# Computation and Bribery of Voting Power in Delegative Simple Games

arXiv: https://arxiv.org/abs/2104.03692 · HTML: https://mlsanity.com/paper/2104.03692/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 59 references that are in the map.
- First posted on arXiv 8 Apr 2021.

## Builds on (most cited first, 12 of 12)

- [The Fluid Mechanics of Liquid Democracy](https://mlsanity.com/paper/1808.01906/) (2018)
- [On Rational Delegations in Liquid Democracy](https://mlsanity.com/paper/1802.08020/) (2018)
- [Binary Voting with Delegable Proxy: An Analysis of Liquid Democracy](https://mlsanity.com/paper/1707.08741/) (2017)
- [Power in Liquid Democracy](https://mlsanity.com/paper/2010.07070/) (2020)
- [Incentivising Participation in Liquid Democracy with Breadth-First Delegation](https://mlsanity.com/paper/1811.03710/) (2018)
- [Voting Behaviour and Power in Online Democracy: A Study of LiquidFeedback in Germany's Pirate Party](https://mlsanity.com/paper/1503.07723/) (2015)
- [On Parameterized Complexity of Liquid Democracy](https://mlsanity.com/paper/2011.14192/) (2020)
- [Popular Branchings and Their Dual Certificates](https://mlsanity.com/paper/1912.01854/) (2019)
- [Improved Approximation Algorithms for (Budgeted) Node-weighted Steiner Problems](https://mlsanity.com/paper/1304.7530/) (2013)
- [False-Name Manipulations in Weighted Voting Games](https://mlsanity.com/paper/1401.3869/) (2014)
- [Quasi-Polynomial Algorithms for Submodular Tree Orienteering and Other Directed Network Design Problems](https://mlsanity.com/paper/1812.01768/) (2018)
- [A Liquid Perspective on Democratic Choice](https://mlsanity.com/paper/2003.12393/) (2020)

## Abstract (arXiv)

Following Zhang and Grossi~(AAAI 2021), we study in more depth a variant of weighted voting games in which agents' weights are induced by a transitive support structure. This class of simple games is notably well suited to study the relative importance of agents in the liquid democracy framework. We first propose a pseudo-polynomial time algorithm to compute the Banzhaf and Shapley-Shubik indices for this class of game. Then, we study a bribery problem, in which one tries to maximize/minimize the voting power/weight of a given agent by changing the support structure under a budget constraint. We show that these problems are computationally hard and provide several parameterized complexity results.