On the other hand, any dataset can be perfectly represented using n-1 dimensions, where n is the number of items scaled. As the number of dimensions used goes up, the stress must either come down or stay the same. It can never go up. Of course, it is not necessary that an MDS map have zero stress in order to be useful. A certain amount of distortion is tolerable.
Different people have different standards regarding the amount of stress to tolerate.
The rule of thumb we use is that anything under 0.1 is excellent and anything over 0.15 is unacceptable. The distortions may be spread out over all pairwise relationships, or concentrated in just a few egregious pairs. In general, however, longer distances tend to be more accurate than shorter distances, so larger patterns are still visible even when stress is high. See the section on Shepard Diagrams and Interpretation for further information on this issue. From a substantive standpoint, stress may be caused either by insufficient dimensionality, or by random measurement error.