More Yes-No Voting

In this chapter, as in Chapter 3, our primary interest is in yes-no voting systems that are not weighted. We begin by returning to the theorem in Chapter 3 that characterized the weighted voting systems as precisely those that are trade robust (meaning that an arbitrary trade among several winning coalitions can never simultaneously render all of them losing). A natural question suggested by this result is whether trade robustness really needs to be stated in terms of “several winning coalitions.” That is, perhaps a yes-no voting system is weighted if and only if a (not necessarily one-for-one) trade between two winning coalitions can never simultaneously render both losing. Recall that in showing that the procedure to amend the Canadian constitution is not trade robust we needed only two winning coalitions.