A Distributed Representation Approach to Group Problem Solving

This article develops a theoretical framework of distributed representations to explore the representational properties in group problem solving. The basic principle of distributed representations is that the representational system of a group problem solving task is distributed across the representations of individuals, which together represent the abstract structure of the task. The framework was used to analyze the distributed representation of the Waitress and Orange task. From this analysis, an experiment was designed to examine group problem solving behaviors under different distributed representations. The experimen shows that (1) different distributed representations across two individuals produced dramatically different group problem solving behaviors even if they had the same abstract structure, and (2) two minds could be better than, not different from, or even worse than one mind, depending on how representations were distributed across the two minds. These results further support the interactionist view of group problem solving, which is that the interactions among individuals can produce group cognitive properties that can neither be reduced to nor be inferred from the cognitive properties of individuals. Group Problem Solving 3 Group problem solving refers to problem solving activities that involve interactions among a group of individuals. One of the critical issues in group problem solving is concerned with the nature of group properties. One view is that the cognitive properties of a group can be entirely determined by the properties of individuals. In this reductionist view, to understand group behavior, all we need is to understand the properties of individuals. Another view is that the interactions among the individuals can produce emergent group properties that cannot be reduced to the properties of the individuals. In this interactionist view, to study group behavior, we not only need to examine the properties of individuals but, more importantly, we also need to consider the interactions among the individuals as the basic units of analysis. The interactionist view has been evidenced by much of the research, as reflected in the recent study of distributed cognition—the study of cognitive tasks that are distributed across the internal mind and the external environment, among a group of individuals, and across space and time (e.g., Hutchins, 1990, 1994, 1995; Norman, 1990, 1993; Zhang, in press; Zhang & Norman, 1994, 1995). For instance, Hutchins (1995) has shown that the cognitive properties of a distributed system such as the airplane cockpit can differ radically from the cognitive properties of the individuals, and they cannot be inferred from the properties of the individuals alone, no matter how detailed the knowledge of the properties of those individuals may be. Another critical issue in group problem solving is concerned with the group effectiveness problem (Foushee & Helmreich, 1988). Most people would argue that two minds are better than one because in a group there are much more resources, task load and memory load are shared and distributed, errors are cross-checked, and so on. This is a condition that can result in what Steiner (1972) called process gain. However, there are also conditions that can result in process loss (Steiner, 1972)—a Group Problem Solving 4 phenomenon that the performance of a group is worse than that of an individual because in a group communication takes time, knowledge may not be shared, different strategies may be used by different individuals, and so on (McNeese, Zaff, & Brown, 1992). Most studies of the group effectiveness problem have focused on social and personality factors (e.g., Hackman & Morris, 1975; Hare, 1972; Janis, 1972; Lanzetta & Roby, 1960; Latane, Williams, & Harkins, 1979). Representational factors, in comparison, have not been extensively studied. This article addresses the above two issues about group properties and group effectiveness from a purely cognitive perspective, focusing on the representational properties in group problem solving. It is divided into four sections. The first section develops a theoretical framework of distributed representations for group problem solving. The second section uses this framework to analyze the distributed representation of the Waitress and Orange problem. From this analysis, the third section designs an experiment to examine the effects of representation distribution on group properties and group effectiveness. Finally, the last section discusses the general implications of the framework of distributed representations for group problem solving. Distributed Representations in Group Problem Solving The basic principle to be explored is that the representational system for a group problem solving task is distributed across the representations of individuals. Figure 1 shows a representational system for a group problem solving task with four individuals. Each individual has a representation for the task. The task has a single abstract task space that represents the abstract structure of the task. The abstract task space is distributed across the representations of the four individuals, which interact with each other and together form a distributed representation space. The Group Problem Solving 5 distributed representation space is the actual space in which the group problem solving task is performed. This framework of distributed representations for group problem solving is interactionist in nature. The representation of a group problem solving task is not in any individual's mind, but distributed across all individuals. In this view, a group problem solving task requires dynamic, interactive, and integrative processing of the information distributed across individual representations. The abstract task space is an emergent group property jointly determined by individual representations: it does not belong to any individual. The abstract task space of a group problem solving task can be distributed across individual representations in different ways. Let us consider a few cases. The first case is that none of the individual representations is a complete representation of the abstract task space but they together represent the complete abstract task space. In this case, individual representations may or may not overlap with each other, that is, there may or may not be redundancy in the distributed representation. The second case is that some individual representations each represent the complete abstract task space whereas others each only represent part of the abstract task space. In this case, there is always redundancy in the distributed representation because the individual representations that represent the complete abstract task space are always supersets of the individual representations that only represent part of the abstract task space. The third case is that every individual representation is a complete representation of the abstract task space. In this case the redundancy in the distributed representation is maximum. Different distributed representations of the same abstract task space may cause dramatically different group problem solving behaviors even if they all represent the same structure at an abstract level. In addition, group problem solving Group Problem Solving 6 behavior may be considerably different from individual problem solving behavior even if their structures are the same. These two issues are examined in the following sections in the representational analysis of the Waitress and Orange problem and the corresponding experiment. The Waitress and Orange Problem In this section, the framework of distributed representations for group problem solving is used to analyze the distributed representation of the Waitress and Orange problem (Zhang & Norman, 1994), which is an isomorph of the Tower of Hanoi problem (see Hayes & Simon, 1977; Kotovsky, Hayes, & Simon, 1985). Figure 2 shows the Waitress and Orange problem. The task is to move the oranges from one configuration to another, following the three rules stated in Figure 2. Figure 3 shows the problem space of this problem. Each rectangle shows one of the 27 possible configurations of the three oranges on the three plates. The lines between the rectangles show the transformations from one state to another when the three rules are followed. Figure 3 is a problem space generated by all of the three rules of the Waitress and Orange problem. In general, any subset of these three rules can generate a problem space. Figures 4 shows the problem spaces generated by Rules 1, 1+2, 1+3, and 1+2+3, respectively. Lines with arrows are uni-directional. Lines without arrows are bi-directional. One important point is that these four problem spaces can be held by different individuals. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Insert Figure 1 about here _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Group Problem Solving 7 Figure 5 shows how the three rules of the Waitress and Orange problem is distributed across two individuals. Individual 1 only knows Rules 1 and 3, which generate Individual 1's problem space. Individual 2 only knows Rules 1 and 2, which generate Individual 2's problem space. Although neither of the two individuals alone knows all three rules, they together know all of them. The problem spaces of the two individuals form the distributed problem space, which is the actual space in which problem solving takes place. The distributed problem space is mapped to the abstract problem space, which is jointly determined by the combined rules of the two individuals (Rules 1, 2, and 3). _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Insert Figure 2 about here _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Insert Figure 3 about here _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Insert Figure 4 about here _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Insert Figure 5 about here _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Group Problem Solving 8