We consider  false-name manipulation  in weighted voting games (WVGs). False-name manipulation involves an agent, termed a  manipulator , splitting its weight among several false identities in anticipation of power increase. False-name manipulation has been identified as a problem in WVGs. Indeed, in open anonymous environments, this manipulation can be easy and cheap to achieve. Previous works have considered false-name manipulation in WVGs using the well-known  Shapley-Shubik  and  Banzhaf  indices to compute agents' power. Upper and lower bounds on the extent of power that a manipulator may gain exist for the case when a manipulator splits into  k=2  false identities for both the Shapley-Shubik and Banzhaf indices. The bounds on the case when an agent splits into  k>2  false identities, until now, has remained open for the two indices. This paper answers this open problem by providing  four  non-trivial bounds on false-name manipulation in WVGs  when an agent splits into false identities for both the Shapley-Shubik and Banzhaf indices. One of the bounds is also shown to be asymptotically tight,  i.e., there exists at least a game in which an agent achieves the proposed bound by splitting into several false identites.
['Ramoni O. Lasisi', 'Vicki H. Allan']
New Bounds on False-Name Manipulations in Weighted Voting Games.