# Comparisons vs. Preferences

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, dandrich@murdoch.edu.au

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

Rasch Publications
Rasch Measurement Transactions (free, online) Rasch Measurement research papers (free, online) Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Applying the Rasch Model 3rd. Ed., Bond & Fox Best Test Design, Wright & Stone
Rating Scale Analysis, Wright & Masters Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr. Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
in Spanish: Análisis de Rasch para todos, Agustín Tristán Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez

 Forum Rasch Measurement Forum to discuss any Rasch-related topic

Go to Top of Page
Go to index of all Rasch Measurement Transactions
AERA members: Join the Rasch Measurement SIG and receive the printed version of RMT
Some back issues of RMT are available as bound volumes
Subscribe to Journal of Applied Measurement

Go to Institute for Objective Measurement Home Page. The Rasch Measurement SIG (AERA) thanks the Institute for Objective Measurement for inviting the publication of Rasch Measurement Transactions on the Institute's website, www.rasch.org.

Coming Rasch-related Events
July 31 - Aug. 3, 2017, Mon.-Thurs. Joint IMEKO TC1-TC7-TC13 Symposium 2017: Measurement Science challenges in Natural and Social Sciences, Rio de Janeiro, Brazil, imeko-tc7-rio.org.br
Aug. 7-9, 2017, Mon-Wed. In-person workshop and research coloquium: Effect size of family and school indexes in writing competence using TERCE data (C. Pardo, A. Atorressi, Winsteps), Bariloche Argentina. Carlos Pardo, Universidad Catòlica de Colombia
Aug. 7-9, 2017, Mon-Wed. PROMS 2017: Pacific Rim Objective Measurement Symposium, Sabah, Borneo, Malaysia, proms.promsociety.org/2017/
Aug. 10, 2017, Thurs. In-person Winsteps Training Workshop (M. Linacre, Winsteps), Sydney, Australia. www.winsteps.com/sydneyws.htm
Aug. 11 - Sept. 8, 2017, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com
Aug. 18-21, 2017, Fri.-Mon. IACAT 2017: International Association for Computerized Adaptive Testing, Niigata, Japan, iacat.org
Sept. 15-16, 2017, Fri.-Sat. IOMC 2017: International Outcome Measurement Conference, Chicago, jampress.org/iomc2017.htm
Oct. 13 - Nov. 10, 2017, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
Oct. 25-27, 2017, Wed.-Fri. In-person workshop: Applying the Rasch Model hands-on introductory workshop, Melbourne, Australia (T. Bond, B&FSteps), Announcement
Jan. 5 - Feb. 2, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
Jan. 10-16, 2018, Wed.-Tues. In-person workshop: Advanced Course in Rasch Measurement Theory and the application of RUMM2030, Perth, Australia (D. Andrich), Announcement
Jan. 17-19, 2018, Wed.-Fri. Rasch Conference: Seventh International Conference on Probabilistic Models for Measurement, Matilda Bay Club, Perth, Australia, Website
April 13-17, 2018, Fri.-Tues. AERA, New York, NY, www.aera.net
May 25 - June 22, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
June 29 - July 27, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com
Aug. 10 - Sept. 7, 2018, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com
Oct. 12 - Nov. 9, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com