Scale construction from a decisional viewpoint

Minds and Machines 16 (3):339-364 (2006)
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Many quantitative scales are constructed using cutoffs on a continuum with scores assigned to the cutoffs. This paper develops a framework for using or constructing such scales from a decision-making standpoint. It addresses questions such as: How many distinct thresholds or cutoffs on a scale (i.e., what levels of granularity) are useful for a rational agent? Where should these thresholds be placed given a rational agent’s preferences and risk-orientation? Do scale score assignments have any bearing on decision-making and if so, how should scores be assigned? Given two possible states of nature , an ordered collection of alternatives from which one is to be selected depending on the probability that A is the case, a simple expected utility condition stipulates when adjacent alternatives are distinguishable and determines the threshold odds separating them. Threshold odds and utilities are mapped onto scale scores via a simple distance model. The placement of the thresholds reflects relative concern over decisional consequences given A versus consequences given ∼ A. Likewise, it is shown that scale scores reflect risk-aversion or risk-seeking not only with respect to A versus ∼ A but also with respect to the rank of the R j . Connections are drawn between this framework and rank-dependent expected utility (RDEU) theory. Implications are adumbrated for both machine and human decision-making.



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Michael Smithson
Australian National University

References found in this work

Prospect Theory: An Analysis of Decision Under Risk.D. Kahneman & A. Tversky - 1979 - Econometrica: Journal of the Econometric Society:263--291.
Common knowledge revisited.Ronald Fagin, Joseph Y. Halpern, Yoram Moses & Moshe Y. Vardi - 1999 - Annals of Pure and Applied Logic 96 (1-3):89-105.

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