this has to do with your error reporting levels. your local machine probably has error_reporting = E_ALL and your host supresses certain errors (for security purposes).
the point is, you still have an error (even though you don't see it when you run your code on the live server). unchecked radio buttons do not return a value so if you are explicitly refering to an unset index in the $_POST array then PHP will spit out an "undefined index" error. you need to use [man]isset[/man] to validate.
as a general rule, you should always test your code on your local dev machine with error_reporting = E_ALL so you can see all of the errors that your code is throwing.