Large-scale cooperation driven by reputation, not fear of divine punishment

Reputational considerations favour cooperation and thus we expect less cooperation in larger communities where people are less well known to each other. Some argue that institutions are, therefore, necessary to coordinate large-scale cooperation, including moralizing religions that promote cooperation through the fear of divine punishment. Here, we use community size as a proxy for reputational concerns, and test whether people in small, stable communities are more cooperative than people in large, less stable communities in both religious and non-religious contexts. We conducted a donation game on a large naturalistic sample of 501 people in 17 communities, with varying religions or none, ranging from small villages to large cities in northwestern China. We found that more money was donated by those in small, stable communities, where reputation should be more salient. Religious practice was also associated with higher donations, but fear of divine punishment was not. In a second game on the same sample, decisions were private, giving donors the opportunity to cheat. We found that donors to religious institutions were not less likely to cheat, and community size was not important in this game. Results from the donation game suggest donations to both religious and non-religious institutions are being motivated by reputational considerations, and results from both games suggest fear of divine punishment is not important. This chimes with other studies suggesting social benefits rather than fear of punishment may be the more salient motive for cooperative behaviour in real-world settings.


Introduction
-There are some recent experiments looking at the effect of group size on cooperation that I think should be mentioned (https://www.nature.com/articles/srep07937; https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0131419; https://www.nature.com/articles/s41598-019-41988-3). These experiments are particularly relevant because, as in the current manuscript, they look at the effect of group size on cooperation in the aseptic setting of a laboratory experiment, rather than in the field. There are also studies looking at group size effect on cooperation using computer simulations, which might be mentioned (https://journals.aps.org/pre/abstract/10.1103/PhysRevE.84.047102).
-I am pretty sure that there is quite a lot of literature looking at the correlation between religiosity and pro sociality. This literature should be reviewed.
-The presentation would be clearer if the authors spell out their hypotheses. They could call them H1, H2, etc.
Participants -The fact that participants were selected at random in public areas does not imply that the sample is representative. For example, if one selects people during the morning, then one does not have represented people who usually go out in the evening and nights. And so on. Plus, it is really unlikely that people choose other people really at random. This is not a big issue, though, just eliminate any reference to representative samples.
Method -The description of the method is very confusing: the terminology Experiment 1 and Experiment 2 makes readers think that these are actually two different experiments. They are not. They are actually the same experiments with two stages. They should be call Stage 1 and Stage 2.
-Please include more details about the measures of religiosity. Since these are important measures, detailed should be included in the main text and not in the SM.

Results
-Since recent meta-analyses show that women donate more than men (https://www.ncbi.nlm.nih.gov/pubmed/26913619; https://www.sciencedirect.com/science/article/pii/S0165176518301952), I think that the authors should discuss gender differences in donations in more details, and relate this with earlier research -Since recent meta-analyses show that women are more honest than men (http://journal.sjdm.org/18/18619a/jdm18619a.html; https://psycnet.apa.org/record/2018-66786-001), I think that the authors should discuss gender differences in cheating in more details, and relate this with earlier research -The analysis would be more convincing if the authors add an interaction term to look at potential differences in the donation game vs the cheating game. It is not indeed very clear that some results (e.g., the relation between community size and donation/cheating) hold in one cases but not in the other one.

Discussion
-"We also detected the majority donated all the money to the institutions in our free donation experiment, in contrast to findings that people donate between half to nothing in some other public goods game experiments or dictator games [12,46,47]". This is not very surprising: donating to an institution is very different from donating to another person in the dictator game.
-"cooperate in an uncalculating decision-making to signal their generosity for reputation concerns, behaving in a calculating way is generally perceived as a sign of doubt or uncertainty [48,49]". Another paper in support of the fact that uncalculating decision-making is a signal of altruism: https://www.sciencedirect.com/science/article/pii/S2214804316300878 General comment -Please revise your English. I've noticed several typos and mistakes.

Review form: Reviewer 2
Is the manuscript scientifically sound in its present form? No

Do you have any ethical concerns with this paper? No
Have you any concerns about statistical analyses in this paper? No

Recommendation?
Major revision is needed (please make suggestions in comments)

Comments to the Author(s)
In this manuscript, the authors conduct two donation experiments (free donation game and dice allocation game) on a large naturalistic sample of 501 people in 17 communities, with varying religions or none, ranging from small villages to large cities. The authors want to know whether people in small, stable communities are more cooperative than people in large, less stable communities. They make four predictions and test them. The results show that donations to both religious and non-religious institutions are being motivated by reputational considerations. Besides, fear of divine punishment is not the more salient motive for cooperative behavior. Overall, this is an interesting study. However, there are some remaining issues with the manuscript, requiring some answers.
Major issues: 1) First, I suggest the authors explain why the number of rounds of two games is set to 2. Are the environments of these two rounds the same? Are onlookers consistent?
2) The authors claim that reputational considerations can be more salient in small communities where the people have the opportunity to get to know each other. But in my opinion, it's not just reputation that works here. There are also other factors, such as kin selection. I believe that excluding the influence of other factors will lead to a better understanding of the present results. 3) In the experimental design stage for free donation game, the whole game process is observable to onlookers. I have some questions. Is the onlooker a game participant or a passer-by? Are these onlookers familiar with the game player? Are game designers included? 4) For Dice allocation game, the authors design that the dices were unobservable by anyone except the participant. Thus I want to know how the authors record the number of the participants who cheated in the game. 5) How can the authors draw the following conclusion: People with higher self-reported religiosity were more likely to donate all the money (line 12 of page 16)? What does self-reported religiosity mean? I didn't find it again in the article. 6) In figure 3, the authors only compare the proportion of donating all in smaller communities and large communities, and claim that those in smaller communities donating all 13.8% are more than those in large communities. However, for other donations (0,2,4,6,8), large communities have more advantages than smaller communities. I think that it is better for authors to describe these results and explain them. 7) In the manuscript, the authors mention divine punishment. It would be interesting to discuss the relationship between divine punishment and the costly punishment (e.g., New J. Phys. 16 (2014) 083016, Phys. Rev. E 92 (2015) 012819, and PLoS Comput. Biol. 14 (2018) e1006347).

19-Jun-2019
Dear Dr Ge, The editors assigned to your paper ("Large-scale cooperation driven by reputation, not fear of divine punishment") have now received comments from reviewers. We would like you to revise your paper in accordance with the referee and Associate Editor suggestions which can be found below (not including confidential reports to the Editor). Please note this decision does not guarantee eventual acceptance.
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Once again, thank you for submitting your manuscript to Royal Society Open Science and I look forward to receiving your revision. If you have any questions at all, please do not hesitate to get in touch. Comments to the Author(s) In this manuscript, the authors report a large experiment (N=501) exploring the effect of community size and religiosity on donations and cheating. The results show that donations to both religious and non-religious institutions are motivated by reputational concerns. The same result does not hold in the domain of cheating. Furthermore, neither donations nor cheating are driven by fear of divine punishment.

Introduction
-There are some recent experiments looking at the effect of group size on cooperation that I think should be mentioned (https://www.nature.com/articles/srep07937; https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0131419; https://www.nature.com/articles/s41598-019-41988-3). These experiments are particularly relevant because, as in the current manuscript, they look at the effect of group size on cooperation in the aseptic setting of a laboratory experiment, rather than in the field. There are also studies looking at group size effect on cooperation using computer simulations, which might be mentioned (https://journals.aps.org/pre/abstract/10.1103/PhysRevE.84.047102).
-I am pretty sure that there is quite a lot of literature looking at the correlation between religiosity and pro sociality. This literature should be reviewed.
-The presentation would be clearer if the authors spell out their hypotheses. They could call them H1, H2, etc.
Participants -The fact that participants were selected at random in public areas does not imply that the sample is representative. For example, if one selects people during the morning, then one does not have represented people who usually go out in the evening and nights. And so on. Plus, it is really unlikely that people choose other people really at random. This is not a big issue, though, just eliminate any reference to representative samples.
Method -The description of the method is very confusing: the terminology Experiment 1 and Experiment 2 makes readers think that these are actually two different experiments. They are not. They are actually the same experiments with two stages. They should be call Stage 1 and Stage 2.
-Please include more details about the measures of religiosity. Since these are important measures, detailed should be included in the main text and not in the SM.

Results
-Since recent meta-analyses show that women donate more than men (https://www.ncbi.nlm.nih.gov/pubmed/26913619; https://www.sciencedirect.com/science/article/pii/S0165176518301952), I think that the authors should discuss gender differences in donations in more details, and relate this with earlier research -Since recent meta-analyses show that women are more honest than men (http://journal.sjdm.org/18/18619a/jdm18619a.html; https://psycnet.apa.org/record/2018-66786-001), I think that the authors should discuss gender differences in cheating in more details, and relate this with earlier research -The analysis would be more convincing if the authors add an interaction term to look at potential differences in the donation game vs the cheating game. It is not indeed very clear that some results (e.g., the relation between community size and donation/cheating) hold in one cases but not in the other one.

Discussion
-"We also detected the majority donated all the money to the institutions in our free donation experiment, in contrast to findings that people donate between half to nothing in some other public goods game experiments or dictator games [12,46,47]". This is not very surprising: donating to an institution is very different from donating to another person in the dictator game.
-"cooperate in an uncalculating decision-making to signal their generosity for reputation concerns, behaving in a calculating way is generally perceived as a sign of doubt or uncertainty [48,49]". Another paper in support of the fact that uncalculating decision-making is a signal of altruism: https://www.sciencedirect.com/science/article/pii/S2214804316300878 General comment -Please revise your English. I've noticed several typos and mistakes.
Reviewer: 2 Comments to the Author(s) In this manuscript, the authors conduct two donation experiments (free donation game and dice allocation game) on a large naturalistic sample of 501 people in 17 communities, with varying religions or none, ranging from small villages to large cities. The authors want to know whether people in small, stable communities are more cooperative than people in large, less stable communities. They make four predictions and test them. The results show that donations to both religious and non-religious institutions are being motivated by reputational considerations. Besides, fear of divine punishment is not the more salient motive for cooperative behavior. Overall, this is an interesting study. However, there are some remaining issues with the manuscript, requiring some answers.
Major issues: 1) First, I suggest the authors explain why the number of rounds of two games is set to 2. Are the environments of these two rounds the same? Are onlookers consistent?
2) The authors claim that reputational considerations can be more salient in small communities where the people have the opportunity to get to know each other. But in my opinion, it's not just reputation that works here. There are also other factors, such as kin selection. I believe that excluding the influence of other factors will lead to a better understanding of the present results.
3) In the experimental design stage for free donation game, the whole game process is observable to onlookers. I have some questions. Is the onlooker a game participant or a passer-by? Are these onlookers familiar with the game player? Are game designers included? 4) For Dice allocation game, the authors design that the dices were unobservable by anyone except the participant. Thus I want to know how the authors record the number of the participants who cheated in the game. 5) How can the authors draw the following conclusion: People with higher self-reported religiosity were more likely to donate all the money (line 12 of page 16)? What does self-reported religiosity mean? I didn't find it again in the article. 6) In figure 3, the authors only compare the proportion of donating all in smaller communities and large communities, and claim that those in smaller communities donating all 13.8% are more than those in large communities. However, for other donations (0, 2, 4, 6, 8), large communities have more advantages than smaller communities. I think that it is better for authors to describe these results and explain them. 7) In the manuscript, the authors mention divine punishment. It would be interesting to discuss the relationship between divine punishment and the costly punishment (e.g., New J. Phys. 16 (2014) 083016, Phys. Rev. E 92 (2015) 012819, and PLoS Comput. Biol. 14 (2018) e1006347).

Comments to the Author(s)
Thanks for addressing all my comments.

Comments to the Author(s)
In the revised manuscript, the authors have addressed my comments accordingly, and I would like to recommend the publication of the work in Royal Society Open Science.

29-Jul-2019
Dear Dr Ge, I am pleased to inform you that your manuscript entitled "Large-scale cooperation driven by reputation, not fear of divine punishment" is now accepted for publication in Royal Society Open Science.
You can expect to receive a proof of your article in the near future. Please contact the editorial office (openscience_proofs@royalsociety.org and openscience@royalsociety.org) to let us know if you are likely to be away from e-mail contact. Due to rapid publication and an extremely tight schedule, if comments are not received, your paper may experience a delay in publication.
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Introduction
-There are some recent experiments looking at the effect of group size on cooperation that I think should be mentioned (https://www.nature.com/articles/srep07937; https://journals.plos.org/plosone/article?i d=10.1371/journal.pone.0131419; https://www.nature.com/articles/s41598-019-41988-3). These experiments are particularly relevant because, as in the current manuscript, they look at the effect of group size on cooperation in the aseptic setting of a laboratory experiment, rather than in the field. There are also studies looking at group size effect on cooperation using computer simulations, which might be mentioned (https://journals.aps.org/pre/abstract/10.1103/PhysRevE.84.047102).

Response: we thank reviewer 1 for helpful comments and suggestions. We have cited the suggested paper.
-I am pretty sure that there is quite a lot of literature looking at the correlation between religiosity and pro sociality. This literature should be reviewed.

Response: we have added references in Introduction section : "Multiple facets of religion have emphasized its role as drivers of prosociality [27-31], but empirical findings on the relationship between religiosity and prosocial behaviour are mixed [32-35]."
-The presentation would be clearer if the authors spell out their hypotheses. They could call them H1, H2, etc.

Response: we have added H1, H2, H3, H4 in the end of Introduction section and echoed them in our results section.
Participants -The fact that participants were selected at random in public areas does not imply that the sample is representative. For example, if one selects people during the morning, then one does not have represented people who usually go out in the evening and nights. And so on. Plus, it is really unlikely that people choose other people really at random. This is not a big issue, though, just eliminate any reference to representative samples.

Response: we have deleted any words about "representative" in 2.1 Participants section.
Method -The description of the method is very confusing: the terminology Experiment 1 and Experiment 2 makes readers think that these are actually two different experiments. They are not. They are actually the same experiments with two stages. They should be call Stage 1 and Stage 2. Figure 1).

Response: we have changed the terminology Experiment 1 and Experiment 2 to "free donation game" and "dice allocation game" to make it more clear, which means two games of one experiment. We didn't call them Stage 1 and Stage 2 given we call stage1 as "Choosing institutions" and stage2 as "Experiment" (As shown in
-Please include more details about the measures of religiosity. Since these are important measures, detailed should be included in the main text and not in the SM.

At the beginning of 2.3 Statistical analysis we added "Variables measuring participants' religiosity are named as "Importance of religion" …… "Religious institution distance";
Moreover, we move our PCA of religiosity to main text as Table 1.

Results
-Since recent meta-analyses show that women donate more than men (https://www.ncbi.nlm.nih.gov/pubmed/26913619; https://www.sciencedirect.com/sci ence/article/pii/S0165176518301952), I think that the authors should discuss gender differences in donations in more details, and relate this with earlier research Response: we have discussed gender differences and added suggested literatures in discussion section as "Furthermore, some previous studies revealed substantial gender differences in donation behaviour…… gender difference in generosity".

Response: we have discussed gender differences in dice allocation game and added suggested literatures in discussion section as "Likewise, in contrast to findings that females…… not gender factor of individual level".
-The analysis would be more convincing if the authors add an interaction term to look at potential differences in the donation game vs the cheating game. It is not indeed very clear that some results (e.g., the relation between community size and donation/cheating) hold in one case but not in the other one.

Discussion
-"We also detected the majority donated all the money to the institutions in our free donation experiment, in contrast to findings that people donate between half to nothing in some other public goods game experiments or dictator games [12,46,47]". This is not very surprising: donating to an institution is very different from donating to another person in the dictator game.

Response: we have deleted this sentence.
-"cooperate in an uncalculating decision-making to signal their generosity for reputation concerns, behaving in a calculating way is generally perceived as a sign of doubt or uncertainty [48,49]". Another paper in support of the fact that uncalculating decision-making is a signal of altruism: https://www.sciencedirect.com/science/article/pii/S2214804316300878

Response: we have added the ref to this discussion part.
General comment -Please revise your English. I've noticed several typos and mistakes.

Response: we have proofread the whole paper and revised these grammatical mistakes.
In this manuscript, the authors conduct two donation experiments (free donation game and dice allocation game) on a large naturalistic sample of 501 people in 17 communities, with varying religions or none, ranging from small villages to large cities. The authors want to know whether people in small, stable communities are more cooperative than people in large, less stable communities. They make four predictions and test them. The results show that donations to both religious and nonreligious institutions are being motivated by reputational considerations. Besides, fear of divine punishment is not the more salient motive for cooperative behavior. Overall, this is an interesting study. However, there are some remaining issues with the manuscript, requiring some answers.
Major issues: 1) First, I suggest the authors explain why the number of rounds of two games is set to 2. Are the environments of these two rounds the same? Are onlookers consistent?

Onlookers varied between rounds, apart from which the environments of these two rounds were the same. We have added more details about calculation of onlookers in our 2.2.1 Free donation game as "The number of onlookers……"
2) The authors claim that reputational considerations can be more salient in small communities where the people have the opportunity to get to know each other. But in my opinion, it's not just reputation that works here. There are also other factors, such as kin selection. I believe that excluding the influence of other factors will lead to a better understanding of the present results.

The local institution they donated to could benefit their kin but the effect could be diluted by people who aren't, so that kin selection would not be as important as reputation.
We also referred to some relevant literatures ( such as Henrich J et al. 2010

3)
In the experimental design stage for free donation game, the whole game process is observable to onlookers. I have some questions. Is the onlooker a game participant or a passer-by? Are these onlookers familiar with the game player? Are game designers included?

4)
For Dice allocation game, the authors design that the dices were unobservable by anyone except the participant. Thus I want to know how the authors record the number of the participants who cheated in the game.

5)
How can the authors draw the following conclusion: People with higher selfreported religiosity were more likely to donate all the money (line 12 of page 16)? What does self-reported religiosity mean? I didn't find it again in the article.

6)
In figure 3, the authors only compare the proportion of donating all in smaller communities and large communities, and claim that those in smaller communities donating all 13.8% are more than those in large communities. However, for other donations (0, 2, 4, 6, 8), large communities have more advantages than smaller communities. I think that it is better for authors to describe these results and explain them.

Response: We have added this analysis in supplementary Table 7, which contains a binomial component predicting whether donating their full stake to institution and a count component (here, with a poisson distribution) predicting the magnitude of money donated for those who didn't donate all.
We explained it in Results section as "Results are robust when using the donation magnitude of those who didn't donate the full stake as dependent variable (see Table S7). Living in large communities and conducting more religious practice are reliably associated with higher donation amounts, but belief in divine punishment and reward has no overall effect".

Response: we have added these suggested references and discussed more about it in our Discussion section as "Although theoretical modeling and lab experiments demonstrate …… costly punishment in addressing common-pool resource or collective actions dilemmas [79-83]".
Minor issues: 1) In lines 37&38 of page 5, there should be a space between "[13]," and "but".

2)
In lines 14&15 of page 8, there should be a space between "1)." and "This".

3)
In lines 12&13 of page 12, "All the dice were…"should be changed to "All the dices were…".

Response: we made all the changes in wording suggested.
For the 4th issue, we used second-order Akaike Information Criterion to explain the full name of AICc, which is used for our dice allocation game analysis given small sample size (17 community level data).