We explore the switching-algebraic computation of the Banzhaf indices for general and monotone or unrestricted systems. This computation is achieved via (a) two Boolean-quotient formulas that are valid when the voting system is not necessarily monotone (e.g., when coalition formation is restricted), (b) four Boolean differencing formulas and six Boolean-quotient formulas that are applicable when the decision switching function is a positively polarized unate one. We also provide switching-algebraic formulas for certain Banzhaf-related indices, including the power-to-initiate index (PII), and the power-to-prevent index (PPI), as well as satisfaction indices. Moreover, we briefly address other Banzhaf-related indices, including the Strict Power Index (SPI) and the Public Good Index (PGI). We illustrate the various indices formulas by way of four examples of voting systems, each considered first as an unrestricted monotone system and then subjected to a restriction on the formation of a coalition between two particular voters.

翻译：我们探讨了通用及单调或非限制系统中班扎夫指数的开关代数计算方法。该方法通过以下方式实现：(a) 两个适用于投票系统非单调（如存在联盟形成限制）情况的布尔商公式；(b) 四个适用于决策开关函数为正极性单凋函数时的布尔差分公式和六个布尔商公式。我们还提供了某些与班扎夫相关的指数的开关代数公式，包括发起权指数（PII）、阻止权指数（PPI）及满意度指数。此外，我们简要讨论了其他与班扎夫相关的指数，包括严格权力指数（SPI）和公共物品指数（PGI）。通过四个投票系统案例，我们分别将每个系统视为无限制单调系统，随后对其施加两个特定投票者之间联盟形成的限制，以此阐述各指数公式的应用。