Simple proof of Ω(n lg n) worst-case bound for uniqueness/distinctness?
I am not sure if I understand the question correctly, but the proof by Dobkin and Lipton [DL79] that the uniqueness problem on n numbers requires Ω(n log n) comparisons in the linear decision tree model is much easier than the stronger result in the algebraic computation tree model by Ben-Or [Ben83] (not surprisingly).

References

[Ben83]  Michael Ben-Or.  Lower bounds for algebraic computation trees.  In Proceedings of the Fifteenth Annual ACM Symposium on Theory of Computing (STOC 1983), pp. 80–86, April 1983.  http://doi.acm.org/10.1145/800061.808735

[DL79] David P. Dobkin and Richard J. Lipton.  On the complexity of computations under varying sets of primitives.  Journal of Computer and System Sciences, 18(1):86–91, Feb. 1979.  http://dx.doi.org/10.1016/0022-0000(79)90054-0