We consider a setting in which agents contribute amounts of a divisible resource (such as money or time) to a common pool, which is used to finance projects of public interest. How the collected resources are to be distributed among the projects is decided by a distribution rule that takes as input a set of approved projects for each agent. An important application of this setting is donor coordination, which allows philanthropists to find an efficient and mutually agreeable distribution of their donations. We analyze various distribution rules (including the Nash product rule and the conditional utilitarian rule) in terms of classic as well as new axioms, and propose the first fair distribution rule that satisfies efficiency and monotonicity. Our main result settles a long-standing open question of Bogomolnaia, Moulin, and Stong (2005) by showing that no strategyproof and efficient rule can guarantee that at least one approved project of each agent receives a positive amount of the resource. The proof reasons about 386 preference profiles and was obtained using a computer-aided method involving SAT solvers.

Randomized voting rules are gaining increasing attention in computational and non-computational social choice. A particularly interesting class of such rules are maximal lottery (ML) schemes, which were proposed by Peter Fishburn in 1984 and have been repeatedly recommended for practical use. However, the subtle differences between different ML schemes are often ignored. Two canonical subsets of ML schemes are C1-ML schemes (which only depend on unweighted majority comparisons) and C2-ML schemes (which only depend on weighted majority comparisons). We prove that C2-ML schemes are the only Pareto efficient---but also among the most manipulable---ML schemes. Furthermore, we evaluate the frequency of manipulable preference profiles and the degree of randomization of ML schemes via extensive computer simulations. In general, ML schemes are rarely manipulable and often do not randomize at all, especially when there are only few alternatives. For up to 21 alternatives, the average support size of ML schemes lies below 4 under reasonable assumptions. The average degree of randomization (in terms of Shannon entropy) of C2-ML schemes is significantly lower than that of C1-ML schemes.