I've attempted with the following code, to check if three radio buttons are checked, then check one if none in the set are:
if ($('input[title="a"]:selected').length == 0 
        && $('input[title="b"]:selected').length == 0
        && $('input[title="c"]:selected').length == 0
    ) {
        console.log("Nothing checked");
        $('input[title="b"]').prop("checked",true);
    }
}
it logs in the console every time (regardless of their states) and doesn't check the radio button.
 
     
    