Abstract
AbstractInspired by the study of control scenarios in elections and complementing manipulation and bribery settings in cooperative games with transferable utility, we introduce the notion of structural control in weighted voting games. We model two types of influence, adding players to and deleting players from a game, with goals such as increasing a given player’s Shapley–Shubik or probabilistic Penrose–Banzhaf index in relation to the original game. We study the computational complexity of the problems of whether such structural changes can achieve the desired effect.
Highlights
A major task in computational social choice [42, 12, 13] is the complexity analysis of the question of whether a certain form of influence is possible in an election under some voting rule
Some simple games G = (N, v) can be compactly represented as weighted voting games (w1, . . . , wn; q), where wi, 1 ≤ i ≤ n, is player i’s weight and q is a quota, and a coalition C ⊆ N wins if i∈C wi ≥ q and otherwise it loses. Note that this representation is not fully expressive, i.e., there are simple games that cannot be represented by weighted voting games
We show that ξ = 0 if and only if there exists a player whose removal from the game causes player 1’s Penrose–Banzhaf power to decrease
Summary
A major task in computational social choice [42, 12, 13] is the complexity analysis of the question of whether a certain form of influence is possible in an election under some voting rule (see, e.g., [42, 13]). On the other hand, an external agent tries to pay voters for them to change their votes such that a certain candidate becomes a winner, and the question is whether the briber can be successful within a given budget. This idea has been introduced and analyzed by Faliszewski et al [24, 25].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
