In participatory budgeting the stakeholders collectively decide which projects from a set of proposed projects should be implemented.
This decision underlies both time and monetary constraints.
In reality it is often impossible to figure out the exact cost of each project in advance, it is only known after a project is finished.
To reduce risk, one can implement projects one after the other to be able to react to higher costs of a previous project.
However, this will increase execution time drastically.
We generalize existing frameworks to capture this setting, study desirable properties of algorithms for this problem, and show that some desirable properties are incompatible.
Then we present and analyze algorithms that trade-off desirable properties.
Many important collective decision-making problems can be seen as multiagent versions of discrete optimisation problems. Participatory budgeting, for instance, is the collective version of the knapsack problem; other examples include collective scheduling, and collective spanning trees. Rather than developing a specific model, as well as specific algorithmic techniques, for each of these problems, we propose to represent and solve them in the unifying framework of judgment aggregation with weighted issues. We provide a modular definition of collective discrete optimisation (CDO) rules based on coupling a set scoring function with an operator, and we show how they generalise several existing procedures developed for specific CDO problems. We also give an implementation based on integer linear programming (ILP) and test it on the problem of collective spanning trees.
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