第三方惩罚对合作的溢出效应：基于社会规范的解释

doi:10.3724/SP.J.1041.2021.00758

摘要/Abstract

摘要：

第三方惩罚对合作的维系可能来自经济功能或规范提示功能。先前研究没有区分这两种功能, 因而未能回答：当惩罚不足以影响违规收益时, 是否还能促进合作?实验1 (N = 252)发现即使第三方惩罚无法降低违规收益, 依然能抑制自利行为。实验2 (N = 179)发现受过惩罚的违规者在其后的独裁者博弈表现出了更高的合作水平。2(是否旁观惩罚)×2(旁观前后)设计的实验3 (N = 179)显示, 旁观惩罚后被试的合作水平显著高于旁观前, 也高于未旁观惩罚的被试。后两个实验中, 社会规范在惩罚与合作之间均起中介作用。这进一步证实惩罚对合作的促进在很大程度上是通过规范激活来实现的, 并存在两种溢出效应：惩罚抑制了曾经的违规者(纵向溢出效应)和旁观者(横向溢出效应)在新博弈情境下的自私行为。这两种溢出效应的发现补充了文献中占主导地位的经济学解释, 并为理解人类社会长时间、大规模的合作提供了新视角。

关键词: 第三方惩罚, 社会规范, 合作, 聚焦理论, 溢出效应

Abstract:

A large body of experimental evidence demonstrates that in presence of third-party punishers, cooperators can gain higher payoffs than defectors. As a result, third-party punishment (TPP) that changes the payoff structure of defectors is believed to be a key in promoting cooperation. However, this rationale is contrary to an important finding in behavioral economics: individuals are not necessarily rational decision makers and do not have purely self-regarding preferences. This contradiction raises an interesting question: can this finding also be applied to defectors? We aim to explore this question through three experiments.
In Experiment 1, 240 undergraduates participated in a Public Goods Game and were divided randomly into three conditions: control condition (CC), low defection cost condition (LC), and high defection cost condition (HC). In each round of the game, participants in CC decided whether to contribute 10 tokens from the initial endowment to the public account. All the tokens contributed to the public account were doubled and evenly allocated to all group members. Participants who retained 10 tokens needed to pay a tax of 1 token. The procedures in LC and HC were identical to that in CC. An exception is that in LC and HC, independent punishers could discipline defectors by paying 5 tokens to reduce the payoff of defectors by 1 token in LC and 10 tokens in HC. In Experiment 2, 179 participants who defected in Stage 1 were selected as sample in Stage 2 and were divided randomly into two conditions: CC (89 participants) and punishment condition (PC, 90 participants). Participants in PC were told they had been punished in Stage 1, whereas those in CC received no feedback. All participants’ levels of norm activation and cooperation in different games were then measured. Experiment 2 was replicated in Experiment 3, where the participants were not game players but spectators, and their levels of norm activation and cooperation were measured before and after the game. The participants in defection condition observed a defection and the consequent punishment, whereas those in norm condition observed a fair offer and no punishment.
In Experiment 1, the defection cost in LC was lower than that in CC, so participants in LC had a stronger incentive to defect. However, the results revealed a significantly higher cooperation level in LC. A plausible explanation is that the defection cost in form of punishment served as a norm reminder, but cost in form of tax lacked this function, implying that even defectors are not necessarily benefit maximizers. The results of Experiment 2 confirmed this explanation: compared with unpunished defectors, the punished ones manifested a higher level of norm activation. The bootstrap analysis showed that the norm activation completely mediated TPP and cooperation. Experiment 2 also found a spillover effect of TPP: the punished defectors still demonstrated a high cooperation in a new different game where the sanction was absent. Finally, Experiment 3 found another spillover effect of TPP: bystanders who did not experience the punishment in person but witnessed it showed a significantly higher cooperation in subsequent interactions.
In conclusion, oftentimes, people defect simply because they are unaware of the existence of a certain norm, and activating people’s norms through TPP can significantly reduce their selfish behaviors. In addition to being an economic means to reduce defectors’ payoff, TPP serves as a norm reminder. The two spillover effects found in this study suggest that TPP as a means of norm activation may be more efficient than as an economic means because of its cost-effectiveness. These findings shed new light on the understanding of extensive cooperation among genetically unrelated individuals.

Key words: third-party punishment, social norm, cooperation, focus theory, spillover effect

中图分类号:

B849: C91

陈思静, 邢懿琳, 翁异静, 黎常. (2021). 第三方惩罚对合作的溢出效应：基于社会规范的解释. 心理学报, 53(7), 758-772.

CHEN Sijing, XING Yilin, WENG Yijing, LI Chang. (2021). Spillover effects of third-party punishment on cooperation: A norm-based explanation. Acta Psychologica Sinica, 53(7), 758-772.

图/表 8

参考文献 70

[1]	Alkan, H. I. (2020). A challenge to homo economicus: Behavioral economics. In I. Akansel (Ed. ), Examining the relationship between economics and philosophy (pp.176-195). Hershey, PA: IGI Global.
[2]	Baldassarri, D., & Grossman, G. (2011). Centralized sanctioning and legitimate authority promote cooperation in humans. Proceedings of the National Academy of Sciences of the United States of America, 108(27), 11023-11027.
[3]	Balliet, D., Mulder, L. B., & van Lange, P.A.M (2011). Reward, punishment, and cooperation: A meta-analysis. Psychological Bulletin, 137(4), 594-615. doi: 10.1037/a0023489 pmid: 21574679
[4]	Bear, A., & Rand, D. G. (2016). Intuition, deliberation, and the evolution of cooperation. Proceedings of the National Academy of Sciences of the United States of America, 113(4), 936-941.
[5]	Bicchieri, C., Dimant, E., & Xiao, E. T. (2018). Deviant or wrong? The effects of norm information on the efficacy of punishment (PPE Working Papers 0016). Philadelphia, PA: Philosophy, Politics and Economics of University of Pennsylvania.
[6]	Bicchieri, C., & Xiao, E. (2009). Do the right thing: But only if others do so. Journal of Behavioral Decision Making, 22(2), 191-208. doi: 10.1002/bdm.v22:2 URL
[7]	Bingham, P. M. (1999). Human uniqueness: A general theory. The Quarterly Review of Biology, 74(2), 133-169. doi: 10.1086/393069 URL
[8]	Camerer, C. F., & Fehr, E. (2006). When does “economic man” dominate social behavior? Science, 311(5757), 47-52. doi: 10.1126/science.1110600 URL
[9]	Carpenter, J. P., Matthews, P. H., & Ong’ong’a, O. (2004). Why punish? Social reciprocity and the enforcement of prosocial norms. Journal of Evolutionary Economics, 14(4), 407-429. doi: 10.1007/s00191-004-0212-1 URL
[10]	Chen, H., Zeng, Z., & Ma, J. (2020). The source of punishment matters: Third-party punishment restrains observers from selfish behaviors better than does second-party punishment by shaping norm perceptions. PloS One, 15(3), e0229510. doi: 10.1371/journal.pone.0229510 URL
[11]	Chen, S. J., He, Q., & Ma, J. H. (2015). The influence of third-party punishment on cooperation: An explanation of social norm activation. Acta Psychologica Sinica, 47(3), 389-405. doi: 10.3724/SP.J.1041.2015.00389 URL
	[陈思静, 何铨, 马剑虹. (2015). 第三方惩罚对合作行为的影响: 基于社会规范激活的解释. 心理学报, 47(3), 389-405.]
[12]	Chen, S. J., Hu, H. M., & Yang, S. S. (2020). Payment vs. retaliation: Impact of cost form on third-party punishment. Journal of Psychological Science, 43(2), 416-422.
	[陈思静, 胡华敏, 杨莎莎. (2020). 支付与报复: 成本形式对第三方惩罚的影响. 心理科学, 43(2), 416-422.]
[13]	Chen, S. J., & Xu, Y. C. (2020). Warmth and competence: Impact of third-party punishment on punishers’ reputation. Acta Psychologica Sinica, 52(12), 1436-1451.
	[陈思静, 徐烨超. (2020). “仁者”还是“智者”: 第三方惩罚对惩罚者声誉的影响. 心理学报, 52(12), 1436-1451.]
[14]	Cialdini, R. B., Kallgren, C. A., & Reno, R. R. (1991). A focus theory of normative conduct: A theoretical refinement and reevaluation of the role of norms in human behavior. Advances in Experimental Social Psychology, 24, 201-234.
[15]	Cialdini, R. B., Reno, R. R., & Kallgren, C. A. (1990). A focus theory of normative conduct: Recycling the concept of norms to reduce littering in public places. Journal of Personality and Social Psychology, 58(6), 1015-1026.
[16]	Cialdini, R. B., & Trost, M. R. (1998). Social influence:Social norms, conformity and compliance. In T. Gilbert, T. Fiske, & G. Lindzey (Eds.), The handbook of social psychology (Vol. 2, pp.151-192.). Boston, MA: McGraw-Hill.
[17]	Csukly, G., Polgár, P., Tombor, L., Réthelyi, J., & Kéri, S. (2011). Are patients with schizophrenia rational maximizers? Evidence from an ultimatum game study. Psychiatry Research, 187(1-2),11-17. doi: 10.1016/j.psychres.2010.10.005 URL
[18]	Cui, L. Y., He, X., Luo, J. L., Huang, X. J., Cao, W. J., & Chen, X. M. (2017). The effects of moral punishment and relationship punishment on junior middle school students’ cooperation behaviors in public goods dilemma. Acta Psychologica Sinica, 49(10), 1322-1333.
	[崔丽莹, 何幸, 罗俊龙, 黄晓娇, 曹玮佳, 陈晓梅. (2017). 道德与关系惩罚对初中生公共物品困境中合作行为的影响. 心理学报, 49(10), 1322-1333.]
[19]	de Kwaadsteniet, E. W., Kiyonari, T., Molenmaker, W. E., & van Dijk, E. (2019). Do people prefer leaders who enforce norms? Reputational effects of reward and punishment decisions in noisy social dilemmas. Journal of Experimental Social Psychology, 84, 103800.
[20]	de Kwaadsteniet, E. W., van Dijk, E., Wit, A., de Cremer, D., & de Rooij, M. (2007). Justifying decisions in social dilemmas: Justification pressures and tacit coordination under environmental uncertainty. Personality and Social Psychology Bulletin, 33(12), 1648-1660.
[21]	Deutsch, M., & Gerard, H. B. (1955). A study of normative and informational social influences upon individual judgment. The Journal of Abnormal and Social Psychology, 51(3), 629-636. doi: 10.1037/h0046408 URL
[22]	Dreber, A., Rand, D. G., Fudenberg, D., & Nowak, M. A. (2008). Winners don’t punish. Nature, 452(7185), 348-351. doi: 10.1038/nature06723 pmid: 18354481
[23]	Fang, J., & Zhang, M. Q. (2012). Assessing point and interval estimation for the mediating effect: Distribution of the product, nonparametric Bootstrap and Markov Chain Monte Carlo methods. Acta Psychologica Sinica, 44(10), 1408-1420.
[24]	方杰, 张敏强. (2012). 中介效应的点估计和区间估计: 乘积分布法、非参数Bootstrap和MCMC法. 心理学报, 44(10), 1408-1420.].
[25]	Fehr, E., & Fischbacher, U. (2003). The nature of human altruism. Nature, 425(6960), 785-791. doi: 10.1038/nature02043 URL
[26]	Fehr, E., & Gächter, S. (2002). Altruistic punishment in humans. Nature, 415(6868), 137-140. doi: 10.1038/415137a URL
[27]	Fehr, E., & Rockenbach, B. (2003). Detrimental effects of sanctions on human altruism. Nature, 422(6928), 137-140. doi: 10.1038/nature01474 URL
[28]	Fehr, E., & Schurtenberger, I. (2018). Normative foundations of human cooperation. Nature Human Behaviour, 2(7), 458-468. doi: 10.1038/s41562-018-0385-5 URL
[29]	Fehr, E., & Williams, T. (2018). Social norms, endogenous sorting and the culture of cooperation. (ECON Working Papers 267). Zurich, Switzerland: Department of Economics of University of Zurich.
[30]	Fischbacher, U. (2007). z-Tree: Zurich toolbox for ready-made economic experiments. Experimental Economics, 10(2), 171-178. doi: 10.1007/s10683-006-9159-4 URL
[31]	Forquesato, P. (2016). Social norms of work ethic and incentives in organizations. Journal of Economic Behavior & Organization, 128, 231-250. doi: 10.1016/j.jebo.2016.05.012 URL
[32]	Gächter, S., Renner, E., & Sefton, M. (2008). The long-run benefits of punishment. Science, 322(5907), 1510-1510.
[33]	Gintis, H., & Fehr, E. (2012). The social structure of cooperation and punishment. Behavioral and Brain Sciences, 35(1), 28-29. doi: 10.1017/S0140525X11000914 URL
[34]	Gintis, H., Smith, E. A., & Bowles, S. (2001). Costly signaling and cooperation. Journal of Theoretical Biology, 213(1), 103-119. doi: 10.1006/jtbi.2001.2406 URL
[35]	Greif, A. (1993). Contract enforceability and economic institutions in early trade: The Maghribi traders’ coalition. The American Economic Review, 83(3), 525-548.
[36]	Grimalda, G., Pondorfer, A., & Tracer, D. P. (2016). Social image concerns promote cooperation more than altruistic punishment. Nature Communications, 7, 12288. doi: 10.1038/ncomms12288 URL
[37]	Guala, F. (2012). Reciprocity: Weak or strong? What punishment experiments do (and do not) demonstrate. Behavioral and Brain Sciences, 35(1), 1-15. doi: 10.1017/S0140525X11000069 URL
[38]	Halevy, N., & Halali, E. (2015). Selfish third parties act as peacemakers by transforming conflicts and promoting cooperation. Proceedings of the National Academy of Sciences of the United States of America, 112(22), 6937-6942.
[39]	Henrich, J., Boyd, R., Bowles, S., Camerer, C., Fehr, E., Gintis, H., & McElreath, R. (2001). In search of homo economicus: Behavioral experiments in 15 small-scale societies. American Economic Review, 91(2), 73-78. doi: 10.1257/aer.91.2.73 URL
[40]	Herrmann, B., Thöni, C., & Gächter, S. (2008). Antisocial punishment across societies. Science, 319(5868), 1362- 1367.
[41]	Huang, S. A., & Zhang, S. (2013). How did cooperative behavior evolve: A summary and review. Social Sciences in China, 7, 77-89.
	[黄少安, 张苏. (2013). 人类的合作及其演进: 研究综述和评论. 中国社会科学, 7, 77-89.]
[42]	Kahneman, D. (2011). Thinking, fast and slow. New York, NY: Macmillan.
[43]	Lois, G., & Wessa, M. (2019). Creating sanctioning norms in the lab: The influence of descriptive norms in third-party punishment. Social Influence, 14(2), 50-63. doi: 10.1080/15534510.2019.1641147 URL
[44]	McDonald, R. I., & Crandall, C. S. (2015). Social norms and social influence. Current Opinion in Behavioral Sciences, 3, 147-151. doi: 10.1016/j.cobeha.2015.04.006 URL
[45]	Nelissen, R. M. A., & Mulder, L. B. (2013). What makes a sanction “stick”? The effects of financial and social sanctions on norm compliance. Social Influence, 8(1), 70-80. doi: 10.1080/15534510.2012.729493 URL
[46]	Noussair, C., & Tucker, S. (2005). Combining monetary and social sanctions to promote cooperation. Economic Inquiry, 43(3), 649-660. doi: 10.1093/ei/cbi045 URL
[47]	Nowak, M. A. (2006). Five rules for the evolution of cooperation. Science, 314(5805), 1560-1563.
[48]	Nowak, M. A., & Sigmund, K. (1998). The dynamics of indirect reciprocity. Journal of Theoretical Biology, 194(4), 561-574. doi: 10.1006/jtbi.1998.0775 URL
[49]	Petty, R. E., & Cacioppo, J. T. (1986). Communication and persuasion: Central and peripheral routes to attitude change. New York, NY: Springer.
[50]	Peysakhovich, A., & Rand, D. G. (2016). Habits of virtue: Creating norms of cooperation and defection in the laboratory. Management Science, 62(3), 631-647. doi: 10.1287/mnsc.2015.2168 URL
[51]	Preacher, K. J., & Hayes, A. F. (2004). SPSS and SAS procedures for estimating indirect effects in simple mediation models. Behavior Research Methods, Instruments, & Computers, 36(4), 717-731. doi: 10.3758/BF03206553 URL
[52]	Raihani, N. J., & Bshary, R. (2015). The reputation of punishers. Trends in Ecology and Evolution, 30(2), 98-103. doi: 10.1016/j.tree.2014.12.003 URL
[53]	Rand, D. G. (2016). Cooperation, fast and slow: Meta-analytic evidence for a theory of social heuristics and self-interested deliberation. Psychological Science, 27(9), 1192-1206.
[54]	Rand, D. G., Armao IV, J. J., Nakamaru, M., & Ohtsuki, H. (2010). Anti-social punishment can prevent the co-evolution of punishment and cooperation. Journal of Theoretical Biology, 265(4), 624-632. doi: 10.1016/j.jtbi.2010.06.010 URL
[55]	Rand, D. G., Brescoll, V. L., Everett, J. A. C., Capraro, V., & Barcelo, H. (2016). Social heuristics and social roles: Intuition favors altruism for women but not for men. Journal of Experimental Psychology: General, 145(4), 389-396. doi: 10.1037/xge0000154 URL
[56]	Rand, D. G., Dreber, A., Ellingsen, T., Fudenberg, D., & Nowak, M. A. (2009). Positive interactions promote public cooperation. Science, 325(5945), 1272-1275.
[57]	Rand, D. G., Peysakhovich, A., Kraft-Todd, G. T., Newman, G. E., Wurzbacher, O., Nowak, M. A., & Greene, J. D. (2014). Social heuristics shape intuitive cooperation. Nature Communications, 5, 3677. doi: 10.1038/ncomms4677 URL
[58]	Shreedhar, G., Tavoni, A., & Marchiori, C. (2018). Monitoring and punishment networks in a common-pool resource dilemma: Experimental evidence (GRI Working Papers 292). London, England: Grantham Research Institute on Climate and the Environment.
[59]	Sood, S., Kostizak, K., Lapsansky, C., Cronin, C., Stevens, S., Jubero, M., ... Obregon, R. (2020). ACT: An evidence- based macro framework to examine how communication approaches can change social norms around Female Genital Mutilation. Frontiers in Communication, 5, 29. doi: 10.3389/fcomm.2020.00029 URL
[60]	Thaler, R. H. (2016). Behavioral economics: Past, present, and future. American Economic Review, 106(7), 1577-1600.
[61]	Trivers, R. L. (1971). The evolution of reciprocal altruism. The Quarterly Review of Biology, 46(1), 35-57. doi: 10.1086/406755 URL
[62]	van den Berg, P., Molleman, L., & Weissing, F. J. (2012). The social costs of punishment. Behavioral and Brain Sciences, 35(1), 42-43. doi: 10.1017/S0140525X11001348 URL
[63]	Voisin, D., Girandola, F., David, M., & Aim, M. A. (2016). Self-affirmation and an incongruent drinking norm: Alcohol abuse prevention messages targeting young people. Self and Identity, 15(3), 262-282. doi: 10.1080/15298868.2015.1121916 URL
[64]	Wallace, B., Cesarini, D., Lichtenstein, P., & Johannesson, M. (2007). Heritability of ultimatum game responder behavior. Proceedings of the National Academy of Sciences of the United States of America, 104(40), 15631-15634.
[65]	Wang, Z. S., Fan, M. S., Chen, C. F., & Yao, J. H. (2004). A History of Greek Philosophy (Volume 2). Beijing: People’s Publishing House.
	[汪子嵩, 范明生, 陈村富, 姚介厚. (2004). 希腊哲学史(第2卷). 北京: 人民出版社.]
[66]	Wei, Q., & Jiang, S.G (2013). How is social cooperative order possible: Exploring mysteries. Economic Research Journal, (11), 140-151.
	[韦倩, 姜树广. (2013). 社会合作秩序何以可能: 社会科学的基本问题. 经济研究, (11), 140-151.]
[67]	Wei, Q., Sun, R. Q., Jiang, S. G., & Ye, H. (2019). Coordinated punishment and the evolution of human cooperation. Economic Research Journal, (7), 174-187.
	[韦倩, 孙瑞琪, 姜树广, 叶航. (2019). 协调性惩罚与人类合作的演化. 经济研究, (7), 174-187.]
[68]	Wen, Z. L., & Ye, B. J. (2014). Different methods for testing moderated mediation models: Competitors or backups? Acta Psychologica Sinica, 46(5), 714-726. doi: 10.3724/SP.J.1041.2014.00714 URL
	[温忠麟, 叶宝娟. (2014) 有调节的中介模型检验方法: 竞争还是替补? 心理学报, 46(5), 714-726.]
[69]	Wu, J., Balliet, D., & van Lange, P. A. (2016). Gossip versus punishment: The efficiency of reputation to promote and maintain cooperation. Scientific Reports, 6, 23919. doi: 10.1038/srep23919 URL
[70]	Xie, D. J., & Su, Y. J. (2019). The evolutionary and cognitive mechanisms of third-party punishment. Journal of Psychological Science, 42(1), 216-222.
	[谢东杰, 苏彦捷. (2019). 第三方惩罚的演化与认知机制. 心理科学, 42(1), 216-222.]

实验条件	${{\text{U}}_{\text{C}}}$	${{\text{U}}_{\text{D}}}$
对照组	$\text{25}+\frac{\text{2(10}{{\text{x}}_{\text{C}}}\text{+10)}}{\text{4}}-\text{10}$	$\text{25}+\frac{\text{20}{{\text{x}}_{\text{C}}}}{\text{4}}-\text{1}$
高收益组	$\text{25+}\frac{\text{2(10}{{\text{x}}_{\text{C}}}\text{+10)}}{\text{4}}-\text{10}$	$\text{25}+\frac{\text{20}{{\text{x}}_{\text{C}}}}{\text{4}}-{{\text{x}}_{\text{D}}}$
低收益组	$\text{25}+\frac{\text{2(10}{{\text{x}}_{\text{C}}}\text{+10)}}{\text{4}}-\text{10}$	$\text{25}+\frac{\text{20}{{\text{x}}_{\text{C}}}}{\text{4}}-\text{10}{{\text{x}}_{\text{D}}}$

实验条件	${{\text{U}}_{\text{C}}}$	${{\text{U}}_{\text{D}}}$
对照组	$\text{25}+\frac{\text{2(10}{{\text{x}}_{\text{C}}}\text{+10)}}{\text{4}}-\text{10}$	$\text{25}+\frac{\text{20}{{\text{x}}_{\text{C}}}}{\text{4}}-\text{1}$
高收益组	$\text{25+}\frac{\text{2(10}{{\text{x}}_{\text{C}}}\text{+10)}}{\text{4}}-\text{10}$	$\text{25}+\frac{\text{20}{{\text{x}}_{\text{C}}}}{\text{4}}-{{\text{x}}_{\text{D}}}$
低收益组	$\text{25}+\frac{\text{2(10}{{\text{x}}_{\text{C}}}\text{+10)}}{\text{4}}-\text{10}$	$\text{25}+\frac{\text{20}{{\text{x}}_{\text{C}}}}{\text{4}}-\text{10}{{\text{x}}_{\text{D}}}$

变量	M₁(描述性规范)		M₂(命令性规范)		M₃ (合作行为)		M₄ (合作行为)
变量	系数	SE	系数	SE	系数	SE	系数	SE
常数	1.87^***	0.51	2.57^***	0.63	1.38^*	0.66	-0.17	0.62
惩罚	0.97^**	0.32	1.53^***	0.40	1.08^**	0.42	0.25	0.39
描述性规范							0.59^***	0.08
命令性规范							0.17^*	0.07
模型	R²	MSE	R²	MSE	R²	MSE	R²	MSE
模型	0.05	4.72	0.08	7.17	0.04	2.79	0.28	5.91

变量	M₁(描述性规范)		M₂(命令性规范)		M₃ (合作行为)		M₄ (合作行为)
变量	系数	SE	系数	SE	系数	SE	系数	SE
常数	1.87^***	0.51	2.57^***	0.63	1.38^*	0.66	-0.17	0.62
惩罚	0.97^**	0.32	1.53^***	0.40	1.08^**	0.42	0.25	0.39
描述性规范							0.59^***	0.08
命令性规范							0.17^*	0.07
模型	R²	MSE	R²	MSE	R²	MSE	R²	MSE
模型	0.05	4.72	0.08	7.17	0.04	2.79	0.28	5.91

来源	均方	F	显著性	偏η²
修正模型	75.98	10.95	0.000	0.09
截距	3129.38	451.16	0.000	0.59
轮次	107.07	15.44	0.000	0.05
分组	27.44	3.96	0.048	0.01
轮次×分组	93.42	13.47	0.000	0.04