Learning about the liveability of cities from young migrants using the combinatiorial-Hodge-theory approach

Migration is a major decision to leave one place and move to another, involving career and life changes. Migration flows provide people's comparisons across places about which is better to live by ``vote with their feet'' (Tiebout, 1956). However, is it possible to derive a consistent measure of the liveability of cities from these flows? We propose a combinatorial-Hodge-theory approach: the empirical liveability of cities is evaluated by a potential governing unbalanced, acyclic migrations between cities. As a case study, we measure the liveability of municipalities in Japan for specific populations such as families with small children and women of reproductive age in a population-decline society. Using these potentials as dependent variables, we perform a regression analysis to identify the factors relevant to liveability. We also derive analytical expressions that allow us to interpret as potentials the standards of living or utilities, estimated in the economics literature (Douglas & Wall, 1993; Douglas, 1997; Douglas & Wall, 2000; Wall, 2001; Nakajima & Tabuchi, 2011). The proposed method extracts a consistent metric of interval scale from the non-transitive, pairwise comparison between locations and provides substantial statistics for urban planning by policymakers.