  Quantum Hall states can be characterized by their chiral edge modes. Upon
softening the edge potential, the edge has long been known to undergo
spontaneous reconstruction driven by charging effects. In this paper we
demonstrate a qualitatively distinct phenomenon driven by exchange effects, in
which the ordering of the edge modes at $\nu=3$ switches abruptly as the edge
potential is made softer, while the ordering in the bulk remains intact. We
demonstrate that this phenomenon is robust, and has many verifiable
experimental signatures in transport.
