Mathematical structures of simple voting games

• Category G defined: an object of G is lattice of all SVGs with given assembly.
• Objects of G characterized lattice-theoretically.
• All known operations on SVGs defined in terms of morphisms of G.
• All these operations shown to be special cases of SVG composition.

We address simple voting games (SVGs) as mathematical objects in their own right, and study structures made up of these objects, rather than focusing on SVGs primarily as co-operative games. To this end it is convenient to employ the conceptual framework and language of category theory. This enables us to uncover the underlying unity of the basic operations involving SVGs.