Guaranteed majority criterion

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The guaranteed majority criterion requires that the winning candidate always get an absolute majority of valid votes in the last round of voting or counting. It is satisfied by runoff voting, MCA-AR, and, if full rankings are required, IRV. However, if there is not a pairwise champion (aka CW), there could always be some candidate who would have gotten a majority over the winner in a one-on-one race. Since, unlike most criteria, this criterion can depend on both counting process and result, there could be two systems with identical results, with only one of them passing the guaranteed majority criterion.