shared_ptr and const

I understand the semantics of why this works the way it does. But I
wonder if there's a reason for the behaviore at the line marked
"QUESTION". I figured if there is an answer, someone here knows it.

Specifically, part 1 is obvious to most anyone. Part 2 is isomorphic
to part 1, yet behaves differently. If a shared_ptr is const, should
it really allow non-const dereferences?

Thanks,

Tim

#include <boost/shared_ptr.hpp>

int main(void)
{
        // part 1
        int *pi = new int(1);
        const int *cpi = new int(2);

        *pi = 11; // ok
        *cpi = 22; // compile error

        // part 2
        boost::shared_ptr<int> spi(new int(3));
        const boost::shared_ptr<int> cspi(new int(4));

        *spi = 33; // ok
        *cspi = 44; // QUESTION: should this be a compile
error?

        // part 3
        boost::shared_ptr<const int> spci(new int(5));
        const boost::shared_ptr<const int> cspci(new int(6));

        *spci = 44; // compile error
        *cspci = 55; // compile error

        return 0;
}