Just for reference, Wei has pointed out that VNM doesn't work for indexical uncertainty because the axiom of independence is violated. I guess Savage's theory fails for the same reason. Maybe it's worthwhile to figure out what mathematical structures would appear if we dropped the axiom of independence, and if there's any other axiom that can pin down a unique such structure for LW-style problems. I'm trying to think in that direction now, but it's difficult.