Joseph L. Zinnes

A Thurstonian view of the analytic hierarchy process

Abstract The application of deterministic decision models in situations characterized by noise and uncertainty is likely to produce results of questionable value. In this paper, some very simple probabilistic models are developed and substituted for the deterministic scales used in the Analytic Hierarchy Process (AHP). It is shown that the use of these probabilistic models can extend the domain of AHP to situations, such as consensual or group decision making, that possess significant amounts of uncertainty. In addition, explicit measures of the variation present in the evaluation of decision alternatives and attributes are obtained.

A paired comparison of pair comparisons

Abstract The theory of choice developed by Luce and the paired comparison theory due to Thurstone are restated so as to permit direct comparison. It is shown that the theories differ in general, but coincide for certain sets of stimuli. The class of stimuli on which they coincide is described, and it is proved that they can coincide on no stimuli outside of the class. The problem of finding a class of stimuli which gives maximal discrepancy between the theories can be posed in a number of ways. For one statement of the problem, solutions are found. Unfortunately, the nature of the solutions makes it very difficult to design an experiment for deciding between the theories. The general problem of an experimental decision is discussed briefly, and some pair comparison data are analyzed. The sets of data conform somewhat more closely to the Thurstone than to the Luce model, but superiority is by no means definitive.

Probabilistic Multidimensional Analysis of Preference Ratio Judgments

A probabilistic multidimensional model is described for analyzing preference ratio judgments. This model combines the unfolding model of Coombs with the probabilistic model of Hefner, in which stimuli and individuals are represented by multivariate normal distributions. A simple procedure is described for approximating the maximum likelihood estimates of the location and variance parameters of the model. Two simulations show how well this procedure works, especially when there is considerable variability in the data.

Single and multidimensional same-different judgments☆

Abstract A probabilistic, multidimensional Thurstonian model for treating same-different judgments was tested in an experiment in which subjects made single-dimensional and two-dimensional same-different judgments. Strong asymmetries in the data required adding temporal bias parameters to the model. The model, with bias parameters, accounted for the single- and two-dimensional judgments reasonably well, but the parameters were not invariant between the different solutions. The two-dimensional judgments were more variable than expected on the basis of the single-dimensional judgments.

Stochastic learning theories for a response continuum with non-determinate reinforcement

Continuous analogues of the finite linear and stimulus sampling theories are developed for non-determinate reinforcement schedules. Closed-form expressions are derived for the asymptotic response distribution and certain sequential statistics. Computations for a target experiment are given to illustrate the character of the theoretical results.

A note on a paper by Rumelhart and Greeno

Abstract The parameters of the models described by Rumelhart and Greeno in this journal (1971) are constrained in certain ways. Neglect of this fact in their paper leads them to an inadmissible set of parameter values, and an invalid argument and statement concerning the equivalence of two models. However, their conclusion that the Restle model fits their data better than the Luce model remains unchanged.

A Continuous-Response Task with Nondeterminate, Contingent Reinforcement

Abstract An experiment dealing with a continuous-response task with nondeterminate contingent reinforcement is analyzed in detail. The subjects task was to attempt to hit a target located at a variable position on the circumference of a circle. The subject could not see this target but was simply told after each response whether he had hit or missed the target. The sixty subjects were randomly assigned to one of two groups, the only difference in the groups being the size of the target. The asymptotic response data are analyzed with respect to three different one-element models. Only one of these three models, the identity model, is at all satisfactory. For the analysis of sequential data this model is extended to an N-element version.