Abstract
The paradigms of cybernetic models of social systems are frequently finite automata. Such models, implicitly or explicitly, require a decision procedure for multi-attribute value aggregation. This decision procedure requires either a hierarchical ordering of sub- and supra-systems, or is reduced to the cyclical majority problem. Many well-known applications of cybernetic concepts to the analysis of social systems have been aimed at constructing formal models of society and using these models to examine processes which could be described by finite automata1. The outstanding work of Buckley2, Parsons3 and Etzioni4 in sociology; of Deutsch5 and Easton6 in political science; and of Forrester7, D. H. Meadows, D. L. Meadows, Randers and Behrens8, and Mesarovic and Pestel9 in social systems simulation exemplify this approach. Simulations of political processes in Shaffer10, Pool11, and Klausner12 typify cybernetic models expressed as implicit theory embodied in computer programs (as noted by Browning)13, as well as showing the behavior of the explicit processes which the programs model.
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Notes
For a model exhibiting an explicit attempt to construct a finite automata see G. H. Kramer, ‘An Impossibility Result Concerning the Theory of Decision Making’ in J. Bernard (ed.) Mathematical Applications in Political Science Dallas, Texas: So. Meth. U. Press; 1966.
W. Buckley, Sociology and Modem Systems Theory. Englewood Cliffs, NJ: Prentice-Hall, 1967, and Modern Systems Research for the Behavioral Scientist Chicago: Aldine, 1968.
T. Parsons, The Social System. Glencoe, Ill: The Free Press; 1951.
A. Etzioni, The Active Society: A Theory of Societal and Political Processes. New York: The Free Press, 1968. See also Breed, W., The Self-Guiding Society. New York: The Free Press, 1971.
K. W. Deutsch, The Nerves of Government. New York: The Free Press, 1963.
D. Easton, A Systems Analysis of Political Life. New York: Wiley, 1965.
J. W. Forrester, ‘Understanding the Counter Intuitive Behavior of Social Systems’ in J. Beishon and G. Peters (eds.), Systems Behavior. London: Harper and Row, 223–240, 1976, J. W. Forrester, Urban Dynamics. Cambridge, Mass.: The M.I.T. Press; 1971, J. W. Forrester, World Dynamics. Cambridge, Mass.: Wright-Allen Press, 1971.
D. H. Meadows, D. L. Meadows, J. Randers and W. W. Behrens III, The Limits to Growth: A Report for the Club of Rome on the Predicament of Mankind. New York: Signet, 1975.
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I. de S. Pool, R. P. Abelson, and S. L. Popkin, Candidates, Issues and Strategies: A Computer Simulation of the 1960 and 1964 Elections, Cambridge, Mass.: The M.I.T. Press, 1965.
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E. Laszlo, Introduction to Systems Philosophy, 98–117 (see Note 14).
H. A. Simon, The Shape of Automation for Men and Management, Harper and Row, p. 102, 99–100, 1965.
H. H. Pattee, Hierarchy Theory, the Challenge of Complex Systems, New York: Braziller, p. xi, 1973.
H. A. Simon, The Shape of Automation, p. 70–71 (see Note 16).
Ibid, p. 72.
See E. Yourdon and L. L. Constantine, Structured Design, New York: Yourdon, 1976; also O. J. Dahl, E. W. Dijkstra, and C. A. R. Hoare, Structured Programming, New York: Academic Press; 1972, especially Part III, ‘Hierarchical Program Structures’ by O. J. Dahl and C. A. R. Hoare.
H. A. Simon, The Shape of Automation, p. 101 (see Note 16).
See A. C. Shaw, The Logical Design of Operating Systems, Englewood Cliffs, NJ: Prentice-Hall, 1974, especially Chap. 8, ‘The Deadlock Problem’.
See E. W. Dijkstra, A Discipline of Programming, Englewood Cliffs, NJ: Prentice-Hall, 1976, and ‘Guarded Commands, Nondeterminacy and Formal Derivation of Programs’ in R. T. Yeh (ed.), Current Trends in Programming Methodology, Vol. I: Software Specification and Design, Englewood Cliffs, NJ: Prentice-Hall, 1977.
See E. Yourdon and L. L. Constantine, Structured Design, esp. Chap. 18, ‘Homologous and Incremental Structures’ (Note 20) and O. J. Dahl, E. W. Dijkstra, and C. A. R. Hoare, Structured Programming, ‘Hierarchical Program Structures’ by O. J. Dahl and C. A. R. Hoare (Note 20). Simon also refers to similar program structures as ‘productions’ in H. H. Pattee (ed.) Hierarchy Theory, ‘The Organization of Complex Systems’, p. 19 (see Note 17).
See J. Martin, Computer Data-Base Organization, Englewood Cliffs, NJ: Prentice Hall, 1975, especially Chap. 20, ‘Chains and Ring Structures’.
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R. G. Niemi, and H. F. Weisberg, ‘A Mathematical Solution for the Probability of the Paradox of Voting.’ Behavioral Science 13, Nr. 4, (July): 317–323, 1968.
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F. S. Roberts, Discrete Mathematical Models, Englewood Cliffs, NJ: Prentice-Hall, 1976, especially Chap. 7, ‘Group Decision Making’.
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R. G. Niemi and H. F. Weisberg, ‘A Mathematical Solution for the Probability of the Paradox of Voting.’ Behavioral Science 13, Nr. 4, (July): 320, 1968. R. G. Niemi and H. F. Weisberg, Probability Models of Collective Decision, Columbus, Ohio: Merrill, 1972, especially Part 3, ‘The Paradox of Voting,’ pp. 181–272.
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P. C. Fishburn, The Theory of Social Choice, Princeton, NJ: Princeton University Press, 1977, and his ‘Arrow’s Impossibility Theorem: Concise Proof and Infinite Voters.’ Journal of Economic Theory 2, 103–106, 1970.
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See P. K. Pattanaik, Voting and Collective Choice, Cambridge, England: Cambridge University Press, 1971.
K. Arrow, Social Choice and Individual Values (see Note 26). Compare especially Theorem 2, p. 59, and Theorem 3 and its corollary, p. 63.
For a formal treatment of Turing machines, see M. Minsky, Computation: Finite and Infinite Machines, Englewood Cliffs, NJ: Prentice-Hall, 1967. For a discussion of NP completeness and complexity hierarchies, see A. V. Aho, J. E. Hopcraft and J. D. Ullman, The Design and Analysis of Computer Algorithms, Reading, Mass.: Addison-Wesley, 1974, also M. A. Arbib, Theories of Abstract Automata, Englewood Cliffs, NJ: Prentice-Hall, 1969.
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Ibid, p. 306.
Ibid, p. 307.
Ibid. Weide also notes: ‘A language L 1 is “polynomially reducible” to L 2 if there is a deterministic polynomial-time algorithm which transforms a stringx into a stringf(x) such that x is in L 1 ifff(x) is in L 2.’
R. M. Karp, ‘Reducibility Among Combinatorial Problems,’ Complexity of Computer Computations (see Note 40), pp. 85–103.
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T. C. T. Kotiah and D. I. Steinberg, ‘Occurrences of Cycling and Other Phenomena Arising in a Class of Linear Programming Models.’ Communications of the ACM 20, Nr. 2 (February): 107–112, 1977.
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See P. K. Pattanaik, Voting and Collective Choice (Note 45). Also Y. Murakami, Logic and Social Choice, New York: Dover, 1968.
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C. H. Coombs, A Theory of Data, New York: Wiley, 1964.
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Ibid, pp. 493–494.
Ibid, p. 488. Niemi defines single-peakedness as follows: ‘A set of preference orderings is single-peaked if there is an ordering of the alternatives on the abscissa such that when utility or degree of preference is indicated by the ordinate, each preference ordering can be represented by a curve which changes its direction at most once, from up to down (i.e. has at most one peak).’
R. Levins, ‘The Limits of Complexity’ in Hierarchy Theory, p. 114, (see Note 17), also S. A. Kauffman, ‘Metabolic Stability and Epigenesis in Randomly Constructed Genetic Nets.’ Journal of Theoretical Biology 22, 437–467.
Ibid, pp. 114–115.
Ibid, p. 115.
See A. Ando, F. M. Fisher and H. A. Simon, Essays on the Structure of Social Science Models, Cambridge, Mass.: The M.I.T. Press, 1963, for an extensive discussion of ‘near-decomposability’.
H. A. Simon, ‘The Organization of Complex Systems,’ Hierarchy Theory, pp. 15–16 (see Note 17).
See L. R. Sayles, ‘Matrix Management, the Structure with a Future,’ Organizational Dynamics 5, Nr. 2 (August): 2–10, 1976; P. R. Lawrence, H. F. Kolodny and S. M. Davis, ‘The Human Side of the Matrix.’ Organizational Dynamics 6, Nr. 1 (Summer): 43–61, 1977; J. R. Galbraith, ‘Matrix Organization Design.’ Business Horizons (February): 21–40, 1971; C. Argyris, ‘Today’s Problems with Tomorrows Organizations,’ The Journal of Management Studies (March): 84–101, 1973; and S. M. Davis and P. R. Lawrence, Matrix, New York: Macmillan, 1977.
R. N. Rosecrance, Action and Reaction in World Politics, Boston: Little, Brown, p. 222, 1963.
Ibid, p. 306.
W. R. Ashby, An Introduction to Cybernetics, New York: Wiley, 1963, especially Chap. 13.
See K. Appel, and W. Haken, ‘The Solution of the Four-Color Map Problem.’ Scientific American 237, Nr. 4 (October): 108–121, 1977.
W. R. Ashby, An Introduction to Cybernetics (see Note 72), 22–23, also Chaps. 5 and 7.
See H. Dooyeweerd, In the Twilight of Western Thought: Studies in the Pretended Autonomy of Philosophical Thought. Grand Rapids, Mich.: Baker, 1960, and his Transcendental Problems in Philosophic Thought. Grand Rapids, Mich.: Baker, 1953.
Simon also cautions against a ‘Laplacian’ reductionism. See H. A. Simon, ‘The Organization of Complex Systems’ in Hierarchy Theory, pp. 24–27 (see Note 17).
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Booker, D.M.M. (1978). Are societies Turing machines? Some implications of the cyclical majority problem, an NP complete problem, for cybernetic models of social systems. In: Geyer, R.F., van der Zouwen, J. (eds) Sociocybernetics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-4095-9_6
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