AI is increasingly used to aid decision-making about the allocation of scarce societal resources, for example housing for homeless people, organs for transplantation, and food donations. Recently, there have been several proposals for how to design objectives for these systems that attempt to achieve some combination of fairness, efficiency, incentive compatibility, and satisfactory aggregation of stakeholder preferences. This paper lays out possible roles and opportunities for AI in this domain, arguing for a closer engagement with the political philosophy literature on local justice, which provides a framework for thinking about how societies have over time framed objectives for such allocation problems. It also discusses how we may be able to integrate into this framework the opportunities and risks opened up by the ubiquity of data and the availability of algorithms that can use them to make accurate predictions about the future.