Solving Recurrences (Divide and Conquer Algorithms)

You have collected n butterfly specimens of different species. You want to know if there is a single species that accounts for more than half of the specimens. You dont know butterflies well enough to name the species of any single specimen, but you can carefully compare any two specimens and judge (correctly) if they are from the same species or not. Design an algorithm that returns true if there are more than n/2 specimens from one species, and returns false otherwise, using only O(n log n) pairwise comparisons.