Donor coordination is a problem in social choice. There are several donors, each of whom wants to donate some money. Each donor supports a different set of targets. The goal is to distribute the total donated amount among the various targets in a way that respects the donors' preferences.
As an example, consider a town with three recreational facilities that require funding: theater, chess club, and basketball field. There are two donors: Alice and George, each of whom wants to donate 3000. Alice wants to donate to indoor activities (theater or chess), whereas George prefers to donate to competitive activities (chess or basketball). Suppose further that the donors consider the facilities substitute goods, so that the utility of a donor is the sum of money distributed to a facility he likes. Consider the following possible distributions:
In the uncoordinated distribution, Alice gives 1500 to each indoor activity, while George gives 1500 to each competitive activity. The resulting distribution is 1500, 3000, 1500. Each donor has a utility of 4500.
In contrast, if they coordinate, they can contribute everything to the chess club, so the distribution becomes 0, 6000, 0. Now, each donor has a utility of 6000, so this distribution Pareto-dominates the previous one.
Alternatively, one can assume that the donors consider the facilities complementary goods, so that the utility of a donor is the minimum amount of money distributed to a facility he likes. In this case, the uncoordinated distribution 1500,3000,1500 gives both donors utility 1500; the distribution 0,6000,0 gives both donors utility 0; but there is an even better distribution:
If the donations are divided equally, the distribution becomes 2000,2000,2000. Now, each donor has a utility of 2000.
In both cases, coordination can improve the efficiency of the allocation.
Donor coordination is a variant of participatory budgeting, in which the budget is donated by the voters themselves, rather than given by the government. Since the donations are voluntary, it is important that the coordination algorithm ensures that each voter weakly gains from participating in the algorithm, i.e., the amount contributed to projects he approves of is weakly higher when he participates than when he does not.
Donor coordination has been studied in several settings, which can be broadly categorized into divisible and indivisible:
In divisible donor coordination, each target can receive and use any amount of funding (as in the opening example). In this setting, targets are often called charities.
In indivisible donor coordination, each target has a pre-determined cost, and it can be either fully funded, or not funded at all. In this setting, targets are often called projects.
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