Coalitions and Catastrophic Climate Change



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.


Climate change  Black swan events Dynamical models The heart as a social choice correspondence 


  1. Acemoglu, D. (2008). Oligarchic versus democratic societies. Journal of the European Economic Association, 6, 1–44.CrossRefGoogle Scholar
  2. Acemoglu, D., & Robinson, J. (2006). Economic origins of dictatorship and democracy. Cambridge: Cambridge University Press.Google Scholar
  3. Acemoglu, D., & Robinson, J. (2008). Persistence of power, elites, and institutions. American Economic Review, 98, 267–293.CrossRefGoogle Scholar
  4. Acemoglu, D., & Robinson, J. (2011). Why nations fail. London: Profile Books.Google Scholar
  5. Acemoglu, D., Johnson, S., Robinson, J., & Yared, P. (2009). Reevaluating the modernization hypothesis. Journal of Monetary Economics, 56, 1043–1058.CrossRefGoogle Scholar
  6. Acemoglu, D., Ozdaglar, A., & Tahbaz-Salehi, A. (2010). Cascades in networks and aggregate volatility. NBER Working Paper # 16516.Google Scholar
  7. Akerlof, G. A., & Shiller, R. J. (2009). Animal spirits. Princeton: Princeton University Press.Google Scholar
  8. Aliprantis, C., & Brown, D. J. (1983). Equilibria in markets with a Riesz space of commodities. Journal of Mathematical Economics, 11, 189–207.Google Scholar
  9. Arrow, K. J. (1951). Social choice and individual values. New Haven: Yale University Press.Google Scholar
  10. Arrow, K. J. (1969). Tullock and an existence theorem. Public Choice, 6, 105–111.CrossRefGoogle Scholar
  11. Arrow, K. (1986). Rationality of self and others in an economic system. Journal of Business, 59, S385–S399.CrossRefGoogle Scholar
  12. Arrow, K., & Debreu, G. (1954). Existence of an equilibrium for a competitive economy. Econometrica, 22, 265–90.CrossRefGoogle Scholar
  13. Austen-Smith, D., & Banks, J. (1996). Information aggregation, rationality, and the Condorcet Jury Theorem. American Political Science Review, 90, 34–45.CrossRefGoogle Scholar
  14. Axelrod, R. (1981). The emergence of cooperation among egoists. American Political Science Review, 75, 306–318.CrossRefGoogle Scholar
  15. Axelrod, R. (1984). The evolution of cooperation. New York: Basic.Google Scholar
  16. Axelrod, R., & Hamilton, W. D. (1981). The evolution of cooperation. Science, 211, 1390–1396.CrossRefGoogle Scholar
  17. Bak, P. (1996). How nature works: The science of self oerganized criticality. Berlin: Springer.Google Scholar
  18. Bak, P., & Sneppen, K. (1993). Punctuated equilibrium and criticality in a simple model of evolution. Physical Review Letters, 71(24), 4083–4086.Google Scholar
  19. Ball, P. (2004). Critical mass. New York: Ferrar, Strauss and Giroux.Google Scholar
  20. Banks, J. S. (1995). Singularity theory and core existence in the spatial model. Journal of Mathematical Economics, 24, 523–536.CrossRefGoogle Scholar
  21. Banks, J., Duggan, J., & Le Breton, M. (2002). Bounds for mixed strategy equilibria and the spatial model of elections. Journal of Economic Theory, 103, 88–105.CrossRefGoogle Scholar
  22. Banks, J., Duggan, J., & Le Breton, M. (2006). Social choice and electoral competition in the general spatial model. Journal of Economic Theory, 126, 194–234.CrossRefGoogle Scholar
  23. Barabasi, A.-L. (2003). Linked. New York: Plume.Google Scholar
  24. Barabasi, A.-L. (2011). Bursts. New York: Dutton.Google Scholar
  25. Barbera, R. (2009). The cost of capitalism: Understanding market mayhem. New York: McGraw Hill.Google Scholar
  26. Bergstrom, T. (1975). The existence of maximal elements and equilibria in the absence of transitivity. Typescript: University of Michigan.Google Scholar
  27. Bergstrom, T. (1992). When non-transitive relations take maxima and competitive equilibrium can’t be beat. In R. Riezman & W. Neuefeind (Eds.), Economic theory and international trade. Berlin: Springer.Google Scholar
  28. Bikhchandani, S., Hirschleifer, D., & Welsh, I. (1992). A theory of fads, fashion, custom, and cultural change as information cascades. Journal of Political Economy, 100, 992–1026.CrossRefGoogle Scholar
  29. Binmore, K. (2005). Natural justice. Oxford: Oxford University Press.CrossRefGoogle Scholar
  30. Binmore, K. (2009). Rational decisions. Princeton, NJ: Princeton University Press.Google Scholar
  31. Bowles, S., et al. (2003). The co-evolution of individual behaviors and socal institutions. Journal of Theoretical Biology, 223, 135–147.CrossRefGoogle Scholar
  32. Boyd, J., & Richerson, P. J. (2005). The origin and evolution of culture. Oxford: Oxford University Press.Google Scholar
  33. Brown, R. (1971). The Lefschetz fixed point theorem. Glenview, IL: Scott and Foreman.Google Scholar
  34. Brouwer, L. E. J. (1912). Uber abbildung von mannigfaltikeiten. Mathematische Annalen, 71, 97–115.CrossRefGoogle Scholar
  35. Buchanan, M. (2001). Ubiquity. New York: Crown.Google Scholar
  36. Buchanan, M. (2003). Nexus. New York: Norton.Google Scholar
  37. Burkhart, J. M., Hrdy, S. B., & van Schaik, C. P. (2009). Cooperative breeding and human cognitive evolution. Evolutionary Anthropology, 18, 175–186.CrossRefGoogle Scholar
  38. Calvin, W. H. (2003). The ascent of mind. New York: Bantam.Google Scholar
  39. Carothers, T. (2002). The end of the transition paradigm. Journal of Democracy, 13, 5–21.CrossRefGoogle Scholar
  40. Cassidy, J. (2009). How markets fail: The logic of economic calamities. New York: Farrar, Strauss and Giroux.Google Scholar
  41. Cavallli-Sforza, L., & Feldman, M. (1981). Cultural transmission and evolution. Princeton, NJ: Princeton University Press.Google Scholar
  42. Chichilnisky, G. (1992). Social diversity, arbitrage, and gains from trade: A unified perspective on resource allocation. American Economic Review, 84, 427–434.Google Scholar
  43. Chichilnisky, G. (1993). Intersecting families of sets and the topology of cones in economics. Bulletin of the American Mathematical Society, 29, 189–207.CrossRefGoogle Scholar
  44. Chichilnisky, G. (1995). Limited arbitrage is necessary and sufficient for the existence of a competitive equilibrium with or without short sales. Economic Theory, 5, 79–107.CrossRefGoogle Scholar
  45. Chichilnisky, G. (1996a). Markets and games: A simple equivalence among the core, equilibrium and limited arbitrage. Metroeconomica, 47, 266–280.CrossRefGoogle Scholar
  46. Chichilnisky, G. (1996b). An axiomatic approach to sustainable development. Social Choice and Welfare, 13, 231–257.CrossRefGoogle Scholar
  47. Chichilnisky, G. (1997a). A topological invariant for competitive markets. Journal of Mathematical Economics, 28, 445–469.CrossRefGoogle Scholar
  48. Chichilnisky, G. (1997b). Limited arbitrage is necessary and sufficient for the existence of a equilibrium. Journal of Mathematical Economics, 28, 470–479.CrossRefGoogle Scholar
  49. Chichilnisky, G. (1997c). Market arbitrage, social choice and the core. Social Choice and Welfare, 14, 161–198.CrossRefGoogle Scholar
  50. Chichilnisky, G. (2000). An axiomatic approach to choice under uncertainty with catastrophic risks. Resource Energy Economics, 22, 221–231.CrossRefGoogle Scholar
  51. Chichilnisky, G. (2009a). The topology of fear. Journal of Mathematical Economics, 45, 807–816.CrossRefGoogle Scholar
  52. Chichilnisky, G. (2009b). Avoiding extinction: Equal treatment of the present and the future. Working Paper, Columbia University.Google Scholar
  53. Chichilnisky, G. (2010). The foundations of statistics with black swans. Mathematical Social Sciences, 59, 184–192.CrossRefGoogle Scholar
  54. Chichilnisky, G., & Eisenberger, P. (2010). Asteroids: Assessing catastrophic risks. Journal of Probability and Statistics Article ID 954750.Google Scholar
  55. Chichilnisky, G. (2011a) Catastrophic risks with finite or infinite states. International Journal of Ecological Economics and Statistics, 23, F11.Google Scholar
  56. Chichilnisky, G. (2011b). Sustainable markets with short sales. Economic Theory (in press).Google Scholar
  57. Christakis, N., & Fowler, J. H. (2011). Connected. New York: Back Bay.Google Scholar
  58. Collier, P. (2009). Wars, guns and votes. New York: Harper.Google Scholar
  59. Collier, P. (2010). The plundered planet. Oxford: Oxford University Press.Google Scholar
  60. Condorcet, N. (1994 [1785]) Essai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité des voix. Paris: Imprimerie Royale. Translated in part in: McLean I, Hewitt F, Condorcet: Foundations of social choice and political theory. London: Edward Elgar.Google Scholar
  61. Corcos, A., et al. (2002). Imitation and contrarian behavior: Hyperbolic bubbles, crashes and chaos. Quantitative Finance, 2, 264–281.Google Scholar
  62. Dasgupta, P. (2005). Three conceptions of intergenerational Justice. In H. Lillehammer & D. H. Mellor (Eds.), Ramsey’s legacy. Oxford: Clarendon Press.Google Scholar
  63. Dawkins, R. (1976). The selfish gene. Oxford: Oxford University Press.Google Scholar
  64. Debreu, G. (1970). Economies with a finite number of equilibria. Econometrica, 38, 387–392.CrossRefGoogle Scholar
  65. Debreu, G. (1976). The application to economics of differential topology and global analysis: Regular differentiable economies. American Economic Review, 66, 280–287.Google Scholar
  66. Deutscher, G. (2006). The unfolding of language. New York: Holt.Google Scholar
  67. Dyson, G. (2012). Turing’s Cathedral. New York: Pantheon.Google Scholar
  68. Easley, D., & Kleinberg, J. (2010). Networks, crowds and markets. Cambridge: Cambridge University Press.Google Scholar
  69. Edwards, P. N. (2010). A vast machine: Computer models, climate data, and the politics of global warming. Cambridge, MA: MIT Press.Google Scholar
  70. Eldredge, N. (1976). Differential evolutionary rates. Paleobiology, 2, 174–177.Google Scholar
  71. Eldredge, N., & Gould, S. J. (1972). Punctuated equilibrium. In T. Schopf (Ed.), Models of paleobiology. New York: Norton.Google Scholar
  72. Fan, K. (1961). A generalization of Tychonoff’s fixed point theorem. Mathematische Annalen, 42, 305–310.CrossRefGoogle Scholar
  73. Ferguson, N. (1997). Introduction. In N. Ferguson (Ed.), Virtual history. London: Picador.Google Scholar
  74. Ferguson, N. (2002). Empire: The rise and demise of the British world order. London: Penguin Books.Google Scholar
  75. Ferguson, N. (2011). Civilization. London: Penguin.Google Scholar
  76. Flyvbjerg, H., Sneppen, K., & Bak, P. (1993). A mean field theory for a simple model of evolution. Physical Review Letters, 71, 4087–4090.CrossRefGoogle Scholar
  77. Fox, J. (2009). The myth of the rational market. New York: Harper.Google Scholar
  78. Fukuyama, F. (2011). The origins of political order. New York: Ferrar, Strauss and Giroux.Google Scholar
  79. Gazzaniga, M.S. (2008). Human. New York: Harper.Google Scholar
  80. Gintis, H. (2000). Strong reciprocity and human sociality. Journal of Theoretical Biology, 206, 169–179.CrossRefGoogle Scholar
  81. Gladwell, M. (2002). The tipping point. New York: Back Bay.Google Scholar
  82. Gleick, J. (1987). Chaos: Making a new science. New York: Viking.Google Scholar
  83. Golub, B., & Jackson, M. (2010). Naive learning in social networks and the wisdom of crowds. American Economic Journal: Microeconomics, 2, 112–149.CrossRefGoogle Scholar
  84. Gould, S. J. (1976). The gnemoic metronome as a null hypothesis. Paleobiology, 2, 177–179.Google Scholar
  85. Gould, S. J. (2002). The structure of evolutionary theory. Cambridge, MA: Belknap Press of Harvard University Press.Google Scholar
  86. Hahn, F. (1973). On the notion of equilibrium in economics. Cambridge: Cambridge University Press.Google Scholar
  87. Hamilton, W. (1964). The genetical evolution of social behavior I and II. Journal of Theoretical Biology, 7, 1–52.CrossRefGoogle Scholar
  88. Hamilton, W. (1970). Selfish and spiteful behavior in an evolutionary model. Nature, 228, 1218–1220.CrossRefGoogle Scholar
  89. Hardin, G. (1968 [1973]). The tragedy of the commons. In H. E. Daly (Ed.), Towards a steady state economy. San Francisco: Freeman.Google Scholar
  90. Hardin, R. (1971). Collective action as an agreeable prisons’ dilemma. Behavioral Sciences, 16, 472–481.CrossRefGoogle Scholar
  91. Hardin, R. (1982). Collective action. Baltimore: Johns Hopkins University Press.Google Scholar
  92. Henrich, J., et al. (2004). Foundations of human sociality. Oxford: Oxford University Press.CrossRefGoogle Scholar
  93. Henrich, J., et al. (2005).‘Economic man’ in cross-cultural perspective: Behavioral experiments in 15 small-scale societies. Behavioral and Brain Sciences, 28, 795–855.Google Scholar
  94. Hirsch, M. (1976). Differential topology. Berlin: Springer.CrossRefGoogle Scholar
  95. Hobbes, T. (2009 [1651]). In J. C. A. Gaskin (Ed.), Leviathan; or the matter, forme, and power of a common-wealth, ecclesiastical and civil. Oxford: Oxford University Press.Google Scholar
  96. Hrdy, S. B. (2011). Mothers and others: The evolutionary origins of mutual understanding. Cambridge, MA: Harvard University Press.Google Scholar
  97. Jablonka, E., & Lamb, M. J. (2006). Evolution in four dimensions: Genetic, epigenetic, behavioral, and symbolic variation in the history of life. Cambridge, MA: MIT Press.Google Scholar
  98. Johnson, S. (2002). Emergence. New York: Scribner.Google Scholar
  99. Karklins, R., & Petersen, R. (1993). Decision calculus of protestors and regime change: Eastern Europe 1989. Journal of Politics, 55, 588–614.CrossRefGoogle Scholar
  100. Kauffman, S. (1993). The origins of order. Oxford: Oxford University Press.Google Scholar
  101. Keohane, R. (1984). After hegemony. Princeton, NJ: Princeton University Press.Google Scholar
  102. Keohane, R., & Nye, R. (1977). Power and interdependence. New York: Little Brown.Google Scholar
  103. Keynes, J. M. (1936). The general theory of employment, interest and money. London: Macmillan.Google Scholar
  104. Kindleberger, C. (1973). The world in depression 1929–1939. Berkeley, CA: University of California Press.Google Scholar
  105. Knaster, B., Kuratowski, K., & Mazurkiewicz, S. (1929). Ein beweis des fixpunktsatzes fur n-dimensionale simplexe. Fundamenta Mathematicae, 14, 132–137.Google Scholar
  106. Konishi, H. (1996). Equilibrium in abstract political economies: With an application to a public good economy with voting. Social Choice and Welfare, 13, 43–50.Google Scholar
  107. Kramer, G. H. (1973). On a class of equilibrium conditions for majority rule. Econometrica, 41, 285–297.CrossRefGoogle Scholar
  108. Kreps, D. M., et al. (1982). Rational cooperation in the finitely repeated prisoners’ dilemma. Journal of Economic Theory, 27, 245–252.CrossRefGoogle Scholar
  109. Ladha, K. (1992). Condorcet’s jury theorem, free speech and correlated votes. American Journal of Political Science, 36, 617–674.CrossRefGoogle Scholar
  110. Ladha, K. (1993). Condorcet’s jury theorem in the light of de Finetti’s theorem: Majority rule with correlated votes. Social Choice and Welfare, 10, 69–86.CrossRefGoogle Scholar
  111. Ladha, K., & Miller, G. (1996). Political discourse, factions and the general will: correlated voting and Condorcet’s jury theorem. In N. Schofield (Ed.), Collective decision making. Boston: Kluwer.Google Scholar
  112. Laplace, P. S. (1951 [1814]). Essai philosophique sur les probabilités. Paris: Gauthiers-Villars. A philosophical essay on probabilities. (trans. Truscott F, Emory F) New York: Dover.Google Scholar
  113. Li, T. Y., & Yorke, J. A. (1975). Period three implies chaos. American Mathematical Monthly, 82, 985–992.CrossRefGoogle Scholar
  114. Lohmann, S. (1994). The dynamics of Information cascades. World Politics, 47, 42–101.CrossRefGoogle Scholar
  115. Lorenz, E. N. (1962). The statistical prediction of solutions of dynamical equations. Proceedings International Symposium on Numerical Weather Prediction, Tokyo.Google Scholar
  116. Lorenz, E. N. (1963). Deterministic non periodic flow. Journal of the Atmospheric Sciences, 130, 141.Google Scholar
  117. Lorenz, E. N. (1993). The essence of chaos. Seattle: University of Washington Press.CrossRefGoogle Scholar
  118. Madison, J. (1999). Federalist X. In J. Rakove (Ed.), Madison: Writings. New York: Library Classics.Google Scholar
  119. Mandelbrot, B., & Hudson, R. (2004). The (mis)behavior of markets. New York: Perseus.Google Scholar
  120. Margolis, H. (1982). Selfishness, altruism and rationality. Cambridge: Cambridge University Press.Google Scholar
  121. Margulis, L., & Sagan, D. (2002). Acquiring genomes. New York: Basic.Google Scholar
  122. Mas-Colell, A. (1979). A selection theorem for open graph correspondences with star-shaped values. Journal of Mathematical Analysis and Applications, 68, 273–275.Google Scholar
  123. Maynard Smith, J. (1982). Evolution and the theory of games. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  124. McKelvey, R. D. (1976). Intransitivities in multidimensional voting models and some implications for agenda control. Journal of Economic Theory, 12, 472–482.CrossRefGoogle Scholar
  125. McKelvey, R. D. (1979). General conditions for global intransitivities in formal voting models. Econometrica, 47, 1085–1112.CrossRefGoogle Scholar
  126. McKelvey, R. D. (1986). Covering, dominance and institution free properties of social choice. American Journal of Political Science, 30, 283–314.CrossRefGoogle Scholar
  127. McKelvey, R. D., & Schofield, N. (1987). Generalized symmetry conditions at a core point. Econometrica, 55, 923–933.CrossRefGoogle Scholar
  128. McWhorter, J. (2001). The power of Babel. New York: Holt.Google Scholar
  129. Merton, R. C. (1973). Theory of rational option pricing. Bell Journal of Economics and Management, 4, 141–183.CrossRefGoogle Scholar
  130. Michael, E. (1956). Continuous selections I. Annals of Mathematics, 63, 361–382.CrossRefGoogle Scholar
  131. Miller, G., & Schofield, N. (2003). Activists and partisan realignment in the U.S. American Political Science Review, 97, 245–260.CrossRefGoogle Scholar
  132. Miller, G., & Schofield, N. (2008). The transformation of the Republican and Democratic party coalitions in the United States. Perspectives on Politics, 6, 433–450.CrossRefGoogle Scholar
  133. Minsky, H. (1975). John Maynard Keynes. New York: Columbia University Press.Google Scholar
  134. Minsky, H. (1986). Stabilizing an unstable economy. New Haven: Yale University Press.Google Scholar
  135. Nakamura, K. (1979). The vetoers in a simple game with ordinal preference. International Journal of Game Theory, 8, 55–61.CrossRefGoogle Scholar
  136. Mokyr, J. (2005). The intellectual origins of modern economic growth. Journal of Economic History, 65, 285–351.CrossRefGoogle Scholar
  137. Mokyr, J. (2010). The enlightened economy: An economic history of Britain 1700–1850. New Haven: Yale University Press.Google Scholar
  138. Mokyr, J., & Nye, V. C. (2007). Distributional coalitions, the industrial revolution, and the origins of economic growth in Britain. Southern Economics Journal, 74, 50–70.Google Scholar
  139. Morris, I. (2010). Why the West rules. New York: Ferrar, Strauss and Giroux.Google Scholar
  140. North, D. C. (1990). Institutions, institutional change and economic performance. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  141. North, D. C., & Weingast, B. R. (1989). Constitutions and commitment: The evolution of institutions governing public choice in seventeenth century England. Journal of Economic History, 49, 803–832.CrossRefGoogle Scholar
  142. North, D. C., Wallis, B., & Weingast, B. R. (2009). Violence and social orders: A conceptual framework for interpreting recorded human history. Cambridge: Cambridge University Press.Google Scholar
  143. Nowak, M. (2011). Supercooperators. New York: Free Press.Google Scholar
  144. Ormerod, P. (2001). Butterfly economics. New York: Basic.Google Scholar
  145. Ostrom, E. (1990). Governing the commons. Cambridge: Cambridge University Press.Google Scholar
  146. Pareto, V. (1935). The mind and society [Trattato di sociologia generale]. Brace, New York: Harcourt.Google Scholar
  147. Parfit, D. (2011). On what matters. Oxford: Oxford University Press.Google Scholar
  148. Penrose, R. (2011). Cycles of time. London: The Bodney Head.Google Scholar
  149. Plott, C. R. (1967). A notion of equilibrium and its possibility under majority rule. American Economic Review, 57, 787–806.Google Scholar
  150. Popper, K. (1959). Prediction and prophecy in the social sciences. In P. Gardiner (Ed.), Theories of history. New York: Free Press.Google Scholar
  151. Penn, E. (2009). A model of far-sighted voting. American Journal of Political Science, 53, 36–54.CrossRefGoogle Scholar
  152. Pugh, C. C. (2002). Real mathematical analysis. Berlin: Springer.CrossRefGoogle Scholar
  153. Rader, T. (1972). Theory of general economic equilibrium. New York: Academic Press.Google Scholar
  154. Richards, D. (1993). A chaotic model of power concentration in the international system. International Studies Quarterly, 37, 55–72.CrossRefGoogle Scholar
  155. Richardson, L. F. (1922). Weather prediction by numerical process. Cambridge: Cambridge University Press.Google Scholar
  156. Saari, D. (1985a). Price dynamics, social choice, voting methods, probability and chaos. In D. Aliprantis, O. Burkenshaw, & N. J. Rothman (Eds.), Lecture notes in economics and mathematical systems, No. 244. Berlin: Springer.Google Scholar
  157. Saari, D. (1985b). A chaotic exploration of aggregation paradoxes. SIAM Review, 37, 37–52.CrossRefGoogle Scholar
  158. Saari, D. (1995). Mathematical complexity of simple economics. Notes American Mathematical Society, 42, 222–230.Google Scholar
  159. Saari, D. (1997). The generic existence of a core for q-rules. Economic Theory, 9, 219–260.Google Scholar
  160. Saari, D. (2001a). Decisions and elections: Explaining the unexpected. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  161. Saari, D. (2001b). Chaotic elections. Providence, RI: American Mathematical Society.Google Scholar
  162. Saari, D. (2008). Disposing dictators, demystifying voting paradoxes. Cambridge: Cambridge University Press.Google Scholar
  163. Schofield, N. (1972a). Is majority rule special?. In R. G. Niemi & H. F. Weisberg (Eds.), Probability models of collective decision-making. Columbus, OH: Charles E. Merrill Publishing Co.Google Scholar
  164. Schofield, N. (1972b). Ethical decision rules for uncertain voters. British Journal of Political Science, 2, 193–207.CrossRefGoogle Scholar
  165. Schofield, N. (1975). A game theoretic analysis of Olson’s game of collective action. Journal of Conflict Resolution, 19, 441–461.Google Scholar
  166. Schofield, N. (1977). The logic of catastrophe. Human Ecology, 5, 261–271.CrossRefGoogle Scholar
  167. Schofield, N. (1978). Instability of simple dynamic games. Review of Economic Studies, 45, 575–594.CrossRefGoogle Scholar
  168. Schofield, N. (1979). Rationality or chaos in social choice. Greek Economic Review, 1, 61–76.Google Scholar
  169. Schofield, N. (1980a). Generic properties of simple Bergson-Samuelson welfare functions. Journal of Mathematical Economics, 7, 175–192.CrossRefGoogle Scholar
  170. Schofield, N. (1980b). Catastrophe theory and dynamic games. Quality Quantity, 14, 529–545.Google Scholar
  171. Schofield, N. (1983a). Equilibria in simple dynamic games. In P. Pattanaik & M. Salles (Eds.), Social choice and welfare (pp. 269–284). Amsterdam: North Holland.Google Scholar
  172. Schofield, N. (1983b). Generic instability of majority rule. Review of Economic Studies, 50, 695–705.CrossRefGoogle Scholar
  173. Schofield, N. (1984a). Existence of equilibrium on a manifold. Mathematics of Operations Research, 9, 545–557.CrossRefGoogle Scholar
  174. Schofield, N. (1984b). Social equilibrium and cycles on compact sets. Journal of Economic Theory, 33, 59–71.CrossRefGoogle Scholar
  175. Schofield, N. (1984c). Classification theorem for smooth social choice on a manifold. Social Choice and Welfare, 1, 187–210.CrossRefGoogle Scholar
  176. Schofield, N. (1985). Anarchy, altruism and cooperation. Social Choice and Welfare, 2, 207–219.CrossRefGoogle Scholar
  177. Schofield, N., & Tovey, C. (1992). Probability and convergence for supra-majority rule with Euclidean preferences. Mathematical and Computer Modelling, 16, 41–58.CrossRefGoogle Scholar
  178. Schofield, N. (1999a). The heart and the uncovered set. Journal of Economics Supplement, 8, 79–113.Google Scholar
  179. Schofield, N. (1999b). A smooth social choice method of preference aggregation. In M. Wooders (Ed.), Topics in mathematical economics and game theory: Essays in honor of R. Aumann. Providence, RI: Fields Institute, American Mathematical Society.Google Scholar
  180. Schofield, N. (1999c). The \(C^{1}-\)topology on the space of smooth preferences. Social Choice and Welfare, 16, 445–470.CrossRefGoogle Scholar
  181. Schofield, N. (2002). Evolution of the constitution. British Journal of Political Sciences, 32, 1–20.Google Scholar
  182. Schofield, N. (2003). Mathematical methods in economics and social choice. Berlin: Springer.Google Scholar
  183. Schofield, N. (2006). Architects of political change. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  184. Schofield, N. (2007). The mean voter theorem: Necessary and sufficient conditions for convergent equilibrium. Review of Economic Studies, 74, 965–980.CrossRefGoogle Scholar
  185. Schofield, N. (2010). Social orders. Social Choice and Welfare, 34, 503–536.CrossRefGoogle Scholar
  186. Schofield, N. (2011). Is the political economy stable or chaotic? Czech Economic Review, 5, 76–93.Google Scholar
  187. Schofield, N., & Schnidman E. (2011). Gridlock or leadership in U.S. Electoral Politics. This volume.Google Scholar
  188. Schweitzer, F., et al. (2009). Economic networks: The new challenges. Science, 325, 422–425.Google Scholar
  189. Shafer, W., & Sonnenschein, H. (1975). Equilibrium in abstract economies without ordered preferences. Journal of Mathematical Economics, 2, 245–248.Google Scholar
  190. Shiller, R. (2003). The new financial order. Princeton: Princeton University Press.Google Scholar
  191. Shiller, R. (2005). Irrational exuberance. Princeton: Princeton University Press.Google Scholar
  192. Smale, S. (1966). Structurally stable systems are not dense. American Journal of Mathematics, 88, 491–496.CrossRefGoogle Scholar
  193. Smale, S. (1974a). Global analysis and economics IIA: Extension of a theorem of Debreu. Journal of Mathematical Economics, 1, 1–14.CrossRefGoogle Scholar
  194. Smale, S. (1974b). Global analysis and economics IV. Finiteness and stability of equilibria with general consumption sets and production. Journal of Mathematical Economics, 1, 119–127.CrossRefGoogle Scholar
  195. Smith, A. (1984 [1759]). The theory of moral sentiments. Indianapolis, IN: Liberty Fund.Google Scholar
  196. Strnad, J. (1985). The structure of continuous-valued neutral monotonic social functions. Social Choice and Welfare, 2, 181–195.CrossRefGoogle Scholar
  197. Strogatz, S. (2004). Sync. New York: Hyperion.Google Scholar
  198. Stern, N. (2007). The economics of climate change. Cambridge: Cambridge University Press.Google Scholar
  199. Stern, N. (2009). The global deal. New York: Public Affairs.Google Scholar
  200. Sunstein, C. R. (2006). Infotopia. Oxford: Oxford University Press.Google Scholar
  201. Sunstein, C. R. (2011). Going to extremes. Oxford: Oxford University Press.Google Scholar
  202. Surowiecki, J. (2005). The wisdom of crowds. New York: Anchor.Google Scholar
  203. Taleb, N. N. (2007). The black swan. New York: Random.Google Scholar
  204. Taleb, N. N., & Blyth, M. (2011). The black swan of Cairo. Foreign Affairs, 90(3), 33–39.Google Scholar
  205. Tataru, M. (1999). Growth rates in multidimensional spatial voting. Mathematical Social Sciences, 37, 253–263.CrossRefGoogle Scholar
  206. Taylor, M. (1976). Anarchy and cooperation. London: Wiley.Google Scholar
  207. Taylor, M. (1982). Community, anarchy and liberty. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  208. Thom, R. (1975). Structural stability and morphogenesis. Reading, MA: Benjamin.Google Scholar
  209. Trivers, R. (1971). The evolution of reciprocal altruism. Quarterly Review of Biology, 46, 35–56.CrossRefGoogle Scholar
  210. Trivers, R. (1985). Social evolution. Menlo Park: Cummings.Google Scholar
  211. Walker, M. (1977). On the existence of maximal elements. Journal of Economic Theory, 16, 470–474.CrossRefGoogle Scholar
  212. Watts, D. (2002). A simple model of global cascades on random networks. Proceedings of the National Academy of Sciences, 99, 5766–5771.CrossRefGoogle Scholar
  213. Watts, D. (2003). Six degrees. New York: Norton.Google Scholar
  214. Weitzman, M. (2009). Additive damages, fat-tailed climate dynamics, and uncertain discounting. Economics, 3, 1–22.Google Scholar
  215. Wilson, E. O. (2012). The social conquest of Earth. New York: W.W. Norton.Google Scholar
  216. Zeeman, E. C. (1977). Catastrophe theory: Selected papers, 1972–77. New York: Addison Wesley.Google Scholar
  217. Zipf, G. K. (1965). Human behavior and the principle of least effort. New York: Hafner.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Center in Political EconomyWashington University in Saint LouisSaint LouisUSA

Personalised recommendations