why can't use ternary operator with different types when boost variable can hold multiple types?

I have something like below, but unable to compile it. I don’t get it why I can’t have different type when my variable can hold different types?

My code:

#include <boost/variant.hpp>
#include <iostream>

typedef boost::variant<int, float, double, std::string> MultiType;

int main() {
    int a = 1;
    std::string b = "b";
    bool c = true;
    MultiType d = c ? a : b;
    return 0;
}

The error:

Error C2446 ‘:’: no conversion from ‘std::string’ to ‘int’

>Solution :

The expression c ? a : b has to have a type. There is no common type between std::string and int, so that expression is invalid.

There is a common type between std::string and MultiType, and between int and MultiType, so c ? MultiType{ a } : b is a valid expression, as is c ? a : MultiType{ b }