Partisan gerrymandering poses a threat to democracy. Moreover, the complexity of the districting task may exceed human capacities. One potential solution is using computational models to automate the districting process by optimizing objective and open criteria, such as how spatially compact districts are. We formulated one such model that minimised pairwise distance between voters within a district. Using US Census Bureau data, we confirmed our prediction that the difference in compactness between the computed and actual districts would be greatest for states that are large and, therefore, difficult for humans to properly district given their limited capacities. The computed solutions highlighted differences in how humans and machines solve this task with machine solutions more fully optimised and displaying emergent properties not evident in human solutions. These results suggest a division of labour in which humans debate and formulate districting criteria whereas machines optimise the criteria to draw the district boundaries. We discuss how criteria can be expanded beyond notions of compactness to include other factors, such as respecting municipal boundaries, historic communities, and relevant legislation.