Haris Aziz, Mike Paterson, and Dennis Leech Efficient Algorithm for Designing Weighted Voting Games
Weighted voting games are mathematical models, used to analyse situations where voters with variable voting weight vote in favour of or against a decision. They have been applied in various political and economic organizations. Similar combinatorial models are also encountered in neuro-science and distributed systems.
The calculation of voting powers of players in a weighted voting game has been extensively researched in the last few years. However, the inverse problem of designing a weighted voting game with a desirable distribution of power has received less attention. We present an elegant algorithm which uses generating functions and interpolation to compute an integer weight vector for target Banzhaf power indices. This algorithm has better performance than any other known to us. It can also be used to design egalitarian two-tier weighted voting games and the representative weighted voting game for a multiple weighted voting game.