Generalized golden sections, repeated bisections and aesthetic pleasure

We generalize the golden section in the sense that we partition a given line segment into a finite sequence of diminishing subsegments, in such a way that the ratio of any pair of adjacent subsegments equals the ratio of the whole and the first subsegment. When the number of subsegments increases, the partitioning approximates the subdivision of the line segment via repeated bisections. This is the basis of the geometric scales in multi-criteria decision analysis, introduced in order to model the gradations of comparative preferential judgement. Since the golden section plays an important role in the analysis of beauty and harmony, we suppose that it is an aesthetic pleasure to observe the resulting pattern of preference modelling.