I very much liked the analogy to Conservation of Expected Evidence---it strikes me as potentially deep; we want a system where EU and VoI are balanced such that it will never 'try' to end up with particular values, just as a Bayesian will never try to find evidence pointing in a particular direction.

I'm not sure who originally coined the phrase "Cake or Death problem" but I have a suspicion that it was me, and if so, I strongly suspect that I said it at a workshop and that I did it just to give the problem a 5-second handle that would work for a workshop. It's possible we should rename it before anyone publishes a paper.