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Weighted voting games apply to a wide variety of multi-agent settings. Theyenable the formalization of power indices which quantify the coalitional powerof players. We take a novel approach to the study of the power of big vs.~smallplayers in these games. We model small (big) players as having single(multiple) votes. The aggregate relative power of big players is measuredw.r.t.~their votes proportion. For this ratio, we show small constantworst-case bounds for the Shapley-Shubik and the Deegan-Packel indices. Insharp contrast, this ratio is unbounded for the Banzhaf index. As anapplication, we define a false-name strategic normal form game where each bigplayer may split its votes between false identities, and study its variousproperties. Together, our results provide foundations for the implications ofplayers' size, modeled as their ability to split, on their relative power.

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