For example, two people want to know who is the older, without disclosing their age. Is there a secure way to do this without a third party involved?
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Of course there are ways to do that.
See for example, Secure Integer Comparison with Applications in Economics which is implemented in VIFF.
Also, solutions to the millionaire's problem would probably do the trick too. There are lots of these. Just search around for solutions to that problem.