Guaranteed majority criterion
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.
Likewise, two systems (such as IRV vs Coombs) could produce completely different results, while still both passing this criterion, since the final round features a majority winner between two candidates, but they could have eliminated a different set of candidates to get to that final round.