A parameterization for a class of complete games with abstention

Abstract

Voting games with abstention are voting systems in which players can cast not only yes and no vote, but are allowed to abstain. This paper centers on the structure of a class of complete games with abstention. We obtain, a parameterization that can be useful for enumerating these games, up to isomorphism. Indeed, any I-complete game is determined by a vector of matrices with non-negative integers entries. It also allows us determining whether a complete game with abstention is a strongly weighted (3, 2) game or not, and for other purposes of interest in game theory.