Some theory and results for metrics for bounded response scales (Q794962)

In an earlier paper [Bull. Psychonomic Soc. 19, 317-319 (1982)], the author introduced a new metric for bounded response scales (MBR), which resembles the city-block metric, but is bounded above. In the present paper he investigates some formal properties of the MBR and proves that it is indeed a metric. Some empirical results are given which contradict the monotonicity hypothesis, stating that dissimilarity judgements tend to be biased towards overestimation of large distances, and the Minkowski metrics, but favor the MBR. Finally, the author defines a subadditive concatenation for bounded norms in the one-dimensional case. This concatenation predicts underestimation for doubling and overestimation for halving and middling tasks.