We consider collective choice problems where a group of agents has to decide on the location of a public facility in a Euclidean space. A well-known solution for such problems is the coordinatewise median of the reported votes and additional fixed ballots. Instead of adding ballots, we extend...

We consider the problem of (re)allocating the total endowment of an infinitely divisible commodity among agents with single-peaked preferences and individual endowments. We propose an extension of the so-called uniform rule and show that it is the unique rule satisfying Pareto optimality,...