Robust comparisons of spatial patterns

A spatial allocation (a so-called pattern) is represented by a finite measure in two-space, and choices between alternative patterns are based on an average value over space. This paper presents rules for robust comparisons of patterns in the sense that one pattern should be uniformly better than another one with respect to all elements of a certain class of valuation functions. In particular, we investigate the optimum location of a new pattern (i) which interacts with a single given center and (ii) which interacts with several given patterns.