Developing and Characterizing Multidimensional Thurstone and Luce Models for Identification and Preference
A. A. J. Marley
A class of situations that has received considerable theoretical and empirical study in psychology, statistics, and economics involves the selection of the single "best" option from some available set of multidimensional options. Two of the major examples of relevance to this book are preference and (absolute) identification. In a typical preference situation a person has simultaneously available some finite set of options from which he or she is to select the most preferred according to some (usually specified) criterion; typical preference situations involve the selection of the preferred mode of transportation among, say, automobile, bus, and subway; the preferred investment portfolio from some set of available options; the preferred house from several currently on the market. In an (absolute) identification situation a person is usually presented with one option from some fixed set of options, which he or she is required to identify, usually in terms of a response from some simple set of responses that have previously been associated with the possible options; a typical identification situation involves identifying which pure tone has been presented from some set of pure tones that vary in, say, frequency and loudness. Note that it is possible to design an identification situation that has the structure of a preference situation--that is, with all the options simultaneously available; a typical situation would be the identification of the brightest of some simultaneously presented set of monochromatic lights.
For simplicity in the following introduction, I refer to choice(s) (among the available options) without distinguishing between preference and identification situations, and I call the relevant models choice models. Particularly in psy-