Representativeness in Visual Studio .NET

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21.2.1 Representativeness
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Representativeness is more often illustrated than precisely de ned (Kahneman et al. 1982). In general, it re ects subjective probability judgments based on the resemblance of particular conditions in one circumstance to those in another. In a classic experiment, subjects are provided with a detailed pro le of the behavior and personality characteristics of a hypothetical person, then asked to estimate the probability that the person is a lawyer vs. an engineer. Subjects told that the individual was drawn from a group of 70 lawyers and 30 engineers produced the same estimates as those told that the group contained 30 lawyers and 70 engineers. The subjects judgments are based on matching the description
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HOW WELL DO PEOPLE ESTIMATE SUBJECTIVE PROBABILITIES
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to stereotypes of lawyers and engineers, ignoring other information in this case prior frequencies. In geotechnical practice, representativeness is often undermined by over-reliance on complex models, while discounting simple observations. Uncertainties remain disguised by embedded approximations, simpli cations, and assumptions so that analysis results are taken as uniquely representative of eld conditions with near-certainty, because it s the best analysis we have (Vick 2002).
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21.2.2 Anchoring and adjustment
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Anchoring-and-adjustment is easily illustrated. When asked to estimate a quantity or an uncertainty, people often start with a best estimate, and adjust up or down. Unfortunately, people tend to stick too close to the initial value, not adjusting suf ciently to re ect uncertainty. Asked to estimate the undrained shear strength of a clay and the uncertainty in that value, one s natural reaction is rst to think about a typical value. What is the average shear strength for this type soil across the many sites I have dealt with How does the present site differ Do I think the soil here is stronger or weaker, stiffer or looser How much should I adjust up or down Might this soil be 10% stronger How different could this site be, to suggest upper and lower bounds These are the questions one asks oneself, but this chain of reasoning is exactly that which has been shown to lead to signi cant overcon dence in resulting estimates. Quite a different result is obtained if one rst states the largest value the strength might have, then the lowest, and only afterwards hones in on a central value. The latter yields a broader range of assessed uncertainty and a better calibration to the physical world. Folayan et al. (1970) present an example from geotechnical practice.
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21.3 How Well do People Estimate Subjective Probabilities
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The heuristics of the last section deal with how people quantify probabilities, but they also in uence how well people do so. The many fallacies that people even technically trained people exhibit at the gambling table should dissuade us from thinking that one s natural tendencies concerning probability are well calibrated to the physical world. People behave as if games of chance even out, or as if pulling the slot machine handle oneself improves the chance of winning, or as if small numbers of observations are highly representative of a random process. These things are all false, and, left to one s own devices, the probabilities we estimate are usually neither coherent nor consistent. In particular, people tend to over-con dence in their assessments, and mis-calibration seems to vary systematically with the dif culty of the assessment.
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21.3.1 Overcon dence
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Overcon dence is the most pervasive bias in assessing subjective probability (Lichtenstein et al. 1982). It manifests in probability estimates that are too extreme at both ends of the probability scale and estimated distributions having insuf cient dispersion about the mean. People even experts rarely assess their uncertainty to be as large as it usually turns
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out to be, sometimes to a shocking extent, as reported in a well-known study by Alpert and Raiffa (1982). Figure 21.1 plots the results of experiments reported by Fischhoff et al. (1997) in which three groups of subjects provided answers to general-knowledge questions as well as estimated probabilities that their answers were correct. The estimated error probabilities were found to be reasonably well calibrated relative to the actual error frequencies only when the actual probabilities were no less than about 0.1. Their overcon dence, expressed as the difference between actual and judged error probabilities, increased dramatically at smaller values of actual error frequency. The subjects estimated a subjective probability of error as small as 10 6 when the actual error frequency was slightly less than 10 1 , a ratio of ve orders of magnitude. Moreover, the subjects showed little ability to distinguish among varying degrees of extreme likelihood, with judged probabilities ranging from 10 2 to 10 6 despite actual error frequencies hovering near 10 1 . A related and surprising nding is that the harder the probability estimation task, the greater the associated overcon dence. For quite easy tasks sometimes under-con dence is displayed, although this effect is poorly understood (McClelland and Bolger 1994). Neither experts in general nor geotechnical experts in particular seem immune from overcon dence. Hynes and Vanmarcke (Hynes and Vanmarcke 1976) reported on predictions of embankment failure height made by seven internationally-known geotechnical engineers for a test embankment on soft clay at the MIT I-95 test site. Figure 21.2 shows each expert s best estimate and 50% con dence interval for the amount of additional ll needed to fail the embankment, the average of the best estimates, and the actual amount required to cause failure. While the average of the seven best estimates is reasonably close to the outcome, no individual estimate had 50% error bounds large enough to encompass the actual outcome. Had the estimates been unbiased, half would have encompassed the actual failure height at the 50% con dence level, but none did so. Figure 21.3 is similar
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