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Some data-analytic methods excel by their sheer elegance. Their
basic principles seem to have a particular attraction, based on a
intricate combination of simplicity, deliberation, and power. They
usually balance on the verge of two disciplines, data-analysis and
foundational measurement, or statistics and psychology. To me,
unfolding has always been one of them. The theory and the original
methodology were created by Clyde Coombs (1912-1988) to describe
and analyze preferential choice data. The fundamental assumptions
are truly psy chological; Unfolding is based on the notion of a
single peaked preference function over a psychological similarity
space, or, in an alternative but equivalent expression, on the
assumption of implicit comparisons with an ideal alternative.
Unfolding has proved to be a very constructive data-analytic
principle, and a source of inspiration for many theories on choice
behavior. Yet the number of applications has not lived up to the
acclaim the theory has received among mathematical psychologists.
One of the reasons is that it requires far more consistency in
human choice behavior than can be expected. Several authors have
tried to attenuate these requirements by turning the deterministic
unfolding theory into a probabilistic one. Since Coombs first put
forth a probabilistic version of his theory, a number of competing
proposals have been presented in the literature over the past
thirty years. This monograph contains a summary and a comparison of
unfolding theories for paired comparisons data, and an evaluation
strategy designed to assess the validity of these theories in
empirical choice tasks."
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