The point is that "approval" voting and "score" (aka "range", aka "rating") voting are not fundamentally different systems. Approval voting is just score voting

The point is that "approval" voting and "score" (aka "range", aka "rating") voting are not fundamentally different systems. Approval voting is just score voting where the voter is restricted to giving each candidate a score of either 0 or 1. Similarly, "relaxed rank" voting is also just a restricted version of score voting. You might argue that a paper version of the "relaxed rank" voting ballot wouldn't be as clear or intuitive to the average voter as an approval or score ballot would be. And I wouldn't necessarily dispute that. What I'm saying is that instead of forcing every voter to learn and embrace a new ballot, you can let them vote as they always have and, optionally, allow them to "refine" or "supplement" their ballot by additionally filling out an approval ballot along with their traditional one. (If the approval ballot contradicts the original one it is discarded/ignored.) If the voter has chosen to fill out an approval ballot, they can subsequently further refine their ballot by filling out a score ballot. I'm just pointing this out because it may be an option that is more acceptable to more people. In fact, you could add these optional "refining" ballots to existing elections with the understanding that they will have no effect on the election, but allow people to see how the election would have turned out had the "refining" ballots been counted. (Like, maybe John Kasich would have been president or something.) If you go to the link I posted, you can login anonymously and try out these "progressive ballots" for yourself. If you register (no personal info required or anything), you can create your own polls if you want to experiment further. (Note that this is not a real site or anything. Don't rely on it, and don't use it for anything serious. Not yet anyway.)