Self-organized criticality: A new theory of political behaviour and some of its implications

British Journal of Political Science

Volumn 31, Issue 2, 2001, Pages 427-445

  Brunk, Gregory G ^a  

^a NONE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038257088     PISSN: 00071234     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0007123401000163     Document Type: Article

References (31)

1. For example, R. Huckfeldt, 'Structure, Indeterminacy and Chaos: A Case for Sociological Law', Journal of Theoretical Politics, 2 (1990), 413-33; C. Brown, Ballots of Tumult (Ann Arbor: University of Michigan Press, 1991).
2. For example, R. Huckfeldt, 'Structure, Indeterminacy and Chaos: A Case for Sociological Law', Journal of Theoretical Politics, 2 (1990), 413-33; C. Brown, Ballots of Tumult (Ann Arbor: University of Michigan Press, 1991).
3. See D. Kiel and E. Elliott, eds., Chaos Theory in the Social Sciences (Ann Arbor: University of Michigan Press, 1996).
4. P. Bak and K. Chen, 'Self-Organized Criticality', Scientific American, 264 (January 1991), 46-53; P. Bak and C. Tang, 'Earthquakes as a Self-Organized Critical Phenomenon', Journal of Geophysical Research, 94 (November 1989), 15635-7; P. Bak, C. Tang and K. Wisenfeld, 'Self-Organized Criticality', Physical Review A, 38 (July 1988), 364-74.
5. P. Bak and K. Chen, 'Self-Organized Criticality', Scientific American, 264 (January 1991), 46-53; P. Bak and C. Tang, 'Earthquakes as a Self-Organized Critical Phenomenon', Journal of Geophysical Research, 94 (November 1989), 15635-7; P. Bak, C. Tang and K. Wisenfeld, 'Self-Organized Criticality', Physical Review A, 38 (July 1988), 364-74.
6. P. Bak and K. Chen, 'Self-Organized Criticality', Scientific American, 264 (January 1991), 46-53; P. Bak and C. Tang, 'Earthquakes as a Self-Organized Critical Phenomenon', Journal of Geophysical Research, 94 (November 1989), 15635-7; P. Bak, C. Tang and K. Wisenfeld, 'Self-Organized Criticality', Physical Review A, 38 (July 1988), 364-74.
7. The Appendix simulates the behaviour of EIPOC (ever increasing probability of cascade) systems, which are constructed using very commonly encountered statistical processes as building blocks. See G. G. Brunk, 'Understanding Self-Organized Criticality as a Statistical Process', forthcoming in Complexity (2000). For programs that generate SOC in other ways, see H. J. Jensen, Self-Organized Criticality: Emergent Complex Behaviour in Physical and Biological Systems (Cambridge: Cambridge University Press, 1998). The EIPOC simulation can be 'tuned' to change the range of fractal similarity by varying the growth rate.
8. The Appendix simulates the behaviour of EIPOC (ever increasing probability of cascade) systems, which are constructed using very commonly encountered statistical processes as building blocks. See G. G. Brunk, 'Understanding Self-Organized Criticality as a Statistical Process', forthcoming in Complexity (2000). For programs that generate SOC in other ways, see H. J. Jensen, Self-Organized Criticality: Emergent Complex Behaviour in Physical and Biological Systems (Cambridge: Cambridge University Press, 1998). The EIPOC simulation can be 'tuned' to change the range of fractal similarity by varying the growth rate.
9. For background, see K. Christensen, Z. Olami and P. Bak, 'Deterministic 1/f Noise in Nonconservative Models of Self-Organized Criticality', Physical Review Letters, 68 (1992), 2417-20; M. Gardner, 'White and Brown Music, Fractal Curves and One-over-f Fluctuations', Scientific American (April 1978), 16-32; B. J. West, 'The Noise in Natural Phenomena', American Scientist, 78 (1990), 40-5; B. J. West and M. F. Schlesinger, 'On the Ubiquity of 1/f Noise', International Journal of Modern Physics B, 3 (1989), 795-819.
10. For background, see K. Christensen, Z. Olami and P. Bak, 'Deterministic 1/f Noise in Nonconservative Models of Self-Organized Criticality', Physical Review Letters, 68 (1992), 2417-20; M. Gardner, 'White and Brown Music, Fractal Curves and One-over-f Fluctuations', Scientific American (April 1978), 16-32; B. J. West, 'The Noise in Natural Phenomena', American Scientist, 78 (1990), 40-5; B. J. West and M. F. Schlesinger, 'On the Ubiquity of 1/f Noise', International Journal of Modern Physics B, 3 (1989), 795-819.
11. For background, see K. Christensen, Z. Olami and P. Bak, 'Deterministic 1/f Noise in Nonconservative Models of Self-Organized Criticality', Physical Review Letters, 68 (1992), 2417-20; M. Gardner, 'White and Brown Music, Fractal Curves and One-over-f Fluctuations', Scientific American (April 1978), 16-32; B. J. West, 'The Noise in Natural Phenomena', American Scientist, 78 (1990), 40-5; B. J. West and M. F. Schlesinger, 'On the Ubiquity of 1/f Noise', International Journal of Modern Physics B, 3 (1989), 795-819.
12. For background, see K. Christensen, Z. Olami and P. Bak, 'Deterministic 1/f Noise in Nonconservative Models of Self-Organized Criticality', Physical Review Letters, 68 (1992), 2417-20; M. Gardner, 'White and Brown Music, Fractal Curves and One-over-f Fluctuations', Scientific American (April 1978), 16-32; B. J. West, 'The Noise in Natural Phenomena', American Scientist, 78 (1990), 40-5; B. J. West and M. F. Schlesinger, 'On the Ubiquity of 1/f Noise', International Journal of Modern Physics B, 3 (1989), 795-819.
13. For example, C. Brown, 'Politics and the Environment: Nonlinear Instabilities Dominate', American Political Science Review, 88 (1994) 292-303.
14. T. Kuhn, The Structure of Scientific Revolutions (Chicago: University of Chicago Press, 1970).
15. Over thirty years ago, Benoit Mandelbrot noted that social science time series are not characterized by random walks and white noise. This insight was ignored because he could offer no plausible explanation for it, and, indeed, none existed at the time of his discovery. See B. B. Mandelbrot, 'Variation of Certain Speculative Prices', Journal of Business, 36 (1963), 394-419.
16. See L. F. Richardson, 'Frequency and Occurrence of Wars and Other Fatal Quarrels', Nature, 148 (15 November 1941), 598, and his subsequent works.
17. In illustrating a power function, it is useful to examine data with a clearly defined lower limit. Such data for wars are provided by G. Bouthoul and R. Carrere, 'A List of the 366 Major Armed Conflicts of the Period 1740-1974', Peace Research, 10 (1978), 83-108. Wars are aggregated into groups of less than 10,000 deaths, less than 20,000 deaths, etc. to a point where zero frequencies dominate at 140,000 and greater deaths. D. L. Turcotte, 'Self-Organized Criticality', Reports on Progress in Physics, 62(1999), 1418-20, found the same relationship using a quite different sample of wars.
18. In illustrating a power function, it is useful to examine data with a clearly defined lower limit. Such data for wars are provided by G. Bouthoul and R. Carrere, 'A List of the 366 Major Armed Conflicts of the Period 1740-1974', Peace Research, 10 (1978), 83-108. Wars are aggregated into groups of less than 10,000 deaths, less than 20,000 deaths, etc. to a point where zero frequencies dominate at 140,000 and greater deaths. D. L. Turcotte, 'Self-Organized Criticality', Reports on Progress in Physics, 62(1999), 1418-20, found the same relationship using a quite different sample of wars.
19. See P. Bak, K. Chen and M. Creutz, 'Self-Organized Criticality in the Game of Life', Nature, 342 (14 December 1989), 780-2; K. Ito, 'Punctuated-Equilibrium Model of Biological Evolution Is Also a Self-Organized-Criticality Model of Earthquakes', Physical Review E, 52 (1995), 3232-3; D. R. Lockwood and J. A. Lockwood, 'Evidence of Self-Organized Criticality in Insect Populations', Complexity, 2 (March 1997), 49-58;
20. See P. Bak, K. Chen and M. Creutz, 'Self-Organized Criticality in the Game of Life', Nature, 342 (14 December 1989), 780-2; K. Ito, 'Punctuated-Equilibrium Model of Biological Evolution Is Also a Self-Organized-Criticality Model of Earthquakes', Physical Review E, 52 (1995), 3232-3; D. R. Lockwood and J. A. Lockwood, 'Evidence of Self-Organized Criticality in Insect Populations', Complexity, 2 (March 1997), 49-58;
21. See P. Bak, K. Chen and M. Creutz, 'Self-Organized Criticality in the Game of Life', Nature, 342 (14 December 1989), 780-2; K. Ito, 'Punctuated-Equilibrium Model of Biological Evolution Is Also a Self-Organized-Criticality Model of Earthquakes', Physical Review E, 52 (1995), 3232-3; D. R. Lockwood and J. A. Lockwood, 'Evidence of Self-Organized Criticality in Insect Populations', Complexity, 2 (March 1997), 49-58;
22. K. Sheppen, P. Bak, H. Flyvbjerg and M. H. Jensen, 'Evolution as a Self-Organized Critical Phenomenon', Proceedings of the National Academy of Science (USA), 92 (1995), 5209-13; R. V. Sole and S. C. Manrubia, 'Are Rainforests Self-Organized in a Critical State?' Journal of Theoretical Biology, 173 (1996), 31-40.
23. K. Sheppen, P. Bak, H. Flyvbjerg and M. H. Jensen, 'Evolution as a Self-Organized Critical Phenomenon', Proceedings of the National Academy of Science (USA), 92 (1995), 5209-13; R. V. Sole and S. C. Manrubia, 'Are Rainforests Self-Organized in a Critical State?' Journal of Theoretical Biology, 173 (1996), 31-40.
24. Until recently, researchers have tried to model such problems using chaos or differential equations. For example, R. M. May, Stability and Complexity in Model Ecosystems (Princeton, NJ: Princeton University Press, 1974).
25. For discussions of multifractal time series, see B. B. Mandelbrot, Multifractals and 1/f Noise: Wild Self-Affinity in Physics (New York: Springer, 1999), and B. B. Mandelbrot, 'A Multifractal Walk Down Wall Street', Scientific American, 280 (February 1999), 70-3.
26. For discussions of multifractal time series, see B. B. Mandelbrot, Multifractals and 1/f Noise: Wild Self-Affinity in Physics (New York: Springer, 1999), and B. B. Mandelbrot, 'A Multifractal Walk Down Wall Street', Scientific American, 280 (February 1999), 70-3.
27. The sources are Congressional Quarterly's Guide to US Elections (1985) and recent editions of the Almanac of American Politics.
28. During the nineteenth century it was common for American parties to change their names. When it is obvious that the same coalition remained in power, e.g., the same person was re-elected governor, this was treated as a victory for the incumbent political coalition. Some voting shifts could not be counted because the tallies had actually been lost, while the American Civil War interrupted elections in the Confederate states. Elections also were eliminated if the incumbent party received all or none of the popular vote since these were not the consequence of a real voting shift, but of a particular electoral rule. As a final safeguard to ensure that the results would not be biased in favour of discovering SOC, situations where the winner was elected with less than a majority were eliminated. Despite these conservative coding procedures, the data decisions had no major effect on the empirical results.
29. P. H. Argersinger, 'A Place on the Ballot: Fusion Politics and Antifusion Laws', American Historical Review, 85 (1980), 287-306; J. G. Rusk, 'The Effect of the Australian Ballot Reform on Split Ticket Voting', American Political Science Review, 64 (1970), 1220-38; H. A. Scarrow, 'Duverger's Law, Fusion, and the Decline of American Third Parties', Western Political Quarterly, 39 (1986), 634-47.
30. P. H. Argersinger, 'A Place on the Ballot: Fusion Politics and Antifusion Laws', American Historical Review, 85 (1980), 287-306; J. G. Rusk, 'The Effect of the Australian Ballot Reform on Split Ticket Voting', American Political Science Review, 64 (1970), 1220-38; H. A. Scarrow, 'Duverger's Law, Fusion, and the Decline of American Third Parties', Western Political Quarterly, 39 (1986), 634-47.
31. P. H. Argersinger, 'A Place on the Ballot: Fusion Politics and Antifusion Laws', American Historical Review, 85 (1980), 287-306; J. G. Rusk, 'The Effect of the Australian Ballot Reform on Split Ticket Voting', American Political Science Review, 64 (1970), 1220-38; H. A. Scarrow, 'Duverger's Law, Fusion, and the Decline of American Third Parties', Western Political Quarterly, 39 (1986), 634-47.