Distances in common: (un-)balanced access to public infrastructure in Germany

Public infrastructure shapes everyday opportunities, yet little is known about how balanced access to work, social reproduction, and leisure as public commons is distributed across households. Existing studies typically assess single services or regional averages, overlooking the relational nature of accessibility of public commons and differences in households' ability to privately substitute for missing public commons. We use German SOEP microdata to construct the relative distance for the three public commons and map households into a ternary space that captures their compositional accessibility. We also develop a Private Substitution Index that identifies the extent to which households rely on private substitutes to offset gaps in public infrastructure. Together, these measures reveal how households position themselves when facing infrastructural trade-offs. Most households exhibit relatively balanced access, but this average masks clear patterns: some live close to work and far from the other public commons, others show the opposite tilt. Urban-rural differences are substantial, while East-West differences are modest. Private substitution capacity rises steeply with income, driven by remote-work feasibility and living-space advantages, whereas public substitution in social reproduction remains limited. These findings show that balanced access to public commons is highly uneven and cannot be understood through single amenities or regional summaries. Policies aimed at spatial justice must consider both positional trade-offs and unequal capacities for private substitution.