decisions.Taken together, our results provide some initial empirical support for the descriptive relevance of contractualism in moral judgment and decision making.
In the lottery ticket game (Studies 1-3), many decisions and judgments are characteristically contractualist: they are mutually beneficial, could not be reasonably rejected by the affected parties, and correspond to what participants identify as the likely outcome of a hypothetical negotiation between the players.These choices also violate key properties of characteristically deontological (i.e., they do not respect P2's (A) Consistent with contractualist reasoning influencing moral judgments, pressing the button was perceived as more morally acceptable where the dice roll matched the color of the player being judged ("same") than where it was "neutral."For a given player, pressing the button was also perceived to be less morally acceptable where the dice roll matched the color of their opponent ("opposite") than where it was "neutral."P-values from linear regression with random intercepts per participant.(B) The same pattern was already present when restricting the analysis to the first judgment made by each participant (equivalent to a betweensubjects design).P-values from linear regression.(C) 48.7% of participants behaved as "virtual bargainers", driving the observed pattern at the aggregate level.P-values from linear regressions with random intercepts per participant.Plots: dots are mean moral acceptability judgments for each participant, central bars are means, and boxes represent SEM.
A. Le Pargneux et al. property rights) and consequentialist (i.e., they do not impartially maximize expected utility) choices.Furthermore, consistent with predictions, moral judgments seem to depend on whether the second player is likely to be identified as an affected party to be included in the tacit agreement by the first player.By contrast, far fewer choices are characteristically deontological or consequentialist.Echoing previous findings (Bostyn, Sevenhant, & Roets, 2018;FeldmanHall et al., 2012), we observe systematic differences between moral judgments (what participants think is morally best) and incentivized decisions (what they actually do), with judgments being more characteristically contractualist than decisions.Finally, we elicit more characteristically contractualist decisions by asking participants to engage in explicit virtual bargaining reasoning (Study 3), a typically contractualist form of reasoning, before making their decision.We also observe that decisions are more characteristically contractualist when participants are first asked to select the most morally acceptable option (Studies 1-2) or to consider the other player's preferred scenario (Study 3).
While the lottery ticket game presents evidence that some participants' choices follow contractualist tendencies, its design does not allow us to conclude that contractualist reasoning (explicit or not) is responsible for choices.Indeed, our results could be explained by alternative interpretations which do not appeal to contractualist reasoning.
First, participants may try to balance egoistic concerns (i.e., maximizing their own payoff) with fairness concerns (e.g., inequity aversion) -or other social preferences (Falk, Fehr, & Fischbacher, 2003;Fehr & Schmidt, 2006) -essentially assigning a (greater) weight to their own payoff and a (smaller) weight to the payoff of the other(s) player(s) in their choices.In this interpretation, the role of fairness may be rather limited: in Studies 1 and 2, respectively 70.1% and 63.9% of decisions (in the Main condition) do not correspond to one of the three "fairest" options (i.e., one ticket/token difference between player 1 and player 2).
Second, it is also possible that participants try to trade off or combine deontological (i.e., not infringing on P2's property rights) and consequentialist concerns (i.e., allocating as many tickets as possible). 7But note that it is precisely because they cannot be traded off (Kagan, 2018) that we usually describe concerns as genuinely "deontological" (what makes them "deontological" is that they represent an uninfringeable or absolute constraint on action, no matter the consequences).Similarly, what makes a concern genuinely "consequentialist" is its non-negotiable commitments to impartiality (i.e., not favoring oneself or one's kin) and aggregate utility maximization 8 (not just taking utility calculations into account) (Everett & Kahane, 2020).
Despite these caveats, these two models stand out as plausible cognitive processes responsible for participants' choices.They do not make explicit reference to agreement-or negotiation-based reasoning, and they cannot definitely be ruled out based on the data presented here.As such, each of them deserves further attention and will require additional research to conclusively address.
On the other hand, one reason people may explicitly or implicitly combine competing concerns in one of these two ways is because they constitute cognitively efficient (i.e., resource rational) ways to approximate the outcome of explicit negotiation (Levine, Chater, Tenenbaum, & Cushman, 2024).Cognitive processes, heuristics, or intuitions that lead to such contractualist approximations could be the result of biological and/or cultural evolution (André et al., 2022) or emerge from prior reasoning, experience, and learning (Le Pargneux & Cushman, 2023).As such, these two alternative models integrate well within a broader contractualist understanding of moral cognition (i.e., at the "ultimate" rather than "proximate" level of analysis).Another possibility is that contractualist reasoning is precisely one mechanism that can be used to tradeoff competing considerations.Under this view, perhaps "it is because the other player would agree to it" that "splitting tickets is fair" (e.g., selfish versus fairness preferences) or "that destroying the other player's ticket is ok" (e.g., deontological versus consequentialist concerns).In fact, fairness is at the core of some contractualist theories (e.g., Rawls, 1971) and the relationship between fairness considerations and what affected parties would agree to do is complex: an action is more likely to be perceived as fair if affected parties are likely to agree to it; but affected parties are also more likely to reject actions that lead to unequal, unequitable, or unfair allocation of resources.
With these limitations in mind, in Studies 4 and 5 we aim to go beyond contractualist tendencies and test for the potential influence of a distinctively contractualist pattern of reasoning on moral judgment and decision making using a different task.In the dice game neither move (pressing or not pressing) is characteristically deontological, consequentialist, contractualist, or egoistic.But by introducing a random devicea colored dice rollwe can isolate the influence of one form of contractualist reasoning (described in detail below) on choices.Indeed, the dice's color does not affect the payoff matrix and players do not know what their partner did in previous rounds.As such, unless they recognize that they can tacitly agree to use the dice as a coordination devicein other words, unless they engage in contractualist reasoning we should expect them to be equally likely to press in all types of rounds (same, opposite, neutral).But this is not what we observe.In Study 4, in the absence of means of communication, many participants' incentivized decisions are consistent with players acting as prescribed by the tacit agreement or virtual bargain ("in red and blue rounds, press only if the dice corresponds to your color").In Study 5, aggregate thirdparty moral judgments also reflect a tendency to moralize violations of this tacit agreement: the same action (pressing the button), with the same payoff matrix, is perceived as more morally appropriate when it respects rather than violates the virtual bargain concerning how behavior should be coordinated in relation to the outcome of the dice.
Genuine recognition of the virtual bargaining (color-based) strategy as viable seems to require engaging in joint reasoning to figure out the "agreed" plan.Indeed, pressing more (less) when it is prescribed (discouraged) by the tacit agreement is not just a matter of "guessing" the opponent's move.Adopting the virtual bargaining strategy is only beneficial if one expects the opponent to also adopt it.And, in the absence of joint reasoning, each player's prediction would depend on their partner's prediction of how they themselves would act, and an infinite regress would ensue (Chater et al., 2022).The strategy implies recognizing that "we" (the players) have mutual interests (the large bonus), share a common goal (coordination), and must play different roles to achieve itand that this plan is sufficiently "obvious".This joint reasoning is aptly labeled contractualist for two reasons.It corresponds to what players would agree to do if they could negotiate.Moreover, it fundamentally consists in recognizing that players can tacitly agree to use the dice as a coordination device.
Interestingly, the virtual bargaining strategy is perceived as the most morally appropriate despite involving stealing credits and leading to unfair allocations.Of course, non-contractualist concerns also matter in this game and, importantly, rules and consequences will affect what people will be willing to agree.But the concept of joint agreement seems required to explain how people can coordinate their actions based on the dice's color.In fact, this strategy is effective to achieve not only "characteristically" contractualist outcomes but also other objectives.Thus, behaviorally, purely selfish, altruistic, or utilitarian players might very 7 Note that if participants were really concerned with trading off deontological concerns with impartial aggregate expected payoff maximization, we would expect the proportion of participants selecting Donate to substantially go up when the deontological concern is no longer relevanti.e., in the Selfdestruction and Third-party destruction conditions.But the proportion of participants selecting Donate remains low across conditions, questions, and studies (between 4% and 9% for Decision and 2% and 3% for Judgment).
8 Without these requirements, the term "consequentialist" is arguably much less meaningful and usefulafter all, many other theories, including egoistic ones (Sinnott-Armstrong, 2023), can be labeled as "consequentialist" if all is meant by that term is that they involve some computations of possible consequences.
well adopt it.Butunless they do so randomly, "mindlessly" or by appeal to "magical" thinking or superstition, which seems to us implausibleusing the color-based strategy implies having recognized that the dice can be used as a coordination device, and therefore to have engaged in contractualist joint reasoning beforehand.In such circumstances, agreement-based reasoning thus precedes and underlies the satisfaction of preferences.In other words, a participant that adopts the color strategy in order to pursue selfish or utilitarian objectives does so because they acknowledge (at some level) that the players can tacitly agree to use the dice as a coordination device.This in turn constitutes evidence that they have engaged in the form of agreement-based jointreasoning just described (even if unconsciously).With its more tightly controlled and constrained experimental paradigm, it seems therefore that the dice game can be used to isolate the influence of one specific form of contractualist reasoning on moral judgment and decision making while keeping rule-, consequence-and fairness-based concerns constant.
As a problem of coordination, the dice game is also a prototypical moral problem: if morality evolved to solve the problem of cooperation (Tomasello & Vaish, 2013), then coordination for mutual advantage is expected to be a central problem for moral cognition and one of the core domains of morality (Curry, 2016).Consistent with this idea, some participants perceived pressing the button as morally unacceptable in all types of rounds.Moreover, pressing the button is perceived as less (more) morally acceptable when it violates (respects) the tacit agreement about what to do, which confirms that the task is indeed construed in ethical terms.And indeed we show that the same action (pressing), with the same payoff matrix, is moralized by third-party judges depending on the dice's color (Study 5), i.e., according to whether players respect or violate the tacit agreement.This would not be expected in a morally neutral task.
Overall, our paper contributes to the moral psychology literature by presenting initial empirical evidence for the descriptive relevance of contractualism in both moral judgments and incentivized decisions.It also introduces two novel experimental paradigms that researchers can use to investigate various aspects of cognitive contractualism alongside well-established moral considerations.Taken together, our findings suggest that in certain morally relevant situations we sometimes act as if we had been able to agree about what to do, without the need to communicate, in a typically contractualist fashion.Intuitively, it seems that violating tacit agreements is morally inappropriate or reprehensible and may trigger emotional moral reactions.Such tacit agreements may operate in the background of many social interactions involving coordinationfrom navigating a crowded train carriage to moving heavy furniture or exchanging gifts (Chater et al., 2022).Thus, cognitive contractualism could shed light on the moral psychology of low-stakes and fleeting social interactions.It is interesting to ask how far such reasoning might extend to high-stakes ethical concerns, as the contractualist philosophical tradition would suggest.
As noted above, further work is required to adjudicate between several candidate processes that could be responsible for observed contractualist tendencies in the lottery ticket game.Future research is also needed to delimitate the circumstances under which the form of contractualist reasoning described in the dice game is likely to occur, and the situations and individual characteristics and differences that can foster it.Our results provide initial evidence that people sometimes exhibit contractualist tendencies and can engage in contractualist reasoning in morally relevant contexts.But in which circumstances and how often they do so remains largely unknown at this stageeven though the contractualist lens can account for a number of empirical phenomena documented across multiple disciplines, see André et al. (2022).In addition, future research should explore if and when virtual bargaining processes can be conscious and explicit, a question that cannot be addressed with the present data.Just as with planning our individual actions, we should expect that planning joint actions through virtual bargaining will largely be implicit and non-conscious.But it seems likely that people can and sometimes do verbalize such reasoning.Furthermore, the present data cannot entirely rule out that some participants in the dice game may be complying with an inferred communicative intent from the experimenter.We view this possibility as unlikely given the reported effect sizes, the fact that in Study 4 choices are incentivized and determine bonus payments, and that Study 5 is exclusively dedicated to third-party moral judgments.Nevertheless, this question could be investigated further in future research on this paradigm.
Finally, as previously suggested, a comprehensive theory of moral cognition is likely to incorporate aspects of contractualism, consequentialism, and deontology, perhaps by reconciling them in a single "Psychological Triple Theory" (Levine, Chater, Tenenbaum, & Cushman, 2024;Parfit, 2011).Here, we do not argue that contractualist tendencies and/or reasoning are sufficient to explain morality.To the contrary, rule-, consequence-and fairness-based considerations all play a key role, both in the above experimental paradigms, and in moral cognition in a variety of contexts.Our findings suggest that clarifying how contractualist tendencies and reasoning relate to traditional accounts in moral psychology may prove crucial to providing an integrated understanding of moral cognition.

Fig. 1 .
Fig. 1.Diagram of possible choices for the Main condition of Study 1 presented to participants (scenario 1 = Refuse; scenario 2 = Donate; scenario 3 with 0 tickets given to P2 = Keep; scenario 3 with 1 to 5 tickets given to P2 = Split).

Fig. 2 .
Fig.2.Incentivized decisions and moral judgments reflect contractualist tendencies in the lottery ticket game.(A) In the Main condition, many incentivized decisions were characteristically contractualist (Split) or egoist (Keep), and fewer were characteristically deontological (Refuse) or consequentialist (Donate).The contractualist choice (Split) was endorsed by the majority of participants as the most morally acceptable one, followed by the deontological choice (Refuse).Similarly, Split and Keep were the scenarios most often selected by participants in the Self-destruction (B) and the Third-party destruction (C) conditions, with Split being unambiguously perceived as most morally acceptable in both conditions.Error bars are standard errors of the mean (SEM).

Fig. 4 .
Fig.4.Incentivized decisions and moral judgments reflect contractualist tendencies in the tokens game.(A) In the Main condition, many incentivized decisions were characteristically contractualist (Split) and fewer were characteristically egoist (Keep), deontological (Refuse), or consequentialist (Donate).The contractualist choice (Split) was endorsed by the majority of participants as the most morally acceptable one, followed by the deontological choice (Refuse).Similarly, Split and Keep were the scenarios most often selected by participants in the Self-destruction (B) and the Third-party destruction (C) conditions, with Split being unambiguously perceived as most morally acceptable in both conditions.Error bars are SEM.
Fig. 5. (A)Consistent with predictions, participants selecting Split as the most morally acceptable choice gave more tickets to the second player in the Main condition than in the Self-destruction and Third-party destruction conditions, in which the second player was less likely to be identified as an affected party by the first player.(B) In the Main condition, judgments of moral acceptability were more characteristically contractualist than incentivized decisions as measured by the number of tickets given to the second player by participants selecting Split.(C) In the Main condition, incentivized decisions were more characteristically contractualist when participants answered the Decision question after the Judgment question (After) than when they directly answered the Decision question (Before).Pvalues from Wilcoxon-Mann-Whitney tests (two-sided).Error bars are SEM.

Fig. 6 .
Fig. 6.Incentivized decisions were more characteristically contractualist when participants were first asked to engage in explicit virtual bargaining reasoning (by imagining what the players would agree to do if they were able to communicate with each other) or to rank each option according to what they thought the affected party (P2) would prefer.P-values from Wilcoxon-Mann-Whitney tests (two-sided).Error bars are SEM.
Fig. 9. (A)Consistent with contractualist reasoning influencing moral judgments, pressing the button was perceived as more morally acceptable where the dice roll matched the color of the player being judged ("same") than where it was "neutral."For a given player, pressing the button was also perceived to be less morally acceptable where the dice roll matched the color of their opponent ("opposite") than where it was "neutral."P-values from linear regression with random intercepts per participant.(B) The same pattern was already present when restricting the analysis to the first judgment made by each participant (equivalent to a betweensubjects design).P-values from linear regression.(C) 48.7% of participants behaved as "virtual bargainers", driving the observed pattern at the aggregate level.P-values from linear regressions with random intercepts per participant.Plots: dots are mean moral acceptability judgments for each participant, central bars are means, and boxes represent SEM.

Table 2
Study 1: Description of Scenarios per Condition.*