Abstract
Liquid Democracy (LD) uses transitive delegations to facilitate joint decision making. In its simplest form, it is used for binary decisions, however its promise holds also for more advanced voting settings. Here we consider LD in the context of Participatory Budgeting (PB), which is a direct democracy approach to budgeting, most usually done in municipal budgeting processes. In particular, we study Knapsack Voting, in which PB voters can approve projects, however the sum of costs of voter-approved projects must respect the global budget limit. We observe inconsistency issues when allowing delegations, as the cost of voter-approved projects may go over the budget limit; we offer ways to overcome such inconsistencies by studying the computational complexity of a related combinatorial problem in which the task is to update as few delegations as possible to arrive—after following all project delegations—to a consistent profile.
An extended abstract of this work appeared in AAMAS 2021 [21].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
There ain’t no such thing as a free lunch.
References
Aziz, H., Lee, B.E., Talmon, N.: Proportionally representative participatory budgeting: axioms and algorithms. In: Proceedings of AAMAS 2018, pp. 23–31 (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
Behrens, J.: The origins of liquid democracy. Liquid Democracy J. 5(2), 7–17 (2017)
Benadè, G., Nath, S., Procaccia, A.D., Shah, N.: Preference elicitation for participatory budgeting. Manag. Sci. 67(5), 2813–2827 (2021)
Bloembergen, D., Grossi, D., Lackner, M.: On rational delegations in liquid democracy. In: Proceedings of AAAI 2019, pp. 1796–1803 (2019)
Blum, C., Zuber, C.I.: Liquid democracy: potentials, problems, and perspectives. J. Polit. Philos. 24(2), 162–182 (2016)
Bredereck, R., Faliszewski, P., Niedermeier, R., Skowron, P., Talmon, N.: Mixed integer programming with convex/concave constraints: fixed-parameter tractability and applications to multicovering and voting. Theor. Comput. Sci. 814, 86–105 (2020)
Brill, M., Talmon, N.: Pairwise liquid democracy. In: Proceedings of IJCAI 2018, pp. 137–143 (2018)
Cabannes, Y.: Participatory budgeting: a significant contribution to participatory democracy. Environ. Urban. 16(1), 27–46 (2004)
Christoff, Z., Grossi, D.: Binary voting with delegable proxy: an analysis of liquid democracy. In: Proceedings of TARK 2017. EPTCS, vol. 251, pp. 134–150 (2017)
Colley, R., Grandi, U., Novaro, A.: Smart voting. In: Proceedings of IJCAI 2020, pp. 1734–1740 (2020)
Cygan, M., et al.: Parameterized Algorithms. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21275-3
Downey, R.G., Fellows, M.R.: Fixed-parameter tractability and completeness I: basic results. SIAM J. Comput. 24(4), 873–921 (1995)
Freeman, R., Pennock, D.M., Peters, D., Vaughan, J.W.: Truthful aggregation of budget proposals. J. Econ. Theory 193, 105234 (2021)
Gandhi, R., Khuller, S., Parthasarathy, S., Srinivasan, A.: Dependent rounding and its applications to approximation algorithms. J. ACM 53(3), 324–360 (2006)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, New York (1979)
Goel, A., Krishnaswamy, A.K., Sakshuwong, S., Aitamurto, T.: Knapsack voting for participatory budgeting. ACM Trans. Econ. Comput. 7(2), 8:1–8:27 (2019)
Gölz, P., Kahng, A., Mackenzie, S., Procaccia, A.D.: The fluid mechanics of liquid democracy. ACM Trans. Econ. Comput. 9(4), 23:1–23:39 (2021)
Green-Armytage, J.: Direct voting and proxy voting. Const. Polit. Econ. 26(2), 190–220 (2015)
Impagliazzo, R., Paturi, R.: On the complexity of k-SAT. J. Comput. Syst. Sci. 62(2), 367–375 (2001)
Jain, P., Sornat, K., Talmon, N.: Preserving consistency for liquid knapsack voting: extended abstract. In: Proceedings of AAMAS 2021, pp. 1542–1544 (2021)
Lenstra, H.W.: Integer programming with a fixed number of variables. Math. Oper. Res. 8(4), 538–548 (1983)
Leskovec, J., Krevl, A.: SNAP Datasets: Stanford Large Network Dataset Collection (2014). http://snap.stanford.edu/data
Socała, A.: Lower bounds under strong complexity assumptions. Ph.D. thesis, University of Warsaw (2017)
Srinivasan, A.: Distributions on level-sets with applications to approximation algorithms. In: Proceedings of FOCS 2001, pp. 588–597 (2001)
Talmon, N., Faliszewski, P.: A framework for approval-based budgeting methods. In: Proceedings of AAAI 2019, pp. 2181–2188 (2019)
Tovey, C.A.: A simplified NP-complete satisfiability problem. Discret. Appl. Math. 8(1), 85–89 (1984)
Acknowledgements
We would like to thank the anonymous reviewers for their helpful comments.
Krzysztof Sornat was partially supported by the SNSF Grant 200021_200731/1 and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 101002854). Nimrod Talmon was supported by the Israel Science Foundation (ISF; Grant No. 630/19).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Jain, P., Sornat, K., Talmon, N. (2022). Preserving Consistency for Liquid Knapsack Voting. 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_13
Download citation
DOI: https://doi.org/10.1007/978-3-031-20614-6_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-20613-9
Online ISBN: 978-3-031-20614-6
eBook Packages: Computer ScienceComputer Science (R0)