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社会引力定律追根溯源

闫小勇

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社会引力定律追根溯源

闫小勇

Exploring the roots of social gravity law

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

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    Porojan A 2001 Open Econ. Rev. 12 265Google Scholar

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    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 e91070Google 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 8387Google Scholar

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    Dodd S C 1950 Am. Sociol. Rev. 15 245Google Scholar

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    Desart H G 1846 Chemin de fer Direct de Bruxelles vers Gand, par Alost, en Communication avec les Stations Diverses (Bruxelles: Devroye) p16

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    Odlyzko A 2015 Economia Hist. Meth. Philos. 5 157

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    Ravenstein E G 1889 J. R. Stat. Soc. 48 167

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    Jung W S, Wang F, Stanley H E 2008 Europhys. Lett. 81 48005Google Scholar

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    Balcan D, Colizza V, Gonçalves B, Hu H, Ramasco J J, Vespignani A 2009 Proc. Natl. Acad. Sci. U.S.A. 106 21484Google Scholar

    [27]

    Kaluza P, Kölzsch A, Gastner M T, Blasius B 2010 J. R. Soc. Interface 7 1093Google Scholar

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    Pan R K, Kaski K, Fortunato S 2012 Sci. Rep. 2 902Google Scholar

    [29]

    Goh S, Lee K, Park J S, Choi M Y 2012 Phys. Rev. E 86 026102Google Scholar

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    Pressé S, Ghosh K, Lee J, Dill K A 2013 Rev. Mod. Phys. 85 1115Google Scholar

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    Yan X Y, Han X P, Wang B H, Zhou T 2013 Sci. Rep. 3 2678Google Scholar

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    Han X P, Hao Q, Wang B H, Zhou T 2011 Phys. Rev. E 83 036117Google Scholar

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    Liang X, Zheng X, Lü W, Zhu T, Xu K 2012 Physica A 391 2153

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    Gallotti R, Bazzani A, Rambaldi S 2012 Int. J Mod. Phys. C 23 1250061Google Scholar

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    黄飞虎, 彭舰, 由明阳 2016 物理学报 65 228901Google Scholar

    Huang F H, Peng J, You M Y 2016 Acta Phys. Sin. 65 228901Google Scholar

    [51]

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    McFadden D 2007 Transp. Policy 14 269Google Scholar

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    [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)

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    Rosenthal R W 1973 Int. J Game Theory 2 65Google Scholar

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    Monderer D, Shapley L S 1996 Games Econ. Behav. 14 124Google Scholar

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    Stouffer S A 1940 Am. Sociol. Rev. 5 845Google Scholar

    [60]

    Simini F, González M C, Maritan A, Barabási A L 2012 Nature 484 96Google Scholar

    [61]

    Yan X Y, Zhao C, Fan Y, Di Z R, Wang W X 2014 J R Soc. Interface 11 20140834Google Scholar

    [62]

    Yan X Y, Wang W X, Gao Z Y, Lai Y C 2017 Nat. Commun. 8 1639Google Scholar

    [63]

    Voorneveld M, Borm P, Van Megen F, Tijs S, Facchini G 1999 Int. Game Theory Rev. 1 283Google Scholar

    [64]

    McFadden D 1980 J. Bus. 1980 S13

    [65]

    Fisk C 1980 Transp. Res. B 14 243Google Scholar

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    Burgess J 1998 Occam's Razor and Scientific Method (Oxford: Clarendon Press) p195

  • [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 物理学报 61 238901Google Scholar

    Ding Y M, Yang C P 2012 Acta Phys. Sin. 61 238901Google 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 1745Google Scholar

    [6]

    Porojan A 2001 Open Econ. Rev. 12 265Google 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 e91070Google 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 8387Google Scholar

    [11]

    Newton I 1729 Mathematical Principles of Natural Philosophy (London: Benjamin Motte Publisher) p5

    [12]

    Dodd S C 1950 Am. Sociol. Rev. 15 245Google 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 677Google Scholar

    [19]

    Tobler W 1995 Urban Geogr. 16 327Google Scholar

    [20]

    Fagiolo G 2010 J. Econ. Interact. Coor. 5 1Google 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 481Google 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 481Google Scholar

    [22]

    徐赞新, 王钺, 司洪波, 冯振明 2011 物理学报 60 040501Google Scholar

    Xu Z X, Wang Y, Si H B, Feng Z M 2011 Acta Phys. Sin. 60 040501Google Scholar

    [23]

    Viboud C, Bjørnstad O N, Smith D L, Simonsen L, Miller M A, Grenfell B T 2006 Science 312 447Google Scholar

    [24]

    Jung W S, Wang F, Stanley H E 2008 Europhys. Lett. 81 48005Google 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 21484Google Scholar

    [27]

    Kaluza P, Kölzsch A, Gastner M T, Blasius B 2010 J. R. Soc. Interface 7 1093Google Scholar

    [28]

    Pan R K, Kaski K, Fortunato S 2012 Sci. Rep. 2 902Google Scholar

    [29]

    Goh S, Lee K, Park J S, Choi M Y 2012 Phys. Rev. E 86 026102Google Scholar

    [30]

    Goh S, Lee K, Choi M Y, Fortin J Y 2014 PloS ONE 9 e89980Google Scholar

    [31]

    Levy M, Goldenberg J 2014 Physica A 393 418Google Scholar

    [32]

    Sheppard E S 1978 Geogr. Anal. 10 386

    [33]

    Hua C I, Porell F 1979 Int. Regional Sci. Rev. 4 97Google Scholar

    [34]

    Wilson A G 1967 Transp. Res. 1 253Google Scholar

    [35]

    Niedercorn J H, Bechdolt Jr B V 1969 J. Regional Sci. 9 273Google 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 9466Google Scholar

    [38]

    Pressé S, Ghosh K, Lee J, Dill K A 2013 Rev. Mod. Phys. 85 1115Google Scholar

    [39]

    Barthélemy M 2011 Phys. Rep. 499 1Google Scholar

    [40]

    Yan X Y, Han X P, Wang B H, Zhou T 2013 Sci. Rep. 3 2678Google 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 269Google Scholar

    [44]

    Brakman S, Garretsen H 2005 Location and Competition (London: Routledge) p205

    [45]

    Brockmann D, Hufnagel L, Geisel T 2006 Nature 439 462Google Scholar

    [46]

    González M C, Hidalgo C A, Barabási A L 2008 Nature 453 779Google Scholar

    [47]

    Han X P, Hao Q, Wang B H, Zhou T 2011 Phys. Rev. E 83 036117Google 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 1250061Google Scholar

    [50]

    黄飞虎, 彭舰, 由明阳 2016 物理学报 65 228901Google Scholar

    Huang F H, Peng J, You M Y 2016 Acta Phys. Sin. 65 228901Google 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 269Google Scholar

    [53]

    Herrnstein R J, Loewenstein G F, Prelec D, Vaughan Jr W 1993 Journal of Behav. Decis. Making 6 149Google 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 65Google Scholar

    [58]

    Monderer D, Shapley L S 1996 Games Econ. Behav. 14 124Google Scholar

    [59]

    Stouffer S A 1940 Am. Sociol. Rev. 5 845Google Scholar

    [60]

    Simini F, González M C, Maritan A, Barabási A L 2012 Nature 484 96Google Scholar

    [61]

    Yan X Y, Zhao C, Fan Y, Di Z R, Wang W X 2014 J R Soc. Interface 11 20140834Google Scholar

    [62]

    Yan X Y, Wang W X, Gao Z Y, Lai Y C 2017 Nat. Commun. 8 1639Google Scholar

    [63]

    Voorneveld M, Borm P, Van Megen F, Tijs S, Facchini G 1999 Int. Game Theory Rev. 1 283Google Scholar

    [64]

    McFadden D 1980 J. Bus. 1980 S13

    [65]

    Fisk C 1980 Transp. Res. B 14 243Google Scholar

    [66]

    Burgess J 1998 Occam's Razor and Scientific Method (Oxford: Clarendon Press) p195

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出版历程
  • 收稿日期:  2019-11-04
  • 修回日期:  2019-11-19
  • 刊出日期:  2020-04-20

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