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The voting paradox … with a single voter? Implications for transitivity in choice under risk

  • David Butler (a1) and Pavlo Blavatskyy (a2)

Abstract

The voting paradox occurs when a democratic society seeking to aggregate individual preferences into a social preference reaches an intransitive ordering. However it is not widely known that the paradox may also manifest for an individual aggregating over attributes of risky objects to form a preference over those objects. When this occurs, the relation ‘stochastically greater than’ is not always transitive and so transitivity need not hold between those objects. We discuss the impact of other decision paradoxes to address a series of philosophical and economic arguments against intransitive (cyclical) choice, before concluding that intransitive choices can be justified.

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Allais, M. 1953. Le comportement de l’homme rationnel devant le risque: critique des postulats et axiomes de l’ecole Americaine. Econometrica 21, 503546.
Anand, P. 1987. Are the preference axioms really rational? Theory and Decision 23, 189214.
Anand, P. 1990. Interpreting axiomatic (decision) theory. Annals of Operations Research 23, 91101.
Anand, P. 1993a. The philosophy of intransitive preference. Economic Journal 103, 337346.
Anand, P. 1993b. Foundations of Rational Choice under Risk. Oxford: Clarendon Press, XI161.
Arieli, A., Ben-Ami, Y. and Rubinstein, A. 2009. Fairness motivations and procedures of choice between lotteries as revealed through eye movements. Mimeo.
Arrow, K. 1951. Social Choice and Individual Values. New York, NY: John Wiley and Sons.
Arrow, K. 1963. Social Choice and Individual Values (2nd edn). New York, NY: John Wiley and Sons.
Baron, J. 2008. Thinking and Deciding (4th edn). Cambridge: Cambridge University Press.
Blavatskyy, P. 2006. Axiomatization of a preference for a probable winner. Theory and Decision 60, 1733.
Blyth, C. 1972. Some probability paradoxes in choice from among random alternatives. Journal of the American Statistical Association 67, 366373.
Butler, D. and Hey, J. 1987. Experimental economics: an introductory survey. Empirica: Austrian Economic Papers 2, 157186.
Butler, D. and Loomes, G. 2007. Imprecision as an account of the preference reversal phenomenon. American Economic Review 97, 277297.
Butler, D. and Loomes, G. 2011. Imprecision as an account of violations of independence and betweenness. Journal of Economic Behavior and Organization 80, 511522.
Butler, D. and Pogrebna, G. 2018. Predictably intransitive preferences. Judgment and Decision Making 13, 217236.
Campbell, D. and Kelly, J. 2002. Chapter 1: impossibility theorems in the Arrovian framework. In Handbook of Social Choice and Welfare, Vol. 1., eds. Arrow, K., Sen, A. and Suzumura, K., 3594. Amsterdam: Elsevier Science.
Condorcet, n.c. 1785. Essai sur l’application de l’analyse a la probabilite des decisions rendues a la pluralite des voix. Paris: Imprimerie Royale.
Conrey, B., Gabbard, J., Grant, K., Liu, A. and Morrison, K. 2016. Intransitive dice. Mathematics Magazine 89, 133143.
Cubitt, R. and Sugden, R. 2001. On money pumps. Games and Economic Behavior 37, 121160.
Davidson, D., McKinsey, J. and Suppes, P. 1955. Outlines of a formal theory of value, I. Philosophy of Science 22, 140160.
De Meyer, F. and Plott, C. 1970. The probability of a cyclical majority. Econometrica 38, 345354.
Dhar, R. and Simonson, I. 2003. The effect of forced choice on choice. Journal of Marketing Research 40, 146160.
Fishburn, P. 1982. Non-transitive measurable utility. Journal of Mathematical Psychology 26, 3167.
Fishburn, P. 1991. Non-transitive preferences in decision theory. Journal of Risk and Uncertainty 4, 113134.
Flood, M. 1952. Some Experimental Games. Rand Corporation report RM-789-1. Santa Monica, CA: Rand Corporation.
Gardner, M. 1970. The paradox of nontransitive dice and the elusive principle of indifference. Scientific American 223, 110114.
Handfield, T. 2016. Essentially comparative value does not threaten transitivity. Thought: A Journal of Philosophy 5, 312.
Handfield, T. and Rabinowicz, W. 2018. Incommensurability and vagueness in spectrum arguments: options for saving transitivity of betterness. Philosophical Studies 175, 23732387.
Herne, K. 1999. The effects of decoy gambles on individual choice. Experimental Economics 2, 3140.
Huber, J., Payne, J. and Puto, C. 1982. Adding asymmetrically dominated alternatives: violations of regularity and the similarity hypothesis. Journal of Consumer Research 9, 9098.
Huber, J. and Puto, C. 1983. Market boundaries and product choice: illustrating attraction and substitution effects. Journal of Consumer Research 10, 3144.
Kahneman, D. and Tversky, A. 1979. Prospect theory: an analysis of decision under risk. Econometrica 47, 263291.
Kavka, G. 1991. Is individual choice less problematic than collective choice? Economics and Philosophy 7, 143165.
Kontek, K. and Lewandowski, M. 2017. Range-dependent utility. Management Science 64, 28122832.
Lichtenstein, S. and Slovic, P. 1971. Reversals of preference between bids and choices in gambling decisions. Journal of Experimental Psychology 89, 4655.
Loomes, G. and Sugden, R. 1982. Regret theory: an alternative theory of rational choice under uncertainty. Economic Journal 92, 805824.
Loomes, G. and Sugden, R. 1987. Some implications of a more general form of regret theory. Journal of Economic Theory 41, 270287.
Louie, K., Haw, M. and Glimcher, P. 2013. Normalization is a general neural mechanism for context-dependent decision making. Proceedings of the National Academy of Sciences USA 110, 61396144.
Louie, K., Glimcher, P. and Webb, R. 2015. Adaptive neural coding: from biological to behavioural decision-making. Current Opinion in Behavioral Sciences 5, 9199.
Luce, D. 1959. Individual Choice Behavior: A Theoretical Analysis. New York, NY: John Wiley and Sons.
Luce, R. and Raiffa, H. 1957. Games and Decisions. New York, NY: John Wiley and Sons.
Noguchi, T. and Stewart, N. 2014. In the attraction, compromise and similarity effects, alternatives are repeatedly compared in pairs on single dimensions. Cognition 132, 4456.
Ray, P. 1973. Independence from irrelevant alternatives. Econometrica 41, 987991.
Regenwetter, M., Dana, J. and Davis-Stober, C. 2011. Transitivity of preferences. Psychological Review 118, 4256.
Riker, W. 1982. Liberalism against Populism. San Francisco, CA: W.H. Freeman.
Rubinstein, A. and Segal, U. 2012. On the likelihood of cyclic comparisons. Journal of Economic Theory 147, 24832491.
Russo, J. and Dosher, B. 1983. Strategies for multi-attribute binary choice. Journal of Experimental Psychology: Learning, Memory and Cognition 9, 676696.
Saari, D. 1995. A chaotic exploration of aggregation paradoxes. Society for Industrial and Applied Mathematics 37, 3752.
Savage, L. J. 1954. The Foundations of Statistics. New York, NY: John Wiley and Sons
Simonson, I. and Tversky, A. 1992. Choice in context: tradeoff contrast and extremeness aversion. Journal of Marketing Research 29, 281295.
Steinhaus, H. and Trybula, S. 1959. On a paradox in applied probabilities. Bulletin of the Polish Academy of Sciences 7, 6769.
Stewart, N., Reimers, S. and Harris, A. 2015. On the origin of utility, weighting and discount functions: how they get their shapes and how to change their shapes. Management Science 61, 687705.
Sugden, R. 1996. Review of ‘Foundations of Rational Choice under Risk’. Utilitas 8, 254255.
Temkin, L. 2012. Rethinking the Good: Moral Ideals and the Nature of Practical Reasoning. Oxford: Oxford University Press.
Trybula, S. 1961. On the paradox of three random variables. Applicationes Mathematicae 5, 321332.
Tversky, A. 1969. Intransitivity of preferences. Psychological Review 76, 3148.
Tversky, A. and Simonson, I. 1993. Context-dependent preferences. Management Science 30, 11791189.
Usiskin, Z. 1964. Max-min probabilities in the voting paradox. Annals of Mathematical Statistics 35, 857862.
von Neumann, J. and Morgenstern, O.. 1944. Theory of Games and Economic Behavior. Princeton, NJ: Princeton University Press.
Voorhoeve, A. 2013. Vaulting intuition: Temkin’s critique of transitivity. Economics and Philosophy 29, 409423.
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