Using relational operators on strings in C/C++ will simply compare the memory addresses of the strings. Obviously "11" and "8" are occupying 2 different areas of memory, so it could be false, unless the address where "11" is stored happens to be stored in an address greater than "8", but it's random.
Keep in mind that you can use string::compare, however, it's comparing the ASCII code's of the strings. Since "1" (ASCII Code 49) is less than "8" (ASCII Code 56), it will still be false. You need to use stoi to convert the string to an integer, then compare the integers.
const char*which is simply comparing pointer addresses, which is useless for what you're probably looking for (lexicographical sorting or maybe numerical sorting?)"11" > "8"is different fromstring("11") > string("8")