A simple solution would be to use std::count() on every element of the vector.
Note, the C++98 code below was not tested.
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std::size_t c=0; // Count of most common element
for (std::vector<int>::const_iterator ci = vi.begin(); ci != vi.end(); ++ci)
c = std::max(std::count(vi.begin(), vi.end(), *ci), c);