polymorphic sorting functors

#include <iostream>
#include <vector>

using namespace std;

class cmp_base : public std::binary_function<int, int, bool> {
   public:
   virtual bool operator()(int i, int j) { return i>j; }
};
class cmp_inc : public cmp_base {
   public:
   virtual bool operator()(int i, int j) { return i<j; }
};
void sort_it(vector<int> *v, cmp_base *cmp) {
   sort(v->begin(), v->end(), *cmp);
}
int main(void) {
   vector<int> v;
   v.push_back(10);v.push_back(1);v.push_back(20);
   cmp_inc cmp;
   sort_it(&v, &cmp);
   for (unsigned int i=0; i<v.size(); ++i) { cout << v.at(i) << endl; }
   return 0;
}

It should be clear what I am trying to implement here: function sort_it shall
sort the given vector according to the comparison functor passed in the
second argument. The base class 'cmp_base' would usually be implemented
purely virtual, but is here given with an implementation for sorting the
vector in decreasing order, for demonstration purposes.

The problem is that although I create an object of type 'cmp_inc', the vector
is sorted in decreasing order. If 'cmp_base' is implemented as an ABC, the
program won't even compile.

As far as I understood, I am following a standard approach here: having a
base class and functions taking pointers to the base class, but in fact
handing pointers to objects of derived classes to these functions. However,
the sort function from the STL expects an object, not a pointer, and so I
pass *cmp to it. This seems to be the cause of all the trouble.

Is there still a way to do this without using templates?