  Simple games cover voting systems in which a single alternative, such as a
bill or an amendment, is pitted against the status quo. A simple game or a
yes-no voting system is a set of rules that specifies exactly which collections
of ``yea'' votes yield passage of the issue at hand. A collection of ``yea''
voters forms a winning coalition.
  We are interested on performing a complexity analysis of problems on such
games depending on the game representation. We consider four natural explicit
representations, winning, loosing, minimal winning, and maximal loosing. We
first analyze the computational complexity of obtaining a particular
representation of a simple game from a different one. We show that some cases
this transformation can be done in polynomial time while the others require
exponential time. The second question is classifying the complexity for testing
whether a game is simple or weighted. We show that for the four types of
representation both problem can be solved in polynomial time. Finally, we
provide results on the complexity of testing whether a simple game or a
weighted game is of a special type. In this way, we analyze strongness,
properness, decisiveness and homogeneity, which are desirable properties to be
fulfilled for a simple game.
