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.

翻译：本文系统探索了构建加权单调投票系统（包括标量加权与向量加权情形）的开关代数理论，重点研究了投票权力核心指标——班扎夫投票指数的计算方法。该计算涉及两个关键操作：(a) 布尔差分（布尔微分）或布尔商构造（布尔限制），以及(b) 开关函数权重（真值向量或极小项数量）的计算。我们针对四类投票系统提出了新颖的基于布尔代数的对称性感知性班扎夫指数计算技术。文章最后勾勒出建立完备的加权单调投票系统开关代数理论所需进一步推进的步骤。全文保持教程式叙述风格，给出多组一致结果的求解方案，并在博弈论投票理论、开关代数与系统可靠性分析之间建立了联系。