Banzhaf Index and Boolean Difference

This paper discusses the relationship between the Banzhaf index which is known as an index to show a definite effect in the weighted-voting system in the field of gaming theory and the Boolean difference which is important in fault detection of logic circuits. Firstly the paper shows that the swing which is necessary to calculate the Banzhaf index can be obtained by the calculation of the Boolean difference. Secondly the paper considers the meanings of the swing derived from the double Boolean difference. Lastly the paper considers the meanings of the ternary swing that has been defined in the previous paper where an extended Banzhaf index was defined in the voting system allowing the notion, neutral. Then the paper defines a ternary Boolean difference based on these considerations.