Diffusion Models of Decision Making 1 Building Bridges between Neural Models and Complex Decision Making Behavior Jerome R. Busemeyer1Ryan K. Jessup1Joseph G. Johnson2 James T. Townsend1March 21, 2006 1) Department of Psychological and Brain Sciences, Indiana University, Bloomington, IN, USA 2) Department of Psychology, Miami University, Oxford, OH, USA This work was supported by a National Institute of Mental Health Cognition and Perception Grant MH068346 to the first author and a National Institute of Mental Health Grant 1 RO1 MH62150-01 to the second author. Send Correspondence to: Jerome R. Busemeyer 1101 E. 10th St. Bloomington, Indiana, 47405 voice: 812 -855 – 4882 fax: (812) 855-4691 [email protected] Models of Decision Making 2 Building Bridges between Neural Models and Complex Decision Making Behavior Diffusion processes, and their discrete time counterparts, random walk models, have demonstrated an ability to account for a wide range of findings from behavioral decision making for which the purely algebraic and deterministic models often used in economics and psychology cannot account. Recent studies that record neural activations in non-human primates during perceptual decision making tasks have revealed that neural firing rates closely mimic the accumulation of preference theorized by behaviorally-derived diffusion models of decision making. This article bridges the expanse between the neurophysiological and behavioral decision making literatures; specifically, decision field theory (Busemeyer & Townsend, 1993), a dynamic and stochastic random walk theory of decision making, is presented as a model positioned between lower-level neural activation patterns and more complex notions of decision making found in psychology and economics. Potential neural correlates of this model are proposed, and relevant competing models are also addressed. Keywords: Models, Dynamic; Choice Behavior; Decision Making; Basal Ganglia; Neuroeconomics; Processes, Diffusion/Random Walk;Diffusion Models of Decision Making 3 The decision processes of sensory-motor decisions are beginning to be fairly well understood both at the behavioral and neural levels. For the past ten years, neuroscientists have been using multiple cell recording techniques to examine spike activation patterns in rhesus monkeys during simple decision making tasks (Britten, Shadlen, Newsome, & Movshon, 1993). In a typical experiment, the monkeys are presented with a visual motion detection task which requires them to make a saccadic eye movement to a location indicated by a noisy visual display, and they are rewarded with juice for correct responses. Neural activity is recorded from either the middle temporal area (an extrastriate visual area), lateral intraparietal cortex (which plays a role in spatial attention), the frontal eye fields (FEF), or superior colliculus (SC, regions involved in the planning and implementation of eye movements, respectively). The typical findings indicate that neural activation regarding stimulus movement information is accumulated across time up to a threshold, and a behavioral response is made as soon as the activation in the recorded area exceeds the threshold (see Schall, 2003; Gold & Shadlen, 2000; Mazurek, Roitman, Ditterich, & Shadlen, 2003; Ratcliff, Cherian, & Segraves, 2003; and Shadlen & Newsome, 2001, for examples). Because areas such as FEF and SC are thought to implement the behavior of interest (in this example, saccadic eye movements), a conclusion that one can draw from these results is that the neural areas responsible for planning or carrying out certain actions are also responsible for deciding the action to carry out, a decidedly embodied notion. Mathematically, the spike activation pattern, as well as the choice and response time distributions, can be well described by what are known as diffusion models (see Smith & Ratcliff, 2004, for a summary). Diffusion models can be viewed as stochastic recurrentDiffusion Models of Decision Making 4 neural network models, except that the dynamics are approximated by linear systems. The linear approximation is important for maintaining a mathematically tractable analysis of systems perturbed by noisy inputs. In addition to these neuroscience applications, diffusion models (or their discrete time, random walk, analogues) have been used by cognitive scientists to model performance in a variety of tasks ranging from sensory detection (Smith, 1995), and perceptual discrimination (Laming, 1968; Link & Heath, 1978; Usher & McClelland, 2001), to memory recognition (Ratcliff, 1978), and categorization (Nosofsky & Palmeri, 1997; Ashby, 2000). Thus, diffusion models provide the potential to form a theoretical bridge between neural models of sensory-motor tasks and behavioral models of complex-cognitive tasks. The purpose of this article is to review applications of diffusion models to human decision making under risk with conflicting objectives. Traditionally, the field of decision making has been guided by algebraic utility theories such as the classic expected utility model (von Neumann & Morgenstern, 1944) or more complex variants such as cumulative prospect theory (Tversky & Kahneman, 1992). However, a number of paradoxical findings have emerged in the field of human decision making that are difficult to explain by traditional utility theories. We show that diffusion models provide a cogent explanation for these complex and puzzling behaviors. First, we describe how diffusion models can be applied to risky decisions with conflicting objectives; second, we explain some important findings using this theory; and finally, we compare this theory with some alternate competing neural network models.Diffusion Models of Decision Making 5 1. Risky Decisions with Multiple Objectives Consider the following type of risky decision with multiple objectives. Suppose a commander is suddenly confronted by an emergency situation, and must quickly choose one action from a set of J actions, labeled here as {A1, …, Aj ,…, AJ}. The payoff for each action depends on one of set of K uncertain states of the world {X1, …, Xk, ,…, XK}. The payoff produced by taking action j under state of the world k is denoted xjk Finally, each payoff can be described in terms of multiple competing objectives (e.g., one objective is to achieve the commander’s mission while another objective is to preserve the