Abstract
In practice , there are many examples when the diversity in a group enhances the group’s ability to solve problems – and thus, leads to more efficient groups, firms, schools, etc. Several papers, starting with the pioneering research by Scott E. Page from the University of Michigan at Ann Arbor, provide a theoretical justification for this known empirical phenomenon. However, when the general advise of increasing diversity is transformed into simple-to-follow algorithmic rules (like quotas), the result is not always successful. In this chapter, we prove that the problem of designing the most efficient group is computationally difficult (NP-hard). Thus, in general, it is not possible to come up with simple algorithmic rules for designing such groups: to design optimal groups, we need to combine standard optimization techniques with intelligent techniques that use expert knowledge.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
O. Castillo, P. Melin, E. Gamez, V. Kreinovich, O. Kosheleva, Intelligence techniques are needed to further enhance the advantage of groups with diversity in problem solving, in Proceedings of the 2009 IEEE Workshop on Hybrid Intelligent Models and Applications HIMA’2009, Nashville, Tennessee, 30 March–2 April 2009 (2009), pp. 48–55
L. Hong, S.E. Page, Problem solving by heterogeneous agents. J. Econ. Theory 97(1), 123–163 (2001)
L. Hong, S.E. Page, Groups of diverse problem solvers can outperform groups of high-ability problem solvers. Proc. Natl. Acad. Sci. 101(46), 16385–16389 (2004)
J.H. Miller, S.E. Page, Complex Adaptive Social Systems: The Interest in Between (Princeton University Press, Princeton, 2006)
S.E. Page, The Difference: How the Power of Diversity Creates Better Groups, Firms, Schools, and Societies (Princeton University Press, Princeton, 2007)
J.E. Gamez, F. Modave, O. Kosheleva, Selecting the most representative sample is NP–hard: need for expert (fuzzy) knowledge, in Proceedings of the IEEE World Congress on Computational Intelligence WCCI’2008, Hong Kong, China, 1–6 June 2008 (2008), pp. 1069–1074
C.C. Kuo, F. Glover, K.S. Dhir, Analyzing and modeling the maximum diversity problem by zero-one programming. Decision Sci. 24(6), 1171–1185 (1993)
V. Kreinovich, E. Johnson-Holubec, L.K. Reznik, M. Koshelev, Cooperative learning is better: explanation using dynamical systems, fuzzy logic, and geometric symmetries, in Proceedings of the Vietnam–Japan Bilateral Symposium on Fuzzy Systems and Applications VJFUZZY’98, HaLong Bay, Vietnam, 30th September–2nd October, 1998, ed. by H.P. Nguyen, A. Ohsato (1998), pp. 154–160
C.H. Papadimitriou, Computational Complexity (Addison Wesley, Reading, 1994)
G.J. Klir, B. Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications (Prentice-Hall, Upper Saddle River, 1995)
H.T. Nguyen, E.A. Walker, A First Course in Fuzzy Logic (CRC Press, Boca Raton, 2006)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 Springer-Verlag GmbH Germany
About this chapter
Cite this chapter
Kosheleva, O., Villaverde, K. (2018). How to Divide Students into Groups: Importance of Diversity and Need for Intelligent Techniques to Further Enhance the Advantage of Groups with Diversity in Problem Solving. In: How Interval and Fuzzy Techniques Can Improve Teaching. Studies in Computational Intelligence, vol 750. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55993-2_25
Download citation
DOI: https://doi.org/10.1007/978-3-662-55993-2_25
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-55991-8
Online ISBN: 978-3-662-55993-2
eBook Packages: EngineeringEngineering (R0)