Spatial Exposure Index

They measure different dimensions of segregation. The dissimilarity index gauges evenness — how unequally a group is distributed across units, independent of group size — and answers what share of one group would have to relocate for an even distribution. The exposure index P* gauges potential contact — the probability that a group member shares a unit with the same or another group — and depends heavily on the relative sizes of the groups. A city can be highly uneven yet, if the minority is tiny, still leave the majority with little exposure to it.

The checkerboard problem is that the standard P* indices use only the composition within each unit and ignore which units are adjacent, so a perfectly alternating arrangement of group-X and group-Y units scores identically whether those units are intermingled or split into two homogeneous halves. Spatial exposure measures fix this by weighting the contribution of nearby units through adjacency or distance-decay functions, so that contact across unit boundaries is counted and the index reflects the actual spatial pattern.

Because they are probabilities of contact, they are mechanically tied to how common each group is. A member of a large group will, on average, encounter their own group frequently almost regardless of spatial arrangement, so isolation tends to be high simply from size; conversely a small minority can only be highly isolated if it strongly concentrates. This size dependence is why analysts report exposure indices together with group proportions and often alongside a size-independent evenness measure like dissimilarity.