An Alternative Perspective on von Winterfeldt et al.’s (1997) Test of Consequence Monotonicity Moon-Ho R. Ho McGill University Michel Regenwetter University of Illinois at Urbana-Champaign Reinhard Niedere ´e Universita ¨t Kiel Dieter Heyer Universita ¨t Halle D. von Winterfeldt, N.-K. Chung, R. D. Luce, and Y. Cho (1997) provided several tests for consequence monotonicity of choice or judgment, using certainty equivalents of gambles. The authors reaxiomatized consequence monotonicity in a probabilistic framework and reanalyzed von Winterfeldt et al.’s main experiment via a bootstrap method. Their application offers new insights into consequence monotonicity as well as into von Winterfeldt et al.’s 3 experimental paradigms: judged certainty equivalents (JCE), QUICKINDIFF, and parameter estimation by sequential testing (PEST). For QUICKINDIFF, the authors found no indication of violations of “random consequence monotonicity.” This sharply contrasts the findings of von Winterfeldt et al., who concluded that axiom violations were the most pronounced under that procedure. The authors found potential evidence for violations in JCE and certainty equivalents derived from PEST. Virtually all descriptive and normative theories of judgment and choice require that a decision maker prefer a ‘better’ choice alternative to a ‘worse’ one (see, e.g., Luce, 2000, for a recent overview of theories of utility). Therefore, when respondents are asked to choose among or judge gambles, standard theories predict that among any two gambles which differ by only one conse- quence, respondents will prefer the gamble with the better conse- quence. This property is called (the axiom of) consequence mono- tonicity for gambles. Formally, writing  for the real numbers x, y, z   for distinct sure consequences (e.g., amounts of money), E for an uncertain event that is neither the null nor the universal event, (x,E;y) for a gamble in which the respondent receives consequence x if E occurs and y otherwise, and  for preference or indifference, conse- quence monotonicity requires the following condition:  x  y N x,E;z   y,E;z N z,E;x   z,E;y . (1) Contemporary research frequently relies on certainty equiva- lents of gambles. The certainty equivalent of a gamble is the amount of money that allows one to be indifferent between the gamble and the fixed amount of money. In terms of certainty equivalents (CEs), the axiom can be stated as follows. Writing CE(x,E;y) for the real valued certainty equivalent of gamble (x,E;y), consequence monotonicity requires that, for any distinct sure consequences, x, y, z  , and for any event E that is neither the certain nor the null event, Condition 2 must hold:  x  y N CE x,E;z  CE y,E;z N CE z,E;x  CE z,E;y . (2) Building on previous work on consequence monotonicity for judged certainty equivalents (Birnbaum, Coffey, Mellers, & Weiss, 1992; Mellers, Weiss, & Birnbaum, 1992), von Winter- feldt, Chung, Luce, and Cho (1997) investigated consequence monotonicity using certainty equivalents of gambles obtained via three different experimental paradigms for eliciting such certainty equivalents: judged certainty equivalents (JCE), QUICKINDIFF, and parameter estimation by sequential testing (PEST). We refer the readers to the original article (von Winterfeldt et al., 1997) for a detailed discussion of these three paradigms, and we provide only a brief summary here. Under the JCE procedure, respondents were offered a binary gamble on each experimental trial and asked to state a sure consequence that would allow them to feel indifferent between the gamble and the sure consequence. Moon-Ho R. Ho, Department of Psychology, McGill University, Mon- tre ´al, Que ´bec, Canada; Michel Regenwetter, Department of Psychology, University of Illinois at Urbana-Champaign; Reinhard Niedere ´e, Depart- ment of Psychology, Universita ¨t Kiel, Kiel, Germany; Dieter Heyer, De- partment of Psychology, Universita ¨t Halle, Wittenberg, Germany. We thank Younghee Cho, R. Duncan Luce, Detlof von Winterfeldt, and Ngar-Kok Chung for generously providing their original data and R. Duncan Luce and Richard Shiffrin for helpful comments at the 2003 Society for Mathematical Psychology meeting, Weber State University, July 2003. We also thank several institutions for facilitating our collabo- ration: The Fuqua School of Business at Duke University and the Center for International Business Education and Research at Duke University, as well as the National Science Foundation Grant SBR98 –18756 to Michel Regenwetter and Aleksandar Pekec ¸ made it possible for us to start our collaboration during Random Utility 2000: Conference and Workshop on Random Utility Theory and Probabilistic Measurement Theory, Duke University, August 2000. The research board of the University of Illinois at Urbana-Champaign supported us via a grant on mixture models and random utility models for individual and group decision making to Michel Regenwetter that funded Moon-Ho R. Ho as a research assistant. Correspondence concerning this article should be addressed to Michel Regenwetter, Department of Psychology, University of Illinois, 603 East Daniel Street, Champaign, IL 61820. E-mail: regenwet@uiuc.edu Journal of Experimental Psychology: Copyright 2005 by the American Psychological Association Learning, Memory, and Cognition 2005, Vol. 31, No. 2, 365–373 0278-7393/05/$12.00 DOI: 10.1037/0278-7393.31.2.365 365