, Volume 64, Issue 1, pp 101–114 | Cite as

Transitivity, the Sorites Paradox, and Similarity-Based Decision-making

  • Alex VoorhoeveEmail author
  • Ken Binmore


A persistent argument against the transitivity assumption of rational choice theory postulates a repeatable action that generates a significant benefit at the expense of a negligible cost. No matter how many times the action has been taken, it therefore seems reasonable for a decision-maker to take the action one more time. However, matters are so fixed that the costs of taking the action some large number of times outweigh the benefits. In taking the action some large number of times on the grounds that the benefits outweigh the costs every time, the decision-maker therefore reveals intransitive preferences, since once she has taken it this large number of times, she would prefer to return to the situation in which she had never taken the action at all. We defend transitivity against two versions of this argument: one in which it is assumed that taking the action one more time never has any perceptible cost, and one in which it is assumed that the cost of taking the action, though (sometimes) perceptible, is so small as to be outweighed at every step by the significant benefit. We argue that the description of the choice situation in the first version involves a contradiction. We also argue that the reasoning used in the second version is a form of similarity-based decision-making. We argue that when the consequences of using similarity-based decision-making are brought to light, rational decision-makers revise their preferences. We also discuss one method that might be used in performing this revision.


Significant Benefit Rational Choice Choice Theory Choice Situation Rational Choice Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Allais, M. 1953‘Le comportement de l’homme rationnel devant le risque: Critique des postulats et axioms de l’école Americaine’Econometrica21503546Google Scholar
  2. Arntzenius, F., McCarthy, D. 1997‘Self Torture and Group Beneficence’Erkenntnis47129144CrossRefGoogle Scholar
  3. Carlson, E. 1996‘Cyclical Preferences and Rational Choice’Theoria62144160Google Scholar
  4. Graff, D. 2001‘Phenomenal Continua and the Sorites’Mind110905935CrossRefGoogle Scholar
  5. Kahneman, D., Tversky, A. 1979‘Prospect Theory’Econometrica47263291Google Scholar
  6. Kahneman, D., Tversky, A. 1984‘Choices, Values, and Frames’American Psychologist39341350Google Scholar
  7. Luce, D. 1956‘Semiorders and a Theory of Utility Discrimination’Econometrica24178191Google Scholar
  8. Luce, D., Raiffa, H. 1957Games and DecisionsJohn WileyNew YorkGoogle Scholar
  9. Mills, E. 2001‘Fallibility and the Phenomenal Sorites’Noûs36384407Google Scholar
  10. Quinn, W. 1990‘The Paradox of the Self-Torturer’Philosophical Studies597990CrossRefGoogle Scholar
  11. Raffman, D. 1994‘Vagueness Without Paradox’Philosophical Review1034174Google Scholar
  12. Regan, D. 2000‘Perceiving Imperceptible Harms: With Other Thoughts on Transitivity, Cumulative Effects, and Consequentialism’Almeida, M. eds. Imperceptible Harms and BenefitsKluwer Academic PublishersDordrecht4973Google Scholar
  13. Rubinstein, A. 1990‘Similarity and Decision-Making Under Risk (Is There a Utility Theory Resolution of the Allais Paradox?)’Journal of Economic Theory4614553Google Scholar
  14. Rubinstein, A. 2003‘Economics and Psychology? The Case of Hyperbolic Discounting’International Economic Review4412071216CrossRefGoogle Scholar
  15. Savage, L. 1972The Foundations of Statistics, 2nd, revised ednDoverNew YorkGoogle Scholar
  16. Tversky, A. 1967‘Intransitivity of Preferences’Psychological Review843148Google Scholar
  17. Tversky, A. 1977‘Features of Similarity’Psychological Review84327352Google Scholar
  18. Vilà, X. 1998‘On the Intransitivity of Preferences Consistent with Similarity Relations’Journal of Economic Theory79281287CrossRefGoogle Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Department of PhilosophyLogic, and Scientific Method London School of EconomicsLondonUK
  2. 2.Economics DepartmentUniversity College LondonLondonUK

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