Weighted and roughly weighted simple games

In this paper we give necessary and sufficient conditions for a simple game to have rough weights. We define two functions f(n) and g(n) that measure the deviation of a simple game from a weighted majority game and roughly weighted majority game, respectively. We formulate known results in terms of lower and upper bounds for these functions and improve those bounds. We also investigate rough weightedness of simple games with a small number of players. (C) 2010 Elsevier B.V. All rights reserved.