me journal 2022 November IPL Information Processing Letters https://www.sciencedirect.com/journal/information-processing-letters arXiv https://arxiv.org/abs/2106.11178 Official journal version https://www.sciencedirect.com/science/article/abs/pii/S0020019022000989 We prove an Ω(n^2) lower bound on the query complexity of local proportionality in the Robertson-Webb cake-cutting model. Local proportionality requires that each agent prefer their allocation to the average of their neighbors' allocations in some undirected social network. It is a weaker fairness notion than envy-freeness, which also has query complexity Ω(n^2), and generally incomparable to proportionality, which has query complexity Θ(n log n). This result separates the complexity of local proportionality from that of ordinary proportionality, confirming the intuition that finding a locally proportional allocation is a more difficult computational problem.