Cognitive Processes in Quantitative Estimation: Analogical Anchors and Causal Adjustment

Cognitive Processes in Quantitative Estimation: Analogical Anchors and Causal Adjustment Praveen K. Paritosh (paritosh@northwestern.edu) Matthew E. Klenk (m-klenk@northwestern.edu) Qualitative Reasoning Group, Northwestern University, Evanston IL 60208 present KNACK, a computational model of the analogical estimation process. Next we present the results of verbal protocols collected for realistic estimation tasks: a used car salesman estimating price of cars, and an apartment realtor estimating apartment rents. These data indicate that analogical estimation is frequently used during quantitative estimation. We then conclude with future work. Abstract Quantities are ubiquitous and an important part of our understanding of the world. How do people solve quantitative estimation problems? A large body of psychological research addressing this question is based on the anchoring and adjustment paradigm (Tversky and Kahneman, 1974). Based on an analysis of verbal protocols of experts engaging in estimation tasks, we claim that similarity and analogy play important roles in quantitative estimation. A similar example for which the answer is known provides an analogical anchor, and comparison provides the grist for making causal adjustments. We present KNACK, a computational model of analogical estimation. Our theoretical analysis of causal adjustments suggests that they might not always be insufficient, as they are based on a discrepancy between assumed strength of causal relationships and that exists in the world (Kareev et al, 1997). 2 Background 1 Introduction Much of the literature relevant to quantitative estimation has focused on its numerical aspects. Even though numerical aspects are important, depending upon one's expertise, one may recruit varying degrees of semantic (non-numeric) knowledge while making estimates. A robust finding is the anchoring bias (Brown, 1953; Tversky and Kahneman, 1974; Kahneman, 1992). One demonstration of the anchoring bias involves the subject making a comparison with an incidental number, called the anchor. Later on, when subjects are asked to come up with a quantitative estimate, then their answers are biased towards the anchor they were initially given. For example, participants were asked to compare the percentage of African nations in the UN as being as higher or lower than an arbitrary number (25% or 65%). Following this, they were asked to estimate the percentage of African nations in the UN. The mean estimates for the subjects who received the high anchor was 45% compared to 25% for the low anchor. Anchoring effects have been found with both domain experts and novices, e.g., real estate agents and students estimating an appraisal value for a house after touring through it (Northcraft and Neale, 1987). There is a growing body of evidence (Mussweiler and Strack, 2001; Chapman and Johnson, 1999) indicating that anchoring is not a purely numeric phenomenon, but has semantic underpinnings. Mussweiler and Strack’s selective accessibility model of anchoring suggests that the anchor causes increased accessibility of anchor-consistent knowledge. For example, with the high (65%) anchor in the Africa example, facts like “Africa is a large continent” and “There are more African countries than I keep in mind” are retrieved. The final numeric estimate is generated based on the easily accessible knowledge (Higgins, 1996), so their estimate is heavily influenced by anchor-consistent knowledge. This line of argument proposes a semantic priming based explanation of the anchoring and adjustment phenomena. Epley and Gilovich (2005) argue that the standard “experimenter-provided” anchors behave differently from “self-generated anchors,” and the former Making rough quantitative estimates is a key component of commonsense reasoning about everyday situations. Let’s look at some examples of quantitative estimation problems: • What is reasonable price for a 2001 Ford Focus hatchback with 41,000 miles on it? • How much does a two bedroom apartment in the Rogers Park neighborhood of Chicago cost? • What is the average points per game scored in the current season by Jason Kidd? • What is the freezing point of Vodka? There are many different factors involved in solving these types of questions. First, there is domain specific knowledge in form of rules and/or examples, e.g., the effect of mileage on price. Second, the knowledge of similar examples, e.g., prices of other Ford Focus models might be relevant. Third, important landmark values, like the freezing point of water, might provide a starting point for answering the last question. A dominant paradigm for research in quantitative estimation has been anchoring and adjustment. This work has been done in domains ranging from information rich, real-world estimation (Northcraft and Neale, 1987) to impoverished guessing (Tversky and Kahneman, 1974, Tenenbaum, in press). In this paper, we look at estimation in knowledge-rich domains and in naturalistic contexts. In such situations, experts routinely use analogical estimation: drawing upon similar examples from their experience while estimating. We begin with a brief survey of the relevant literature including a catalog of estimation processes. Next, we present our theory of analogical estimation. We then