Abstract
We put forward a formal model of participatory budgeting where projects can incur costs with respect to several different resources, such as money, energy, or emission allowances. We generalise several well-known mechanisms from the usual single-resource setting to this multi-resource setting and analyse their algorithmic efficiency, the extent to which they are immune to strategic manipulation, and the degree of proportional representation they can guarantee. We also prove a general impossibility theorem establishing the incompatibility of proportionality and strategyproofness for this model.
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Notes
- 1.
Note that negative costs can be appropriate as well (e.g., planting trees has “negative environmental cost”). We shall occasionally comment on the effects of doing so.
- 2.
Observe that for condition (i) it is important to count the number of voters who vote for S exactly rather than those who vote for a (not necessarily proper) superset of S. Indeed, weakening the conditions for the applicability of the axiom in this sense would immediately render it impossible to satisfy in general. To see this, consider a single-resource scenario in which we need to divide a budget of \(b=2\) amongst three projects of cost 1, and in which there are two voters, with approval ballots \(A_1 = \{p_1,p_2\}\) and \(A_2 = \{p_3\}\). Then each project forms a singleton set S for which \(n \cdot \frac{c(S)}{b} = 1\), while \(|\{i \in N : A_i \supseteq S\}| = 1\). But we cannot select all three projects.
- 3.
Note that dropping condition (ii) would render this axiom unsatisfiable in general, since sets satisfying the first condition can exceed the budget for some \(k\not \in R\).
- 4.
We are able to circumvent the need for this additional efficiency requirement because we do not impose exhaustiveness (which in multiwinner voting is an implicit part of the basic model). This gives us more freedom for the inductive lemmas we need to prove. At the same time, our result is weaker than that of Peters in other respects: his proportionality axiom is subtly weaker (as it needs to be imposed only for so-called party-list profiles) and his result applies even under subset preferences.
- 5.
We found these 14 profiles and the derivation of Table 1 by first encoding the requirements of F as a set of clauses in propositional logic, and then applying a SAT-solver to that set to compute a minimally unsatisfiable set exhibiting the impossibility of finding a mechanism of the required kind. For an introduction to this approach, the reader may wish to consult the expository article of Geist and Peters [8].
- 6.
Observe that \(F'\) might not be exhaustive, with the implications discussed above.
- 7.
The question of whether these constraints can be relaxed is of some technical interest, but arguably less relevant to practice. Indeed, we would want our mechanism to work for arbitrary numbers of voters (including those that are multiples of a budget limit).
- 8.
When all resources are relevant (in the single-resource case for instance ), there is a trivial mechanism of this kind: simply return the union of all singletons satisfying condition (i) in the definition of proportionality. To see this, recall that condition (ii) is vacuous if there are only relevant resources.
- 9.
Recall that the approval score of a set S for a given profile \(\boldsymbol{A}\) is defined as \(s_{\boldsymbol{A}}(S) = \sum _{i\in N} |S\cap A_i|\), and that \(F_{\textsc {m}}\) seeks to maximise that score.
References
Aziz, H., Lee, B.E., Talmon, N.: Proportionally representative participatory budgeting: axioms and algorithms. In: Proceedings of the 17th International Conference on Autonomous Agents and Multiagent Systems (AAMAS) (2018)
Aziz, H., Shah, N.: Participatory budgeting: models and approaches. In: Rudas, T., Péli, G. (eds.) Pathways Between Social Science and Computational Social Science. CSS, pp. 215–236. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-54936-7_10
Benade, G., Nath, S., Procaccia, A.D., Shah, N.: Preference elicitation for participatory budgeting. Manage. Sci. 67(5), 2813–2827 (2021)
Brandt, F., Conitzer, V., Endriss, U., Lang, J., Procaccia, A.D. (eds.): Handbook of Computational Social Choice. Cambridge University Press, Cambridge (2016)
Faliszewski, P., Skowron, P., Slinko, A., Talmon, N.: Multiwinner voting: a new challenge for social choice theory. In: Endriss, U. (ed.) Trends in Computational Social Choice, chap. 2, pp. 27–47. AI Access (2017)
Fluschnik, T., Skowron, P., Triphaus, M., Wilker, K.: Fair knapsack. In: Proceedings of the 33rd AAAI Conference on Artificial Intelligence (AAAI) (2019)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H, Freeman and Co (1979)
Geist, C., Peters, D.: Computer-aided methods for social choice theory. In: Endriss, U. (ed.) Trends in Computational Social Choice, chap. 13, pp. 249–267. AI Access (2017)
Goel, A., Krishnaswamy, A.K., Sakshuwong, S., Aitamurto, T.: Knapsack voting: voting mechanisms for participatory budgeting. ACM Trans. Econ. Comput. 7(2), 8 (2019)
Goldfrank, B.: Lessons from Latin America’s experience with participatory budgeting. In: Shah, A. (ed.) Participatory Budgeting, chap. 3, pp. 91–126. Public Sector Governance and Accountability Series, The World Bank, Washington, DC (2007)
Hershkowitz, D.E., Kahng, A., Peters, D., Procaccia, A.D.: District-fair participatory budgeting. In: Proceedings of the 35th AAAI Conference on Artificial Intelligence (AAAI) (2021)
Jain, P., Sornat, K., Talmon, N.: Participatory budgeting with project interactions. In: Proceedings of the 29th International Joint Conference on Artificial Intelligence (IJCAI) (2020)
Jain, P., Sornat, K., Talmon, N., Zehavi, M.: Participatory budgeting with project groups. In: Proceedings of the 30th International Joint Conference on Artificial Intelligence (IJCAI) (2021)
Janson, S.: Phragmén’s and Thiele’s election methods. arXivpreprint: arXiv:1611.08826 (2016)
Kellerer, H., Pferschy, U., Pisinger, D.: Multidimensional knapsack problems. In: Knapsack Problems, chap. 9, pp. 235–283. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24777-7_9
Lackner, M., Maly, J., Rey, S.: Fairness in long-term participatory budgeting. In: Proceedings of the 30th International Joint Conference on Artificial Intelligence (IJCAI) (2021)
Laruelle, A.: Voting to select projects in participatory budgeting. Eur. J. Oper. Res. 288(2), 598–604 (2021)
Patel, D., Khan, A., Louis, A.: Group fairness for knapsack problems. In: Proceedings of the 20th International Conference on Autonomous Agents and Multiagent Systems (AAMAS) (2021)
Peters, D.: Proportionality and strategyproofness in multiwinner elections. In: Proceedings of the 17th International Conference on Autonomous Agents and Multiagent Systems (AAMAS) (2018)
Peters, D.: Fair Division of the Commons. DPhil thesis, University of Oxford (2019)
Peters, D., Pierczynski, G., Skowron, P.: Proportional participatory budgeting with additive utilities. In: Proceedings of the 35th Annual Conference on Neural Information Processing Systems (NeurIPS) (2021)
Rey, S., Endriss, U., de Haan, R.: Designing participatory budgeting mechanisms grounded in judgment aggregation. In: Proceedings of the 17th International Conference on Principles of Knowledge Representation and Reasoning (KR) (2020)
Rey, S., Endriss, U., de Haan, R.: Shortlisting rules and incentives in an end-to-end model for participatory budgeting. In: Proceedings of the 30th International Joint Conference on Artificial Intelligence (IJCAI) (2021)
Rose, J., Omolo, A.: Six Case Studies of Local Participation in Kenya. The World Bank, Washington, DC (2013). http://hdl.handle.net/10986/17556
Sánchez-Fernández, L., Fernández-García, N., Fisteus, J.A., Brill, M.: The maximin support method: An extension of the d’Hondt method to approval-based multiwinner elections. Mathematical Programming (2022). (in press)
Schrijver, A.: Theory of Linear and Integer Programming. John Wiley & Sons, New York (1998)
Shah, A. (ed.): Participatory Budgeting. Public Sector Governance and Accountability Series, The World Bank, Washington, DC (2007)
Talmon, N., Faliszewski, P.: A framework for approval-based budgeting methods. In: Proceedings of the 33rd AAAI Conference on Artificial Intelligence (AAAI) (2019)
Acknowledgements
This paper grew out of a student project that started in the context of a course on computational social choice at the University of Amsterdam in 2020. We acknowledge the contribution of Gerson Foks during that initial stage. We also would like to thank several anonymous reviewers for their feedback.
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Motamed, N., Soeteman, A., Rey, S., Endriss, U. (2022). Participatory Budgeting with Multiple Resources. In: Baumeister, D., Rothe, J. (eds) Multi-Agent Systems. EUMAS 2022. Lecture Notes in Computer Science(), vol 13442. Springer, Cham. https://doi.org/10.1007/978-3-031-20614-6_19
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