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Jun 12, 2011 at 16:24 comment added Richard Rast The third paragraph of this answer still answers your question, since one possible utility ordering would be the lexicographic one, and even a quite small subspace of the set of tuples can't be embedded into $\mathbb{R}$. It is possible that <i>some</i> orderings of the tuples do embed into $\mathbb{R}$, but this is in some sense the most natural, and can't work.
Dec 10, 2009 at 23:45 comment added Casebash I've clarified the question
Dec 7, 2009 at 5:49 history edited David Eppstein CC BY-SA 2.5
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Dec 7, 2009 at 5:40 history answered David Eppstein CC BY-SA 2.5