An examination of the proportional difference model to describe and predict health decisions Claudia González-Vallejo a,⇑ , Jason L. Harman a , Etienne Mullet b , Maria T. Muñoz Sastre c a Department of Psychology, Ohio University, Athens, OH 45701, United States b Laboratoire Ethique et Travail, Maison de la - Recherche, F-31058 Toulouse Cedex 09, France c Department of Psychology, Universite de Toulouse Le Mitral, 31078 Toulouse Cedex, France article info Article history: Received 25 January 2011 Accepted 20 December 2011 Available online 10 February 2012 Accepted by Julie Irwin Keywords: Stochastic choice model Trade-offs Health decisions Preferences Decisions under risk Under certainty abstract Three studies tested whether the proportional difference rule, PD, of the Stochastic Difference Model (SDM, González-Vallejo, 2002) describes decisions under both risk and certainty with a single rule. The SDM characterizes how individuals make trade-offs between non-comparable attributes when choosing. The PD rule assumes that options are compared attribute-wise: proportional advantages favoring an option in a given attribute move the decision maker towards that option; proportional disadvantages move the decision maker away from that option. The model was tested in health domains: choices of health treatments and of health products. Health treatment options were described in terms of probabil- ity of survival and probability of side effects resulting from the treatment. More invasive treatments offered higher survival rates, but were also more likely to result in side effects. Health products were cereals and energy drinks. Data across the different health domains showed good support for PD using different model evaluation methods. Ó 2012 Elsevier Inc. All rights reserved. Introduction Making choices may require statistical thinking, as when choos- ing between investment portfolios, or economic thinking, as when choosing between computers to purchase. But perhaps, decision makers make choices via simple comparative rules that do not re- quire fully developed statistical or economic considerations. The Stochastic Difference Model (SDM) (González-Vallejo, 2002) ad- vanced that decision makers can evaluate options that offer con- flicting values using a basic comparative mechanism that focuses on relative attribute differences. A choice situation that requires making trade-offs is exemplified by the standard binary gamble task. In this task, a decision maker must choose between pairs of options that that have a high probability of yielding a small posi- tive outcome, and options with low probabilities offering higher outcomes. The proportional difference rule within SDM (called PD, González-Vallejo, 2002) assumes that individuals compare the op- tions attribute-wise so that proportional advantages that favor an option in a given dimension (e.g., probability) move the decision maker towards that option, while proportional disadvantages have the opposite effect. In addition, the process is assumed to be noisy (stochastic), so that perfect calculations of proportions are not re- quired and preferences are allowed to vary. The main focus of the present study is to provide further tests of PD as a basic decision process that can describe decisions for op- tions other than gambles. From a theoretical perspective, a key test is whether PD can describe choices when making decisions with risks and without them (i.e., decisions under risk and under cer- tainty). In addition, from an applied perspective, the study at- tempts to evaluate the appropriateness of the model in predicting choices that affect health. Two health decision contexts were used for this purpose: health treatments and food selections. Finally, other models were compared to PD. Thus, this study at- tempts to provide a comprehensive analysis of a simple compara- tive process that may underlie choice behavior in many situations. Theoretical considerations Standard rational models of decision making treat decisions un- der risk and certainty in different ways, albeit using the common construct of utility. We owe the concept of personal utility to Ber- noulli (1738/1954). Generically, one can assume that levels of attri- butes (e.g., how many calories a cereal has) produce subjective experiences of value that can be mapped into numerical descrip- tions of such experiences, or into utilities. Von Neumann and Mor- genstern (1947) and later Savage (1954/1972), provided the axiomatic underpinnings for the translation of preferences into 0749-5978/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. doi:10.1016/j.obhdp.2011.12.003 ⇑ Corresponding author. E-mail addresses: gonzalez@ohio.edu (C. González-Vallejo), harmanj1@ohio.edu (J.L. Harman), etienne.mullet@wanadoo.fr (E. Mullet), munoz@univ-tlse2.fr (M.T. Muñoz Sastre). Organizational Behavior and Human Decision Processes 118 (2012) 82–97 Contents lists available at SciVerse ScienceDirect Organizational Behavior and Human Decision Processes journal homepage: www.elsevier.com/locate/obhdp