Condorcet solutions in frugal models of budget allocation

We study a voting model with incomplete information in which the evaluation of social welfare must be based on information about agents’ top choices plus general qualitative background conditions on preferences. The former is elicited individually, while the latter is not. We apply this ‘frugal aggregation’ model to multi-dimensional budget allocation problems, relying on the specific assumptions of convexity and separability of preferences. We propose a solution concept of ex-ante Condorcet winners which is widely and flexibly applicable and naturally incorporates the epistemic assumptions of particular frugal aggregation models. We show that for the case of convex preferences, the ex-ante Condorcet approach naturally leads to a refinement of the Tukey median. By contrast, in the case of separably convex preferences, the same approach leads to different solution, the 1-median, i.e. the minimization of the sum of the L1-distances to the agents’ tops. An algorithmic characterization renders the latter solution analytically tractable and efficiently computable.