Actually, you are not granting a person the right to do something that you don't have the right to do yourself.  

You are surrendering some of your rights to an abstract entity called democratic government , and you are only surrendering them under the condition that every other person living under this governments also surrenders their rights.

Even the leaders working for that government have surrendered their rights just like you. They are not privileged as individuals. They cannot exert power arbitrarily. They can only do so as a collective.