We consider a situation in which policymakers in a local community have to choose an optimal site for a controversial and essential project in a democratic setting. Policymakers have either single-dipped or multi-dipped preferences over a Euclidean space of possible locations. We provide two existence results for this issue. There exists at most two optimal sites if the size of policymakers is odd, and they have single-dipped preferences over a one-dimensional site space.
Tondji, Jean-Baptiste, Locating an Optimal Site for a Controversial Facility (September 14, 2019). Available at SSRN: https://ssrn.com/abstract=3509819 or http://dx.doi.org/10.2139/ssrn.3509819