Can Everyone Benefit from Social Integration?

There is no matching mechanism that satisfies integration monotonicity and stability. If we insist on integration monotonicity, not even Pareto optimality can be achieved: the only option is to remain segregated. A weaker monotonicity condition can be combined with Pareto optimality but not with path independence, which implies that the dynamics of social integration matter. If the outcome of integration is stable, integration is always approved by majority voting, but a non-vanishing fraction of agents always oppose segregation. The side who receives the proposals in the deferred acceptance algorithm suffers significant welfare losses, which nevertheless become negligible when societies grow large.