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Power, Voting, and Voting Power: 30 Years After pp 725–762Cite as

Coalitions and Catastrophic Climate Change

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Abstract

This chapter surveys the results in general equilibrium theory based on dynamical models, and emphasizes the role of structural stability. In this context it is natural to consider a preference field H for the society, combining economic fields, associated with the preferred changes wrought by agents in the economic market place, together with fields of preferred changes in the polity. A preference field specifies at each point \( x\in \) the space of states, X, a set of feasible vectors of change. A condition called half-openness of H is sufficient to guarantee existence of a local direction gradient, d, for the society, and thus of a social choice. when half openness fails then the dynamical system so defined can be chaotic. We apply some of these abstract ideas to the question of dealing with climate change.

This chapter is based on work supported by NSF grant 0715929.

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Notes

  1. 1.

    See for example Hardin (1971, 1982), Taylor (1976, 1982), Axelrod and Hamilton (1981), Axelrod (1981); Axelrod (1984), Kreps et al. (1982), Margolis (1982).

  2. 2.

    See the discussion in Schofield (2011).

  3. 3.

    Weitzman (2009) and Chichilnisky (2010). See also Chichilinisky ((1996b, 2000, 2011a, b) and Eisenberger (2010) on other catastrophic events such as collision with an asteroid.

  4. 4.

    See Schofield (1977); Schofield (1980a); Schofield (1980b). In a sense these voting theorems can be regarded as derivative of Arrow’s Impossibility Theorem (Arrow 1951). See also Arrow (1986).

  5. 5.

    The theory of chaos or complexity is rooted in Smale’s fundamental theorem (Smale 1966) that structural stability of dynamical systems is not “generic” or typical whenever the state space has more than two dimensions.

  6. 6.

    In their early analysis of chaos, Li and Yorke (1975) showed that in the domain of a chaotic transformation \(f\) it was possible for almost any pair of positions \((x,y)\) to transition from \(x\) to \(y=f^{r}(x),\) where \(f^{r}\) means the \(r\) times reiteration of \(f.\)

  7. 7.

    See Minsky (1975); Minsky (1986).

  8. 8.

    Karklins and Petersen (1993), Lohmann (1994). See also Bikhchandani et al. (1992).

  9. 9.

    The response by the citizens of these countries to the demise of Osama bin Laden on May 2, 2011, is in large degree also unpredictable.

  10. 10.

    See for example Carothers (2002) and Collier (2009).

  11. 11.

    Golub and Jackson (2010).

  12. 12.

    See Henrich et al. (2004, 2005), which reports on experiments in fifteen “small-scale societies,” using the game theoretic tools of the “prisoners’ dilemma,” the “ultimatum game,” etc.

  13. 13.

    See also Acemoglu and Robinson (2008).

  14. 14.

    The popular protests in N.Africa and the Middle East in 2011 were in opposition to oligarchic and autocratic power.

  15. 15.

    See also Shafer and Sonnenschein (1975).

  16. 16.

    In other words, there exists \(d\) such that \(d(v)>0\) for all \(v\in H(x)\subset T_{x}W\), whenever \(H(x)\ne \Upphi .\)

  17. 17.

    That is a critical Nash equilibrium which is an attractor of the integral curves.

  18. 18.

    Schofield (1972a, b), Ladha (1992, 1993, 1995, 1996), Ladha and Miller (1996).

  19. 19.

    Sunstein (2006, 2011) also notes that belief aggregation can lead to a situation where subgroups in the society come to hold very disparate opinions.

  20. 20.

    Gleick (1987), Buchanan (2001); Buchanan (2003), Gladwell (2002), Johnson (2002), Barabasi (2003); Barabasi (2011), Strogatz (2004), Watts (2002, 2003), Surowiecki (2005), Ball (2004), Christakis and Fowler (2011).

  21. 21.

    See, for example, Mandelbrot and Hudson (2004), Shiller (2003); Shiller (2005), Taleb (2007), Barbera (2009), Cassidy (2009), Fox (2009).

  22. 22.

    See also the earlier work by Richardson (1922) and by the team under von Neumann at the Institute for advanced Studies at Princeton using the computer known as ENIAC as described by Dyson (2012).

  23. 23.

    See for example Cavallli-Sforza and Feldman (1981), Bowles et al. (2003).

  24. 24.

    See also Eldredge (1976), Gould (1976).

  25. 25.

    See Maynard Smith (1982) for the game theoretic notion of evolutionary stable strategy.

  26. 26.

    Indeed as I understand the dynamical models, the chaotic episodes are due to the complex interactions of dynamical processes in the oceans, on the land, in weather, and in the heavens. These are very like interlinked coalitions of non-gradient vector fields.

  27. 27.

    This can be shown adapting the proof technique of Banks et al. (2002, 2006).

  28. 28.

    This depends on the extension of Michael’s selection theorem by Mas-Colell (1979).

  29. 29.

    It is bounded by median arcs such as \((M_{1},M_{2}).\)

  30. 30.

    See also Arrow (1969) and later analyses of such games in Schofield and Tovey (1992).

  31. 31.

    I use this as a metaphor derived from the notion of inflation in cosmology (Penrose 2011). If we can use the term entropy to characterise the distribution of events in the heart, then entropy increases dramatically at the inflationary point.

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  1. Center in Political Economy, Washington University in Saint Louis, 1 Brookings Drive, Saint Louis, MO, 63130, USA

    Norman Schofield

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  1. Institute of SocioEconomics, Department of Economics, University of Hamburg, Von-Melle-Park 5, Hamburg, 10146, Germany

    Manfred J Holler

  2. Department of Political Science and, Contemporary History, University of Turku, Assistentinkatu 7, Turku, 20014, Finland

    Hannu Nurmi

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Schofield, N. (2013). Coalitions and Catastrophic Climate Change. In: Holler, M., Nurmi, H. (eds) Power, Voting, and Voting Power: 30 Years After. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35929-3_39

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