社会引力定律追根溯源

闫小勇

doi:10.7498/aps.69.20191686

摘要

在交通出行、人口迁移、商品贸易、信息流通、社会交往、科研合作等大量人、物、信息的空间流动现象中, 都存在类似万有引力定律的规律, 即两地之间的某种流动量与两地活力的乘积成正比、与两地距离的幂成反比. 类比万有引力定律建立的引力模型也在交通出行分布预测、人口迁移量预测、地区间贸易量预测等诸多方面获得了广泛应用. 但复杂的社会系统中为何会有这样简单的引力定律存在? 这是个非常有趣也有价值的问题. 本文对从统计物理学、微观经济学和博弈论等不同视角探索社会引力定律根源的研究进行了综述.

关键词:

Abstract

Many spatial mobility of people, goods and information, such as human travel, population migration, commodity trade, information communication, social interaction and scientific cooperation, follow a law similar to Newton’s law of universal gravitation. This law, named social gravity law, is that the flow between two locations is directly proportional to the product of the vitality of these two locations, and inversely proportional to a power function of their distance. The gravity model established by analogy with the gravity law has also been widely used to predict trip distribution, population migration, interregional trade flows, etc. But why do many complex social systems have such a simple law? It is an interesting and valuable issue. This paper reviews the research on exploring the roots of the social gravity law from various perspectives, including statistical physics, microeconomics, and game theory.

Keywords:

作者及机构信息

闫小勇^1,2

1.
北京交通大学, 交通系统科学与工程研究院, 北京　100044

2.
电子科技大学, 复杂性实验室, 成都　611731

通信作者: 闫小勇, yanxy@bjtu.edu.cn

基金项目: 国家级-国家自然科学基金优秀青年科学基金项目(71822102)

Authors and contacts

Yan Xiao-Yong^1,2

1.
Institute of Transportation System Science and Engineering, Beijing Jiaotong University, Beijing 100044, China

2.
Complex Labortary, University of Electronic Science and Technology of China, Chengdu 611731, China

Corresponding author: Yan Xiao-Yong, yanxy@bjtu.edu.cn

文章全文 : translate this paragraph

参考文献

[1]	闫小勇 2019 超越引力定律 (北京: 科学出版社) 第iii页 Yan X Y 2019 Beyond Gravity Law (Beijing: China Science Press) piii (in Chinese)
[2]	丁益民, 杨昌平 2012 61 238901 Google Scholar Ding Y M, Yang C P 2012 Acta Phys. Sin. 61 238901 Google Scholar
[3]	Fotheringham A S, O'Kelly M E 1989 Spatial Interaction Models: Formulations and Applications (Dordrecht: Kluwer Academic Publishers) p1
[4]	Sen A, Smith T 1995 Gravity Models of Spatial Interaction Behavior (Berlin: Springer) p1
[5]	Karemera D, Oguledo V I, Davis B 2000 Appl. Econ. 32 1745 Google Scholar
[6]	Porojan A 2001 Open Econ. Rev. 12 265 Google Scholar
[7]	de Dios Ortuzar J, Willumsen L G 2011 Modelling Transport (West Sussex: John Wiley & Sons) p182
[8]	Liu J H, Zhang Z K, Chen L, Liu C, Yang C, Wang X 2014 PloS ONE 9 e91070 Google Scholar
[9]	Ma L L, Ma C, Zhang H F, Wang B H 2015 Physica A 451 205
[10]	Li Z, Ren T, Ma X Q, Liu S M, Zhang Y X, Zhou T 2019 Sci. Rep. 9 8387 Google Scholar
[11]	Newton I 1729 Mathematical Principles of Natural Philosophy (London: Benjamin Motte Publisher) p5
[12]	Dodd S C 1950 Am. Sociol. Rev. 15 245 Google Scholar
[13]	Desart H G 1846 Chemin de fer Direct de Bruxelles vers Gand, par Alost, en Communication avec les Stations Diverses (Bruxelles: Devroye) p16
[14]	Odlyzko A 2015 Economia Hist. Meth. Philos. 5 157
[15]	Carey H C 1858 Principles of Social Science (Philadelphia: Lippincott) p28
[16]	Ravenstein E G 1889 J. R. Stat. Soc. 48 167
[17]	Reilly W J 1929 Methods for the Study of Retail Relationships (Texas: University of Texas Bulletin) p2944
[18]	Zipf G K 1946 Am. Sociol. Rev. 11 677 Google Scholar
[19]	Tobler W 1995 Urban Geogr. 16 327 Google Scholar
[20]	Fagiolo G 2010 J. Econ. Interact. Coor. 5 1 Google Scholar
[21]	周涛, 韩筱璞, 闫小勇, 杨紫陌, 赵志丹, 汪秉宏 2013 电子科技大学学报 42 481 Google Scholar Zhou T, Han X P, Yan X Y, Yang Z M, Zhao Z D, Wang B H 2013 J. Uiv. Electron. Sci. Technol. China 42 481 Google Scholar
[22]	徐赞新, 王钺, 司洪波, 冯振明 2011 60 040501 Google Scholar Xu Z X, Wang Y, Si H B, Feng Z M 2011 Acta Phys. Sin. 60 040501 Google Scholar
[23]	Viboud C, Bjørnstad O N, Smith D L, Simonsen L, Miller M A, Grenfell B T 2006 Science 312 447 Google Scholar
[24]	Jung W S, Wang F, Stanley H E 2008 Europhys. Lett. 81 48005 Google Scholar
[25]	Krings G, Calabrese F, Ratti C, Blondel V D 2009 J. Stat. Mech. 2009 L07003
[26]	Balcan D, Colizza V, Gonçalves B, Hu H, Ramasco J J, Vespignani A 2009 Proc. Natl. Acad. Sci. U.S.A. 106 21484 Google Scholar
[27]	Kaluza P, Kölzsch A, Gastner M T, Blasius B 2010 J. R. Soc. Interface 7 1093 Google Scholar
[28]	Pan R K, Kaski K, Fortunato S 2012 Sci. Rep. 2 902 Google Scholar
[29]	Goh S, Lee K, Park J S, Choi M Y 2012 Phys. Rev. E 86 026102 Google Scholar
[30]	Goh S, Lee K, Choi M Y, Fortin J Y 2014 PloS ONE 9 e89980 Google Scholar
[31]	Levy M, Goldenberg J 2014 Physica A 393 418 Google Scholar
[32]	Sheppard E S 1978 Geogr. Anal. 10 386
[33]	Hua C I, Porell F 1979 Int. Regional Sci. Rev. 4 97 Google Scholar
[34]	Wilson A G 1967 Transp. Res. 1 253 Google Scholar
[35]	Niedercorn J H, Bechdolt Jr B V 1969 J. Regional Sci. 9 273 Google Scholar
[36]	Domencich T A, Mcfadden D 1975 Urban Travel Demand: A Behavioral Analysis (Amsterdam: North-Holland) p1
[37]	Yan X Y, Zhou T 2019 Sci. Rep. 9 9466 Google Scholar
[38]	Pressé S, Ghosh K, Lee J, Dill K A 2013 Rev. Mod. Phys. 85 1115 Google Scholar
[39]	Barthélemy M 2011 Phys. Rep. 499 1 Google Scholar
[40]	Yan X Y, Han X P, Wang B H, Zhou T 2013 Sci. Rep. 3 2678 Google Scholar
[41]	Hensher D A, Button K J 2000 Handbook of Transport Modelling (Oxford: Pergamon) p20
[42]	Chalasani V S, Engebretsen Ø, Denstadli J M, Axhausen K W 2005 J. Transp. Stat. 2 1
[43]	Rietveld P, Zwart B, Van Wee B, van den Hoorn T 1999 Ann. Regional Sci. 33 269 Google Scholar
[44]	Brakman S, Garretsen H 2005 Location and Competition (London: Routledge) p205
[45]	Brockmann D, Hufnagel L, Geisel T 2006 Nature 439 462 Google Scholar
[46]	González M C, Hidalgo C A, Barabási A L 2008 Nature 453 779 Google Scholar
[47]	Han X P, Hao Q, Wang B H, Zhou T 2011 Phys. Rev. E 83 036117 Google Scholar
[48]	Liang X, Zheng X, Lü W, Zhu T, Xu K 2012 Physica A 391 2153
[49]	Gallotti R, Bazzani A, Rambaldi S 2012 Int. J Mod. Phys. C 23 1250061 Google Scholar
[50]	黄飞虎, 彭舰, 由明阳 2016 65 228901 Google Scholar Huang F H, Peng J, You M Y 2016 Acta Phys. Sin. 65 228901 Google Scholar
[51]	Ben-Akiva M E, Lerman S R 1985 Discrete Choice Analysis: Theory and Application to Travel Demand (Cambridge: MIT Press) p1
[52]	McFadden D 2007 Transp. Policy 14 269 Google Scholar
[53]	Herrnstein R J, Loewenstein G F, Prelec D, Vaughan Jr W 1993 Journal of Behav. Decis. Making 6 149 Google Scholar
[54]	Train K E 2009 Discrete Choice Methods with Simulation (Cambridge: Cambridge University Press) p38
[55]	Takemura K 2014 Behavioral Decision Theory: Psychological and Mathematical Descriptions of Human Choice Behavior (Berlin: Springer) p52
[56]	何大韧, 刘宗华, 汪秉宏 2009 复杂系统与复杂网络 (北京: 高等教育出版社) 第59页 He D R, Liu Z H, Wang B H 2009 Complex Systems and Complex Networks (Beijing: Higher Education Press) p59 (in Chinese)
[57]	Rosenthal R W 1973 Int. J Game Theory 2 65 Google Scholar
[58]	Monderer D, Shapley L S 1996 Games Econ. Behav. 14 124 Google Scholar
[59]	Stouffer S A 1940 Am. Sociol. Rev. 5 845 Google Scholar
[60]	Simini F, González M C, Maritan A, Barabási A L 2012 Nature 484 96 Google Scholar
[61]	Yan X Y, Zhao C, Fan Y, Di Z R, Wang W X 2014 J R Soc. Interface 11 20140834 Google Scholar
[62]	Yan X Y, Wang W X, Gao Z Y, Lai Y C 2017 Nat. Commun. 8 1639 Google Scholar
[63]	Voorneveld M, Borm P, Van Megen F, Tijs S, Facchini G 1999 Int. Game Theory Rev. 1 283 Google Scholar
[64]	McFadden D 1980 J. Bus. 1980 S13
[65]	Fisk C 1980 Transp. Res. B 14 243 Google Scholar
[66]	Burgess J 1998 Occam's Razor and Scientific Method (Oxford: Clarendon Press) p195

施引文献

[1]	闫小勇 2019 超越引力定律 (北京: 科学出版社) 第iii页 Yan X Y 2019 Beyond Gravity Law (Beijing: China Science Press) piii (in Chinese)
[2]	丁益民, 杨昌平 2012 61 238901 Google Scholar Ding Y M, Yang C P 2012 Acta Phys. Sin. 61 238901 Google Scholar
[3]	Fotheringham A S, O'Kelly M E 1989 Spatial Interaction Models: Formulations and Applications (Dordrecht: Kluwer Academic Publishers) p1
[4]	Sen A, Smith T 1995 Gravity Models of Spatial Interaction Behavior (Berlin: Springer) p1
[5]	Karemera D, Oguledo V I, Davis B 2000 Appl. Econ. 32 1745 Google Scholar
[6]	Porojan A 2001 Open Econ. Rev. 12 265 Google Scholar
[7]	de Dios Ortuzar J, Willumsen L G 2011 Modelling Transport (West Sussex: John Wiley & Sons) p182
[8]	Liu J H, Zhang Z K, Chen L, Liu C, Yang C, Wang X 2014 PloS ONE 9 e91070 Google Scholar
[9]	Ma L L, Ma C, Zhang H F, Wang B H 2015 Physica A 451 205
[10]	Li Z, Ren T, Ma X Q, Liu S M, Zhang Y X, Zhou T 2019 Sci. Rep. 9 8387 Google Scholar
[11]	Newton I 1729 Mathematical Principles of Natural Philosophy (London: Benjamin Motte Publisher) p5
[12]	Dodd S C 1950 Am. Sociol. Rev. 15 245 Google Scholar
[13]	Desart H G 1846 Chemin de fer Direct de Bruxelles vers Gand, par Alost, en Communication avec les Stations Diverses (Bruxelles: Devroye) p16
[14]	Odlyzko A 2015 Economia Hist. Meth. Philos. 5 157
[15]	Carey H C 1858 Principles of Social Science (Philadelphia: Lippincott) p28
[16]	Ravenstein E G 1889 J. R. Stat. Soc. 48 167
[17]	Reilly W J 1929 Methods for the Study of Retail Relationships (Texas: University of Texas Bulletin) p2944
[18]	Zipf G K 1946 Am. Sociol. Rev. 11 677 Google Scholar
[19]	Tobler W 1995 Urban Geogr. 16 327 Google Scholar
[20]	Fagiolo G 2010 J. Econ. Interact. Coor. 5 1 Google Scholar
[21]	周涛, 韩筱璞, 闫小勇, 杨紫陌, 赵志丹, 汪秉宏 2013 电子科技大学学报 42 481 Google Scholar Zhou T, Han X P, Yan X Y, Yang Z M, Zhao Z D, Wang B H 2013 J. Uiv. Electron. Sci. Technol. China 42 481 Google Scholar
[22]	徐赞新, 王钺, 司洪波, 冯振明 2011 60 040501 Google Scholar Xu Z X, Wang Y, Si H B, Feng Z M 2011 Acta Phys. Sin. 60 040501 Google Scholar
[23]	Viboud C, Bjørnstad O N, Smith D L, Simonsen L, Miller M A, Grenfell B T 2006 Science 312 447 Google Scholar
[24]	Jung W S, Wang F, Stanley H E 2008 Europhys. Lett. 81 48005 Google Scholar
[25]	Krings G, Calabrese F, Ratti C, Blondel V D 2009 J. Stat. Mech. 2009 L07003
[26]	Balcan D, Colizza V, Gonçalves B, Hu H, Ramasco J J, Vespignani A 2009 Proc. Natl. Acad. Sci. U.S.A. 106 21484 Google Scholar
[27]	Kaluza P, Kölzsch A, Gastner M T, Blasius B 2010 J. R. Soc. Interface 7 1093 Google Scholar
[28]	Pan R K, Kaski K, Fortunato S 2012 Sci. Rep. 2 902 Google Scholar
[29]	Goh S, Lee K, Park J S, Choi M Y 2012 Phys. Rev. E 86 026102 Google Scholar
[30]	Goh S, Lee K, Choi M Y, Fortin J Y 2014 PloS ONE 9 e89980 Google Scholar
[31]	Levy M, Goldenberg J 2014 Physica A 393 418 Google Scholar
[32]	Sheppard E S 1978 Geogr. Anal. 10 386
[33]	Hua C I, Porell F 1979 Int. Regional Sci. Rev. 4 97 Google Scholar
[34]	Wilson A G 1967 Transp. Res. 1 253 Google Scholar
[35]	Niedercorn J H, Bechdolt Jr B V 1969 J. Regional Sci. 9 273 Google Scholar
[36]	Domencich T A, Mcfadden D 1975 Urban Travel Demand: A Behavioral Analysis (Amsterdam: North-Holland) p1
[37]	Yan X Y, Zhou T 2019 Sci. Rep. 9 9466 Google Scholar
[38]	Pressé S, Ghosh K, Lee J, Dill K A 2013 Rev. Mod. Phys. 85 1115 Google Scholar
[39]	Barthélemy M 2011 Phys. Rep. 499 1 Google Scholar
[40]	Yan X Y, Han X P, Wang B H, Zhou T 2013 Sci. Rep. 3 2678 Google Scholar
[41]	Hensher D A, Button K J 2000 Handbook of Transport Modelling (Oxford: Pergamon) p20
[42]	Chalasani V S, Engebretsen Ø, Denstadli J M, Axhausen K W 2005 J. Transp. Stat. 2 1
[43]	Rietveld P, Zwart B, Van Wee B, van den Hoorn T 1999 Ann. Regional Sci. 33 269 Google Scholar
[44]	Brakman S, Garretsen H 2005 Location and Competition (London: Routledge) p205
[45]	Brockmann D, Hufnagel L, Geisel T 2006 Nature 439 462 Google Scholar
[46]	González M C, Hidalgo C A, Barabási A L 2008 Nature 453 779 Google Scholar
[47]	Han X P, Hao Q, Wang B H, Zhou T 2011 Phys. Rev. E 83 036117 Google Scholar
[48]	Liang X, Zheng X, Lü W, Zhu T, Xu K 2012 Physica A 391 2153
[49]	Gallotti R, Bazzani A, Rambaldi S 2012 Int. J Mod. Phys. C 23 1250061 Google Scholar
[50]	黄飞虎, 彭舰, 由明阳 2016 65 228901 Google Scholar Huang F H, Peng J, You M Y 2016 Acta Phys. Sin. 65 228901 Google Scholar
[51]	Ben-Akiva M E, Lerman S R 1985 Discrete Choice Analysis: Theory and Application to Travel Demand (Cambridge: MIT Press) p1
[52]	McFadden D 2007 Transp. Policy 14 269 Google Scholar
[53]	Herrnstein R J, Loewenstein G F, Prelec D, Vaughan Jr W 1993 Journal of Behav. Decis. Making 6 149 Google Scholar
[54]	Train K E 2009 Discrete Choice Methods with Simulation (Cambridge: Cambridge University Press) p38
[55]	Takemura K 2014 Behavioral Decision Theory: Psychological and Mathematical Descriptions of Human Choice Behavior (Berlin: Springer) p52
[56]	何大韧, 刘宗华, 汪秉宏 2009 复杂系统与复杂网络 (北京: 高等教育出版社) 第59页 He D R, Liu Z H, Wang B H 2009 Complex Systems and Complex Networks (Beijing: Higher Education Press) p59 (in Chinese)
[57]	Rosenthal R W 1973 Int. J Game Theory 2 65 Google Scholar
[58]	Monderer D, Shapley L S 1996 Games Econ. Behav. 14 124 Google Scholar
[59]	Stouffer S A 1940 Am. Sociol. Rev. 5 845 Google Scholar
[60]	Simini F, González M C, Maritan A, Barabási A L 2012 Nature 484 96 Google Scholar
[61]	Yan X Y, Zhao C, Fan Y, Di Z R, Wang W X 2014 J R Soc. Interface 11 20140834 Google Scholar
[62]	Yan X Y, Wang W X, Gao Z Y, Lai Y C 2017 Nat. Commun. 8 1639 Google Scholar
[63]	Voorneveld M, Borm P, Van Megen F, Tijs S, Facchini G 1999 Int. Game Theory Rev. 1 283 Google Scholar
[64]	McFadden D 1980 J. Bus. 1980 S13
[65]	Fisk C 1980 Transp. Res. B 14 243 Google Scholar
[66]	Burgess J 1998 Occam's Razor and Scientific Method (Oxford: Clarendon Press) p195

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