8. The Bennet family consists of both parents, Tom and Jane, and the three children Rachel,...

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8. The Bennet family consists of both parents, Tom and Jane, and the three children Rachel, Melissa, and Rob. When making major decisions like whether to go to Cape Cod again this year for vacation or try something new, they use the following voting system: To pass, any decision must have the support of at least one parent and two children. (a) List all winning coalitions. (b) Is this voting system swap robust? Either explain why it is in two or three sentences, or produce two winning coalitions and a swap that illustrate why it is not. 8. The Bennet family consists of both parents, Tom and Jane, and the three children Rachel, Melissa, and Rob. When making major decisions like whether to go to Cape Cod again this year for vacation or try something new, they use the following voting system: To pass, any decision must have the support of at least one parent and two children. (a) List all winning coalitions. (b) Is this voting system swap robust? Either explain why it is in two or three sentences, or produce two winning coalitions and a swap that illustrate why it is not.