Comparison 1 Comparison Geometric Models and Multidimensional Scaling

Introduction It might not be immediately clear why the topic of comparison warrants a whole chapter in a book on human thinking. Of course, we are often required to make decisions that involve comparing two or more alternatives and assessing their relative value. Which car should I buy? Which job is more suited to my long-term goals? Would I rather have the soup or the salad? But in the grand scheme of human cognition, it might seem that such processes could be relegated to a subheading in a chapter on decision making. In fact, comparison is one of the most integral components of human thought. Along with the related construct of similarity, comparison plays a crucial role in almost everything that we do. Furthermore, comparison itself is a powerful cognitive tool—in addition to its supporting role in other mental processes, research has demonstrated that the simple act of comparing two things can produce important changes in our knowledge. One primary function of comparison is simply to assess the similarity of two things. To understand why this is such an important part of cognition, consider the variety of processes that are hypothesized to use similarity as an input. In models of memory, recognition and reminding have been argued to rely on the similarity between a stimulus and a long-term representation (Hintzman, 1986; Shiffrin & Steyvers, 1997). Models of categorization have proposed that new examples are classified based on their similarity to other category members (Medin & Schaffer, 1978; Nosofsky, 1984), or to a prototype of a category (Reed, 1972). When making inferences about unknown properties, people often appear to rely on their knowledge about other similar entities and situations to make reasonable predictions (Osherson, et al, 1990; Shepard, 1987), and people are very likely to look to similar situations from their past when understanding and solving new problems it is a rare moment in our lives when comparison and similarity do not seem to play a role. However, comparison does more than simply assess existing representations—it can also affect our understanding of the things that are being compared. For example, research in decision making has shown that people's judgments and preferences may vary significantly based on the particular comparisons that are made (Huber, Payne & Puto, 1982; Simonson, 1989). More direct evidence comes from Medin and colleagues (1993), who found that participants interpreted the features of an item differently when it …