An anonymous reviewer of this book accurately suspected that more was involved with the topological decision issues introduced in Section 2.1.3. To indicate other concepts (with the same assumptions), in this appendix I outline key ideas that Jason Kronewetter and I developed for [24]. As one must expect, this discussion emphasizes the connecting themes of the book – the structure of the domain and the dimensionality curse.

In introducing alternative ways to think about group decisions on domains with holes, I hope to interest others in exploring these new, fairly simple non topological arguments. My comments start, as in Section 2.1.3, with choice problems on a circle. The motivating story was to select a beach location on an island: However, applications arise in any number of disciplines. After all, a point on a circle defines a direction, so this discussion applies to any topic where a selected direction is based on information from two or more other directions.

Consider this illustration: A current psychology project with Louis Narens involves a colored disk placed in the center of a surrounding colored background. It is well known that the perceived color of the disk in this “center-surround” framework depends on the colors of the disk and the surrounding background.