DYNAMIC PAIRED-COMPARISON SCALING

This paper describes an approach to paired-comparison scaling that may be useful when underlying scale values change with time. Sequentially revised estimates of scale values underlying a fixed set of choice objects are calculated from binary choice data collected on discrete trials. The system is defined by a reward function that controls the sequential increments and decrements to the estimates. Results of the reward system depend jointly on the difference between the current estimates and the binary choice data. Natural restrictions on reward systems are presented that imply uniqueness up to a scaling factor. Asymptotic properties are provided for a particular reward system based on a uniform distribution function, and other methods for obtaining results for other distributions are discussed. One-object, two-object, and many-object estimation problems are formulated. It is shown that the two-object problem based on a uniform reward system corresponds to the Bush-Mosteller linear operator model for two-choice learning; that the one-object problem can be related to both adaptive testing and adaptive threshold estimation; and that the many-object problem provides a sequential estimation scheme for dynamic paired-comparison systems. Refinements include a method for introducing a draw or no-preference cutcome into the reward system. © 1992.