It can't be mentioned enough that Approval Voting works with existing voting machines. One of the unfortunate difficulties with IRV is that it often requires a wholesale replacement of the voting infrastructure. The Center for Election Science is a big supporter of IRV as a better system than our current "Choose One" voting method, but we've found that Approval Voting is both more descriptive and less prone to strategy, as well as being significantly easier to implement and use.

NB: I'm the Chair of the Board for The Center for Election Science. AMA.