A Distributed Representation Approach to Group Problem Solving

Task Space Distributed Representation Space Figure 1. The framework of distributed representation for group cognitive tasks. The abstract task space, which represents the abstract structure of the task, is distributed across the representations of individuals. 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. 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, Group Problem Solving 4 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 two 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). Rule 1: Only one orange can be moved