The Deferral of Attacks: SP/A Theory as a Model of Terrorist Choice when Losses Are Inevitable


When a terrorist group’s aspirations far exceed the outcomes that can be expected to result from any of the available attack methods, an outcome below the terrorist group’s aspiration level is inevitable. A primary prediction of SP/A theory when applied to the study of terrorist behaviour is that when losses are inevitable the terrorist group will be risk averse and inclined to defer further action until expected outcomes improve, new attack method innovations are developed or the memory of the event that shaped aspirations has faded sufficiently that the aspiration level can be ‘reset’. This complements existing predictions of loss aversion and risk seeking behaviour over the domain of avoidable losses and provides a starting point for developing explanations for patterns of behaviour that are observed in the terrorism context, including pauses in violence, even during brutality contests, and time-lags between terrorist attacks.

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  • Abdellaoui, M. 2000. Parameter-free Elicitation of Utility and Probability Weighting Functions. Management Science, 46, 1497-1512.

  • Allais, M. 1953. Le Comportement de l’Homme Rationnel devant le Risque, Critique des Postulats et Axiomes de l’Ecole Americaine. Econometrica, 21, 503-546.

  • Barberis, Nicholas C. 2013. Thirty Years of Prospect Theory in Economics: A Review and Assessment. Journal of Economic Perspectives, 27, 173-96.

  • Battalio, R.C., Kagel, J.H. & MacDonald, D.N. 1985. Animals’ Choices over Uncertain Outcomes: Some Initial Experimental Results. American Economic Review, 75, 597-613.

  • Bell, D.E. 1982. Regret in Decision-Making Under Uncertainty. Operations Research, 30, 961-981.

  • Berns, G.S., Capra, C.M., Chappelow, J., Moore, S. & Noussair, C. 2008. Nonlinear Neurobiological Probability Weighting Functions for Aversive Outcomes. NeuroImage, 39, 2047-2057.

  • Birnbaum, M.H., Patton, J.N. & Lott, M.K. 1999. Evidence against Rank-Dependent Utility Theories: Tests of Cumulative Independence, Interval Independence, Stochastic Dominance and Transitivity. Organisational Behaviour and Human Decision Processes, 77, 44-83.

  • Bosch-Doménech, A. & Silvestre, J. 2006. Reflections on Gains and Losses: A 2×2×7 Experiment. Journal of Risk and Uncertainty, 33, 217-235.

  • Bruhin, A., Fehr-Duda, H. & Epper, T. 2010. Risk and Rationality: Uncovering Heterogeneity in Probability Distortion. Econometrica, 78, 1375-1412.

  • Caruso, R. & Schneider, F. 2013. Brutality of Jihadist Terrorism: A Contest Theory Perspective and Empirical Evidence for the Period 2002 to 2010. Journal of Policy Modeling, 35, 685-696.

  • Camerer, C.F. & Ho, T.H. 1994. Violations of the Between-ness Axiom and Non-Linearity in Probability. Journal of Risk and Uncertainty, 8, 167-196.

  • Das, S., Markowitz, H., Scheid, J. & Statman, M. 2010. Portfolio Optimisation With Mental Accounts. Journal of Financial and Quantitative Analysis, 45, 311-334.

  • Diecidue, E. & van de Ven, J. 2008. Aspiration Level, Probability of Success and Failure and Expected Utility. International Economic Review 49, 683-700.

  • Ellsberg, D. 1954. Classic and Current Notions of Measurable Utility. Economic Journal, 64, 528-556.

  • Ellsberg, D. 1961. Risk, Ambiguity and the Savage Axioms. Quarterly Journal of Economics, 75, 643-669.

  • Enders, W. & Sandler, T. 2002. Patterns of Transnational Terrorism, 1970-1999: Alternative Time-Series Estimates. International Studies Quarterly, 46, 145-165.

  • Fishburn, P.C. 1989. Retrospective on the Utility Theory of von Neumann & Morgenstern. Journal of Risk and Uncertainty, 2, 127-158.

  • Frey, B. & Luechinger, S. 2003. How to Fight Terrorism: Alternatives to Deterrence. Defence and Peace Economics, 14, 237-249.

  • Gonzalez, R. & Wu, G. 1999. On the Shape of the Probability Weighting Function. Cognitive Psychology, 38, 129-166.

  • Hadar, J. and Russell, W.R., 1969. Rules for Ordering Uncertain Prospects, American Economic Review, 59, pp.25-34.

  • Hanoch, G. and Levy, H., 1969. The Efficiency Analysis of Choices Involving Risk, Review of Economic Studies, 36, pp.335-346.

  • He, X.D. & Zhou, X.Y. 2013. Hope, Fear and Aspirations. Mathematical Finance, 26, 3-50.

  • Kahneman, D. & Tversky, A. 1979. Prospect Theory: An Analysis of Decision Under Risk. Econometrica 47, 263-292.

  • Kataoka, S. 1963. A Stochastic Programming Model. Econometrica, 31, 181-196.

  • Kolmogorov, A.N. 1933. Grundbegriffe der Wahrscheinlichkeitsrechnung. Springer, Berlin.

  • Landes, W. 1978. An Economic Study of U.S. Aircraft Hijacking: 1961 to 1976. Journal of Law and Economics, 21, 1-31.

  • Levy, H., 1992. Stochastic Dominance and Expected Utility: Survey and Analysis, Management Science, 38, pp.555-593.

  • Loomes, G. & Sugden, R. 1982. Regret Theory: An Alternative Theory of Rational Choice Under Uncertainty. Economic Journal, 92, 805-824.

  • Lopes, L.L. 1987. Between Hope and Fear: The Psychology of Risk. Advances in Experimental Social Psychology, 20, 255-295.

  • Lopes, L.L. 1995. An Information Processing Perspective on Choice. In Decision Making From a Cognitive Perspective. Edited by Douglas Medin, Jerome Busemeyer & Reid Hastie, Academic Press, San Diego, California.

  • Lopes, L.L. 2013. Goals and the Organisation of Choice Under Risk. Working Paper, University of Iowa.

  • Lopes, L.L. & Oden, G.C. 1999. The Role of Aspiration Level in Risky Choice: A Comparison of Cumulative Prospect Theory and SP/A Theory. Journal of Mathematical Psychology, 43, 286-313.

  • Machina, M.J. 1982. Expected Utility Analysis Without the Independence Axiom. Econometrica, 50, 277-323.

  • Machina, M.J. 1987. Choice Under Uncertainty: Problems Solved and Unsolved. Journal of Economic Perspectives, 1, 121-154.

  • Markowitz, H.M. 1952. Portfolio Selection. Journal of Finance, 77-91.

  • Meyer, J., 1977a. Further Application of Stochastic Dominance to Mutual Fund Performance, Journal of Financial and Quantitative Analysis, 12, pp.235-242.

  • Meyer, J., 1977b. Choice Among Distributions, Journal of Economic Theory, 14, pp.326-336.

  • Neumann, J. von & Morgenstern, O. 1947. Theory of Games and Economic Behaviour, Princeton University Press, Princeton, NJ.

  • Phillips, P.J. 2009. Applying Modern Portfolio Theory to the Analysis of Terrorism: Computing the set of Attack Method Combinations from which the Rational Terrorist Group will Choose in Order to Maximise Injuries and Fatalities. Defence and Peach Economics, 20, 193-213.

  • Phillips, P.J. 2013. In Pursuit of the Lone Wolf Terrorist: Investigative Economics and New Horizons for the Economic Analysis of Terrorism, Nova Science, New York, New York.

  • Phillips, P.J. 2016. The Economics of Terrorism. Taylor & Francis (Routledge), Abingdon, Oxon & New York, New York.

  • Phillips, P.J. & Pohl, G. 2014. Prospect Theory and Terrorist Choice. Journal of Applied Economics, 17, 139-160.

  • Phillips, P.J. & Pohl, G. 2017. Terrorist Choice: A Stochastic Dominance and Prospect Theory Analysis. Defence and Peace Economics 28, 150-164.

  • Pohl, G. 2015. Media and Terrorist Choice: A Risk-Reward Analysis. Journal of Applied Security Research, 10, 60-76.

  • Pohl, G. 2017. Terrorist Choice and the Media. PhD Dissertation, University of Southern Queensland, Unpublished.

  • Prelec, D. 1998. The Probability Weighting Function. Econometrica, 66, 497-527.

  • Quiggin, J. 1982. A Theory of Anticipated Utility. Journal of Economic Behaviour and Organisation, 3, 323-343.

  • Rieger, M.O. 2010. SP/A and CPT: A Reconciliation of Two Behavioural Decision Theories. Economics Letters, 108, 327-329.

  • Rothschild, M. and Stiglitz, J.E., 1970. Increasing Risk: I. A Definition, Journal of Economic Theory, 2, pp.225-243.

  • Rothschild, M. and Stiglitz, J.E., 1971. Increasing Risk: II. Its Economic Consequences, Journal of Economic Theory, 3, pp.66-84.

  • Roy, A.D. 1952. Safety First and the Holding of Assets. Econometrica, 20, 431-449.

  • Sandler, T., Tschirhart, J.T. & Cauley, J. 1983. A Theoretical Analysis of Transnational Terrorism. American Political Science Review, 77, 36-54.

  • Schmeidler, D. 1989. Subjective Probability and Expected Utility Without Additivity. Econometrica, 57, 571-587.

  • Shefrin, H. & Statman, M. 2000. Behavioural Portfolio Theory. Journal of Financial and Quantitative Analysis, 35, 127-151.

  • Starmer, C. 2000. Developments in Non-Expected Utility Theory: The Hunt for a Descriptive Theory of Choice Under Risk. Journal of Economic Literature, 38, 332-382.

  • Telser, L. 1956. Safety First and Hedging. Review of Economic Studies, 23, 1-16.

  • Tversky, A. & Kahneman, D. 1992. Advances in Prospect Theory: Cumulative Representation of Uncertainty. Journal of Risk and Uncertainty, 5, 297-323.

  • Wu, G. & Gonzalez, R. 1996. Curvature of the Probability Weighting Function. Management Science, 42, 1676-1690.

  • Yaari, M.E. 1987. The Dual Theory of Choice Under Risk. Econometrica, 55, 95-115.


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