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Poorest person?
I'm not clear. Why would somebody of low income agree to pay for an entire expensive meal, just to get out of a 1/N share of a lesser meal? I can't see that ever making sense. Or are they agreeing only to pay 2/(N-1) at the next meal? That would make sense for somebody who is just a little short one week.
We don't seem to have the problem with people being short of cash because the restaurants mostly will take more than one credit card in a pinch, and the latest innovation is that you ask somebody to cover you, and you paypal them the money when you get home. Or even from your cell phone. (Paypal's original business plan involved payments from PDAs in fact.)