Interesing business model for this US cafe (via freakonomics). Essentially you pay what you like. The idea is that the honour system will cause most people to pay and some will overpay (for a warm glow) subsidising those who underpay.
I think it will succeed; not much different from other business models which undercharge for some goods (in this case the coffee) and then overcharge on others (the warm glow effects). I think it would also have to rely heavily on repeat business. Would you rip off your barista if you are going to him everyday?