Fuzzy Modeling of Economic Institutional Rules

  • Christopher FrantzEmail author
  • Martin K. Purvis
  • Maryam A. Purvis
  • Mariusz Nowostawski
  • Nathan D. Lewis


Modeling collective social action is challenging not only because of the opacity of the underlying social processes, but even more because of the insufficient information detail concerning the activities under investigation. Such information gaps are customarily filled using the modeler’s intuition or randomization techniques. A promising alternative is to employ fuzzy reasoning. We have built on this potential to employ fuzzy methods as an alternative mechanism to integrate numerous opinions in order to model the establishment of economic institutional rules. Our empirical application domain is based on a historic trade scenario in which traders established rules and shared information in order to prevent the sellers of their goods from cheating them. We address this modeling problem by employing two different group decision-making mechanisms—majority-based voting on the one hand (which follows the original historical case) and preference aggregation using interval type-2 fuzzy sets on the other hand. We compare the outcomes of these two approaches and identify significantly lower sensitivity of the outcomes (i.e., instability of the outcomes to small changes in parameter settings) using fuzzy-set-based approaches in contrast to majority votes. The results suggest that the use of abstract decision-making mechanisms (such as preference aggregation) may be more useful in scenarios that prescribe a decision-making mechanism, but do not provide information to model this process in its entirety. Based on our finding, the potential for a wider use of fuzzy logic in the context of social simulation is discussed and pointers for future investigations are provided.


Membership Function Employment Level Preference Aggregation Social Choice Theory Cheat Behavior 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    J.K. Arrow, Social Choice and Individual Values, 2nd edn. (Wiley, New York, 1963)Google Scholar
  2. 2.
    R. Axelrod, The Evolution of Cooperation (Basic Books, New York, 1984)Google Scholar
  3. 3.
    R. Axelrod, Advancing the art of simulation in the social sciences, in Simulating Social Phenomena, ed. by R. Conte, R. Hegselmann, P. Terna (Springer, Berlin, 1997), pp. 21–40Google Scholar
  4. 4.
    R.F. Baumeister, E. Bratslavsky, C. Finkenauer, Bad is stronger than good. Rev. Gen. Psychol. 5(4), 323–370 (2001)CrossRefGoogle Scholar
  5. 5.
    S. Brams, P. Fishburn, Voting procedures, in Handbook of Social Choice and Welfare, ed. by K.J. Arrow, A.K. Sen, K. Suzumura (Elsevier, Amsterdam, 2004)Google Scholar
  6. 6.
    F.J. Cabrerizo, S. Alonso, I.J. Pérez, E. Herrera-Viedma, On consensus measures in fuzzy group decision making, in Modeling Decisions for Artificial Intelligence, ed. by V. Torra, Y. Narukawa, vol. 5285 of Lecture Notes in Computer Science (Springer, Sabadell, 2008), pp. 86–97Google Scholar
  7. 7.
    Y. Chevaleyre, U. Endriss, J. Lang, N. Maudet, A short introduction to computational social choice, in \textit33rd Conference on Current Trends in Theory and Practice of Computer Science, ed. by J. van Leeuwen, G.F. Italiano, W. van der Hoek, C. Meinel, H. Sack, F. Plasil (Springer, Berlin, 2007)Google Scholar
  8. 8.
    L. Conradt, C. List, Group decisions in humans and animals: A survey. Philos. Trans. R. Soc. B 364, 719–742 (2009)CrossRefGoogle Scholar
  9. 9.
    E. Durkheim, The Division of Labour in Society (Free Press 1933, New York, 1893)Google Scholar
  10. 10.
    D. Eckert, G. Pigozzi, Judgment aggregation, and some links with social choice theory, in Belief Change in Rational Agents: Perspectives from Artificial Intelligence, Philosophy and Economics, Dagstuhl Seminar Proceedings, ed. by J. Delgrande, J. Lang, J. Rott, J.-M. Tallon (IBFI, Germany 2005)Google Scholar
  11. 11.
    E. Ephrati, J.S. Rosenschein, Deriving consensus in multiagent systems. Artif. Intell. 87(1–2), 21–74 (1996)CrossRefMathSciNetGoogle Scholar
  12. 12.
    J. Epstein, R. Axtell, Growing Artificial Societies—Social Science from the Bottom Up (Brookings Institution/MIT Press, Cambridge, 1996)Google Scholar
  13. 13.
    J. Forrester, Counterintuitive behavior of social systems. Technol. Rev. 73(3), 52–68 (1971)Google Scholar
  14. 14.
    C. Frantz, M.K. Purvis, M. Nowostawski, B.T.R. Savarimuthu, nADICO: A nested grammar of institutions, in PRIMA 2013: Principles and Practice of Multi-Agent Systems, ed. by G. Boella, E. Elkind, B.T.R. Savarimuthu, F. Dignum, M.K. Purvis, vol. 8291 of LNAI (Springer, Dunedin, 2013), pp. 429–436Google Scholar
  15. 15.
    C. Frantz, M.K. Purvis, M. Nowostawski, B.T.R. Savarimuthu, Modelling institutions using dynamic deontics, in Coordination, Organizations, Institutions and Norms in Agent Systems IX, ed. by T. Balke, A. Chopra, F. Dignum, B. van Riemsdijk (Springer, Dunedin 2014)Google Scholar
  16. 16.
    J.M.T. García, M.J. del Moral, M.A. Martínez, E. Herrera-Viedma, A consensus model for group decision making problems with linguistic interval fuzzy preference relations. Expert Syst. Appl. 39(11), 10022–10030 (2012)CrossRefGoogle Scholar
  17. 17.
    M.P. Georgeff, B. Pell, M.E. Pollack, M. Tambe, M. Wooldridge, The belief-desire-intention model of agency, in Proceedings of the 5th International Workshop on Intelligent Agents V, Agent Theories, Architectures, and Languages, ATAL '98, ed. by J. Muller, M.P. Singh, A.S. Rao (Springer, London, 1999), pp. 1–10Google Scholar
  18. 18.
    N. Ghasem-Aghaee, T. Ören, Towards fuzzy agents with dynamic personality for human behavior simulation. Proceedings of the 2003 Summer Computer Simulation Conference, Montreal, 20–24 July 2003, pp. 3–10 (SCS)Google Scholar
  19. 19.
    L.J. Goldberg, Trade and Institutions in the Medieval Mediterranean: The Geniza Merchants and their Business World (Cambridge University Press, Cambridge, 2012)CrossRefGoogle Scholar
  20. 20.
    R. Goodin, C. List, A conditional defense of plurality rule: Generalizing May’s theorem in a restricted informational environment. Am. J. Polit. Sci. 50, 940–949 (2006)CrossRefGoogle Scholar
  21. 21.
    A. Greif, Contract enforceability and economic institution in early trade: The Maghribi traders` coalition. Am. Econ. Rev. 83(3), 525–548, (1993)MathSciNetGoogle Scholar
  22. 22.
    A. Greif, Institutions and the Path to the Modern Economy (Cambridge University Press, New York, 2006)CrossRefGoogle Scholar
  23. 23.
    V. Grimm, Ten years of individual-based modelling in ecology: What have we learned and what could we learn in the future? Ecol. Model. 115(2–5), 129–148 (1999)CrossRefGoogle Scholar
  24. 24.
    H. Hagras, A hierarchical type-2 fuzzy logic control architecture for autonomous mobile robots. IEEE Trans. Fuzzy Syst. 12, 524–539 (2004)CrossRefGoogle Scholar
  25. 25.
    H. Hagras, Type-2 FLCs: A new generation of fuzzy controllers. IEEE Comput. Intell. Mag. 2(1), 30–43 (2007)CrossRefGoogle Scholar
  26. 26.
    S. Hassan, L. Garmendia, J. Pavón, Agent-based social modeling and simulation with fuzzy sets, in Innovations in Hybrid Intelligent Systems, Advances in Soft Computing (Springer Berlin, Heidelberg, 2008), pp. 40–47Google Scholar
  27. 27.
    S. Hassan, M. Salgado, J. Pavón, Friendship dynamics: Modelling social relationships through a fuzzy agent-based simulation. Discret. Dyn. Nat. Soc. 2011, 19 p, Article ID 765640, (2011). doi:10.1155/2011/765640Google Scholar
  28. 28.
    E. Herrera-Viedma, F. Herrera, F. Chiclana, A consensus model for multiperson decision making with different preference structures. IEEE Trans. Syst. Man Cybern. Part A 32(3), 394–402 (2002)CrossRefGoogle Scholar
  29. 29.
    G. Klir, T. Folger, Fuzzy Sets, Uncertainty and Information (Prentice Hall, Englewood Cliffs, 1988)zbMATHGoogle Scholar
  30. 30.
    M. Lesani, N. Montazeri, Fuzzy trust aggregation and personalized trust inference in virtual social networks. Comput. Intell. 25(2), 51–83 (2009)CrossRefMathSciNetGoogle Scholar
  31. 31.
    K. Lewin, A Dynamic Theory of Personality (McGraw-Hill, New York, 1935)Google Scholar
  32. 32.
    K. Lewin, Defining the “Field at a Given Time”. Psychol. Rev. 50, 292–310 (1943)CrossRefGoogle Scholar
  33. 33.
    K. Lewin, Field Theory in Social Science (Tavistock, London, 1952)Google Scholar
  34. 34.
    K. Leyton-Brown, Y. Shoham, Essentials of Game Theory: A Concise Multidisciplinary Introduction. Synthesis Lectures on Artificial Intelligence and Machine Learning. (Morgan & Claypool, San Rafael, CA, USA, 2008)Google Scholar
  35. 35.
    C. Li, Y. Wang, H.D. Yang, Combining fuzzy partitions using fuzzy majority vote and KNN. JCP 5(5), 791–798 (2010)Google Scholar
  36. 36.
    F. Liu, J.M. Mendel, Encoding words into interval type-2 fuzzy sets using an interval approach. IEEE Trans. Fuzzy Syst. 16(6), 1503–1521 (2008)CrossRefGoogle Scholar
  37. 37.
    C.-F. Liu, C.-Y. Yeh, S.-J. Lee, Application of type-2 neuro-fuzzy modeling in stock price prediction. Appl. Soft. Comput. 12(4), 1348–1358 (2012)CrossRefGoogle Scholar
  38. 38.
    B. Márquez, M. Castanon-Puga, J. Castro, E. Suarez, S. Magdaleno-Palencia, Fuzzy models for complex social systems using distributed agencies in poverty studies, in Software Engineering and Computer Systems, Communications in Computer and Information Science, vol. 179, ed. by J. Mohamad Zain, W. Wan Mohd, E. El-Qawasmeh (Springer, Berlin, 2011), pp. 391–400Google Scholar
  39. 39.
    K. May, A set of independent, necessary and sufficient conditions for simple majority decision. Econometrica 20, 680–684 (1952)CrossRefzbMATHGoogle Scholar
  40. 40.
    J. Mendel, Uncertain Rule-based Fuzzy Logic Systems: Introduction and New Directions (Prentice Hall, Upper Saddle River, 2001)Google Scholar
  41. 41.
    J.M. Mendel, Fuzzy sets for words: A new beginning. IEEE FUZZ Conference, St. Louis, 26–28 May 2003, pp. 37–42Google Scholar
  42. 42.
    J.M. Mendel, Computing with words: Zadeh, Turing, Popper and Occam. IEEE Comput. Intell. Mag. 2, 10–17 (2007)CrossRefGoogle Scholar
  43. 43.
    J.M. Mendel, R.I. John, F. Liu, Interval type-2 fuzzy logic systems made simple. IEEE Trans. Fuzzy Syst. 14, 808–821 (2006)CrossRefGoogle Scholar
  44. 44.
    P.R. Milgrom, D.C. North, B.R. Weingast, The role of institutions in the revival of the trade: The law merchant, private Judges, and the champagne fairs. Econ. Polit. 2, 1954–1985 (1990)CrossRefGoogle Scholar
  45. 45.
    S. Miller, M.A. Góngora, J.M. Garibaldi, R. John, Interval type-2 fuzzy modelling and stochastic search for real-world inventory management. Soft. Comput. 16(8), 1447–1459 (2012)CrossRefGoogle Scholar
  46. 46.
    H. Moulin. Axioms of Cooperative Decision Making (Econometric Society Monographs). (Cambridge University Press, Cambridge, 1991)Google Scholar
  47. 47.
    D.C. North, Institutions, Institutional Change, and Economic Performance (Cambridge University Press, Cambridge, 1990)CrossRefGoogle Scholar
  48. 48.
    H. Nurmi, Fuzzy social choice: A selective retrospect. Soft. Comput. 12, 281–288 (2008)CrossRefzbMATHGoogle Scholar
  49. 49.
    T. Ören, N. Ghasem-Aghaee, Personality representation processable in fuzzy logic for human behavior simulation. Proceedings of the 2003 Summer Computer Simulation Conference, Montreal, 20–24 July 2003, pp. 11–18 (SCS)Google Scholar
  50. 50.
    J.I. Peláez, M.J. Do˜na, A majority model in group decision making using QMA–OWA operators. Int. J. Intell. Syst. 21(2), 193–208 (2006)CrossRefzbMATHGoogle Scholar
  51. 51.
    C.L. Ramírez, O. Castillo, P. Melin, A.R. Díaz, Simulation of the bird age-structured population growth based on an interval type-2 fuzzy cellular structure. Inf. Sci. 181(3), 519–535 (2011)CrossRefGoogle Scholar
  52. 52.
    E. Sabeur, G. Denis, Human behavior and social network simulation: Fuzzy sets/logic and agents-based approach, in SpringSim 2007, ed. by M.J. Ades, vol. 2 (SCS/ACM, San Diego, 2007), pp. 102–109Google Scholar
  53. 53.
    D. Sumpter, S. Pratt, Quorum responses and concensus decision making. Philos. Trans. R. Soc. B 364, 743–753 (2009)CrossRefGoogle Scholar
  54. 54.
    A. Vermeule, Submajority rules: Forcing accountability upon majorities. J. Polit. Philos. 13, 74–98 (2005)Google Scholar
  55. 55.
    P. Visscher, Group decision making in nest-site selection among social insects. Annu. Rev. Entomol. 52, 255–275 (2007)CrossRefGoogle Scholar
  56. 56.
    T.M. Vu, P.-O. Siebers, C. Wagner, Comparison of crisp systems and fuzzy systems in agent-based simulation. 13th UK Workshop on Computational Intelligence (UKCI), University of Surrey, pp. 54–61, 2013Google Scholar
  57. 57.
    D. Wu, A brief tutorial on interval type-2 fuzzy sets and systems (2012), Accessed 10 Aug 2014
  58. 58.
    D. Wu, W. Tan, Genetic learning and performation evaluation of type-2 fuzzy logic controllers. Eng. Appl. Artif. Intell. 19(8), 829–841 (2006)CrossRefGoogle Scholar
  59. 59.
    L.A. Zadeh, Fuzzy sets. Inf. Comput. 8, 338–353 (1965)zbMATHMathSciNetGoogle Scholar
  60. 60.
    L. Zadeh, Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans. Syst. Man Cybern. 1, 28–44 (1973)CrossRefMathSciNetGoogle Scholar
  61. 61.
    L.A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning-I. Inf. Sci. 8, 199–249 (1975)CrossRefzbMATHMathSciNetGoogle Scholar
  62. 62.
    L.A. Zadeh, A computational approach to fuzzy quantifiers in natural language. Comput. Math. Appl. 9(1), 149–184 (1983)CrossRefzbMATHMathSciNetGoogle Scholar
  63. 63.
    L.A. Zadeh, Fuzzy logic = computing with words. IEEE Trans. Fuzzy Syst. 4(2), 103–111 (1996)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2015

Authors and Affiliations

  • Christopher Frantz
    • 1
    Email author
  • Martin K. Purvis
    • 1
  • Maryam A. Purvis
    • 1
  • Mariusz Nowostawski
    • 1
  • Nathan D. Lewis
    • 1
  1. 1.Department of Information ScienceUniversity of OtagoDunedinNew Zealand

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