It is important to distinguish between "comparisons" and "preferences". The person makes a comparison as to which of the pair of stimuli has more of the property, e.g., comparing cups of coffee as to which is sweeter. This comparison should essentially not be a function of the person's liking for sugar in coffee. A sweeter cup should, in general, taste sweeter to everyone (and, when we have relative similar amounts of sugar, we get proportions rather than perfection in the numbers deciding one way or the other.)
In the case of preferences, the person parameter ("ideal point" in the language of Clyde Coombs) plays a central role. Taking the sweetness of coffee example again, the person is asked which of each pair of cups of coffee the person prefers as to sweetness, not which is sweeter (irrespective of the person's preference). In this case, the person will prefer the cup of coffee which is closest to the person's ideal amount of sweetness relative to those cups that are both less and more sweet.
It is very important to distinguish the instructions that are given to people and to consider which model is the most appropriate (i.e., has the correct properties). It is convenient to use the word "comparison" when the person's location is not supposed to be involved, and the word "preference" when the person's location is supposed to be involved.
This is confused in the literature. For instance, there is Luce's so-called choice axiom (1959). This essentially states that, when there are several alternatives available, the probability of the preferred option is independent of the sequence of decisions. When this axiom is expressed algebraically, no person parameter is specified. But preferences are obviously decision-maker dependent. The same flaw is evident in the algebraic formulation of the Shepard-Luce choice rule, which can be expressed: "Choice probability increases with strength of evidence that an object belongs to a category." These have added further to the confusion of terminology, models and response processes.
David Andrich, firstname.lastname@example.org
Luce RD (1959) Individual Choice Behavior. New York: Wiley.
Shepard, Roger N. (1964), "On Subjectively Optimum Selection among Multi-Attribute Alternatives," in Human Judgments and Optimality, eds. M.W. Shelley and G. L. Bryan, N.Y.: John Wiley.
Comparisons vs. preferences. Andrich DA. 16:1 p.859
Comparisons vs. preferences. Andrich DA. Rasch Measurement Transactions, 2002, 16:1 p.859
Please help with Standard Dataset 4: Andrich Rating Scale Model
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