This is cool, and a really fun reminder that "majority" isn't required for quorum systems (it just happens to be the simplest way of thinking about it, and optimal in some senses). Moving from majorities to some other definition of quorum isn't super practical all that often, but is an interesting tool when you think about systems that don't have a uniform probability of failure or disconnection. That's not infrequent - large scale networks have very variable amounts of redundancy depending on geography and distance.

The idea of non-MDS erasure codes isn't quite the same, but they're related in the way that MDS codes are the easiest to think about, and non-MDS codes come with interesting complexities while opening up some cool new options for system design and recovery.

Using "majority" as the criterion has been around for a long time (e.g. Gifford in '79 https://pages.cs.wisc.edu/~remzi/Classes/739/Fall2015/Papers..., and Thomas also in '79 https://dl.acm.org/doi/10.1145/320071.320076). Also related is the idea of weighted voting (e.g. Peleg and Wool in '95 https://www.sciencedirect.com/science/article/pii/S089054018...).