Abstract
Liquid democracy has a natural graphical representation, the delegation graph. Consequently, the strategic aspects of liquid democracy can be studied as a game over delegation graphs, called the liquid democracy game. Our main result is that this game has bicriteria approximation guarantees, in terms of both rationality and social welfare. Specifically, we prove the price of stability for \(\epsilon \)-Nash equilibria is exactly \(\epsilon \) in the liquid democracy game.
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Notes
- 1.
Dodgson was a parson and a mathematician but, as the author of “Alice in Wonderland”, is more familiarly known by his nom de plume, Lewis Carroll.
- 2.
This option is particularly useful where potential delegates may have assorted competencies. For example, Alice may prefer to delegate to the Hatter on matters concerning tea-blending but to the Queen of Hearts on matters concerning horticulture.
- 3.
Indeed, if this is not the case then liquid democracy has no relevance.
- 4.
We remark that our results hold even when agents who abstain or have no guru obtain positive utility.
- 5.
This is not an unreasonable assumption for both pirates and many of the inhabitants of Wonderland!.
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Acknowledgements
We thank Bundit Laekhanukit for interesting discussions. We are also grateful to the reviewers for suggestions which greatly improved the paper.
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Noel, J.A., Suzuki, M., Vetta, A. (2021). Pirates in Wonderland: Liquid Democracy has Bicriteria Guarantees. In: Caragiannis, I., Hansen, K.A. (eds) Algorithmic Game Theory. SAGT 2021. Lecture Notes in Computer Science(), vol 12885. Springer, Cham. https://doi.org/10.1007/978-3-030-85947-3_26
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