  This paper provides a serious attempt towards constructing a
switching-algebraic theory for weighted monotone voting systems, whether they
are scalar-weighted or vector-weighted. The paper concentrates on the
computation of a prominent index of voting powers, viz., the Banzhaf voting
index. This computation involves two distinct operations: (a) either Boolean
differencing (Boolean differentiation) or Boolean quotient construction
(Boolean restriction), and (b) computation of the weight (the number of true
vectors or minterms) of a switching function. We introduce novel Boolean-based
symmetry-aware techniques for computing the Banzhaf index by way of four voting
systems. The paper finally outlines further steps needed towards the
establishment of a full-fledged switching-algebraic theory of weighted monotone
voting systems. Througout the paper, a tutorial flavour is retained, multiple
solutions of consistent results are given, and a liasion is established among
game-theoretic voting theory, switching algebra, and sytem reliability
analysis.
