Worst-case Bounds on Power vs. Proportion in Weighted Voting Games with Application to False-Name Manipulation

Yotam Gafni, Ron Lavi, Moshe Tennenholtz

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Weighted voting games apply to a wide variety of multi-agent settings. They enable the formalization of power indices which quantify the coalitional power of players. We take a novel approach to the study of the power of big vs. small players in these games. We model small (big) players as having single (multiple) votes. The aggregate relative power of big players is measured w.r.t. their votes proportion. For this ratio, we show small constant worst-case bounds for the Shapley-Shubik and the Deegan-Packel indices. In sharp contrast, this ratio is unbounded for the Banzhaf index. As an application, we define a false-name strategic normal form game where each big player may split its votes between false identities, and study its various properties. Together, our results provide foundations for the implications of players’ size, modeled as their ability to split, on their relative power.

Original languageEnglish
Pages (from-to)99-135
Number of pages37
JournalJournal of Artificial Intelligence Research
Publication statusPublished - 23 Sept 2021

Bibliographical note

Funding Information:
Yotam Gafni and Moshe Tennenholtz were supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant No. 740435). Ron Lavi was partially supported by the ISF-NSFC joint research program (grant No. 2560/17).

ASJC Scopus subject areas

  • Artificial Intelligence

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