A generic dynamic control task for behavioral research and education

Abstract

Recent research in behavioral sciences presents strong evidence of poor human understanding for dynamic systems. Computer-based dynamic control tasks have an important potential for helping behavioral scientists advance research that investigates reasons for poor understanding and for helping students understand how dynamic systems work. In this paper, we introduce a simulation called Dynamic Stocks and Flows (DSF) that portrays the basic building blocks of dynamic systems: an accumulation; an inflow and outflow determined by an environment; and an inflow and outflow determined by a decision maker. In DSF, decision makers control the accumulation to a goal level by making repeated inflow and outflow decisions. We provide details of an experiment conducted with DSF that highlight some problems people face in controlling a dynamic system with different kinds of environmental inflow and outflow functions. DSF is flexible enough to represent dynamic systems with continuous or discrete accumulations, and with real-time or event-driven decision-making. We suggest that these and other features in DSF make it a good research and educational tool.

Introduction

The world is complex and dynamic. Complexity is often associated with the number of interdependent variables in a system (Dörner, 1997). For example, policymakers wanting to reduce future global warming must consider the complexity of the earth’s climate, and the relationship between increases in carbon-dioxide (CO₂) emissions and the corresponding increases in the CO₂ accumulation and atmospheric temperature. Furthermore, even simple dynamic systems are often dynamically complex given the interaction of variables and different time delays over time (Sterman, 2000). Sterman (1989a) discussed the stock management problem, a common dynamic decision-making task that involves the control of an accumulation or a system’s state. In multiple real world activities, decision makers might seek to maintain a quantity of accumulation (i.e., capital, production, inventory, or personnel) within acceptable ranges despite the usage, losses, or disturbances that push the accumulation away from optimal levels. Thus, the stock management problem is a pervasive dynamic problem in everyday life that arises at different temporal, spatial, and organizational scales (Cronin, Gonzalez, & Sterman, 2009); and that is found at multiple levels, including macroeconomic and individual (Sterman, 1989a).

Because dynamic systems are so pervasive, an understanding of the basic building blocks of dynamic systems such as accumulation, flows, and feedback is essential for dealing with dynamic problems in the real world. Some examples of dynamic problems include the following: global warming (Sterman and Booth Sweeney, 2002, Sterman and Booth Sweeney, 2007); factory production, demands, and prices of goods (Forrester, 1961); and the depletion of natural resources (Moxnes, 2004). Most of these real-world dynamic problems can be represented by very simple dynamic systems used for research in a laboratory, where the problem’s dynamics are reduced to simple elements without losing the important characteristics of the problem: one accumulation or stock (a resource that accumulates or depletes over time) and flows that alter the accumulation level (an inflow that increases or an outflow that decreases the accumulation). For example, the problem of climate change could be thought of as the accumulation of the carbon-dioxide (CO₂) greenhouse gas in the atmosphere due to a large inflow of yearly manmade CO₂ emissions into the atmosphere and a very small outflow of yearly natural CO₂ absorption from the atmosphere (Dutt and Gonzalez, 2009a, Dutt and Gonzalez, 2009b).

Unfortunately, there is strong and increasing evidence of poor human understanding in these simple dynamic systems. For example, Booth Sweeney and Sterman (2000) presented MIT graduate students with a paper-and-pencil dynamic problem concerning the accumulation of water in a bathtub with an inflow (faucet) and an outflow (drain), and asked students to sketch the path of the water accumulation in the bathtub over time. Despite the apparent simplicity of this task, they found that only 36% of the students drew the shape correctly. More recently, researchers have found that this poor understanding of dynamic problems is more fundamental; a phenomenon that has been termed the stock-flow failure (SF failure, Cronin and Gonzalez, 2007, Cronin et al., 2009). Poor performance in the interpretation of very simple dynamic problems cannot be attributed to an inability to interpret graphs, contextual knowledge, motivation, or cognitive capacity (Cronin et al., 2009). Rather, SF failure is a robust phenomenon that appears difficult to overcome.

The SF failure in past research has been commonly investigated in stationary dynamic problems without feedback (Cronin and Gonzalez, 2007, Cronin et al., 2009, Sterman, 2002, Sterman and Booth Sweeney, 2002, Sterman and Booth Sweeney, 2007). In these static problems, participants are provided with a graph on a paper, representing a dynamic system. The graph represents the inflow (that increases an accumulation) and the outflow (that decreases an accumulation) over a time period. Then, people are asked to judge the level of flows shown in the graph (time point with maximum inflow and time point with maximum outflow) and the level of accumulation (time point with highest and lowest accumulation). In addition, people are given only one chance to answer the stock and flows questions, with no feedback regarding the accuracy of their answers.

Unlike the stationary, one-time, and paper-and-pencil decision-making problems representing dynamic systems, we suggest that people’s SF failure in dynamic systems may be investigated using interactive dynamic control tasks. In these tasks, people attempt to balance the accumulation by making repeated decisions about the inflow and outflow, and by receiving feedback about their decisions’ outcomes in each time period. An interactive dynamic control task might help people to build cause–effect relationships, resulting in an implicit understanding of the SF problem and further an adequate system’s control (see Gonzalez, Lerch, and Lebiere (2003) for the instance-based learning theory of dynamic decision-making). For example, there is some recent evidence that dynamic control tasks help people improve their understanding of accumulation in dynamic systems. In a recent study, Dutt and Gonzalez (2009a) have documented success in using a task called the Dynamic Climate Change Simulation (DCCS) to help people overcome their difficulty in understanding problems of carbon-dioxide accumulation in the earth’s atmosphere. In one condition of the study, participants were asked to experience the accumulation problem in the DCCS. Participants that played in the DCCS needed to control the CO₂ accumulation to a pre-defined goal by using the total emissions and absorption over a period of 100 years. Then, participants were given a paper-and-pencil problem with a graph of the CO₂ accumulation over the next 100 years. They were asked to infer the shape of total CO₂ emissions and absorption over the 100 years that would correspond to the accumulation shape. In another independent condition, participants did not play the DCCS, and were just asked to infer the shape of the total CO₂ emissions and absorption over time that corresponded to the CO₂ accumulation in the paper-and-pencil problem. More participants that experienced the DCCS correctly inferred the emissions and absorption shapes compared to participants who did not experience the DCCS.

Guided by the motivations above, we constructed a simple dynamic system called “Dynamic Stock and Flows” (DSF)¹ (Dutt and Gonzalez, 2007, Gonzalez and Dutt, 2007). DSF has the ability to portray the basic building blocks of simple dynamic systems: an accumulation that needs to be controlled to a goal in each time period using a decision maker’s inflow and outflow, and against an environment’s inflow and outflow that acts as a disturbance that drives the accumulation away from the goal. In DSF, the inflows increase the accumulation and the outflows decrease it in each time period. Using DSF, we are interested in finding out how decision makers learn to control an accumulation to a goal over time, while the environment’s net inflow (=inflow–outflow) functions of different positive and negative slopes also act on the accumulation. The environment’s net inflow functions result from the positive or negative slope environment’s inflow functions and a constant environment’s outflow function over time. These functions are not known to decision makers; rather, decision makers only observe their values over many time periods in DSF.

Our interest in trying two different environmental slope functions in DSF is motivated by two findings in the decision-making literature of dynamic systems. First, people are generally able to detect linear increasing (or positive slope) quantities given enough trials with outcome feedback, but they may have difficulty detecting decreasing (or negative slope) quantities (Brehmer, 1980). Second, it has been found in stationary dynamic problems that a majority of people follow a correlation heuristic (CH), whereby they judge the accumulation as having the same shape or behavior as the environment’s inflow (Cronin et al., 2009). If this observation holds for dynamic stock and flow systems, then participants would expect the accumulation to increase when the inflow increases (has a positive slope), and to decrease when the inflow decreases (has a negative slope) over time periods. However, if an environment’s outflow is constant over time and is less than the environment’s inflow in DSF, then the environment’s net inflow (=inflow–outflow) will increase regardless of the slope of the inflow (positive or negative) and will cause an increase in the accumulation. However, due to the CH, a negatively sloped Environment Inflow would produce some “mismatch” between the human expectations of a decrease and the actual increase in the accumulation. This mismatch results in participants showing poorer control over the accumulation when the environment’s inflow is negatively sloped compared to when it is positively sloped. Thus, we expect that:

• Hypothesis: Better control of the accumulation in DSF when the environment’s inflow is positively sloped compared to when environment’s inflow is negatively sloped.

We test this hypothesis in an experiment, and in the last part of this paper we discuss other features of DSF that highlight the task’s potential to contribute to other areas in behavioral research and education. The next section provides more details about DSF.