Who gets to decide if an idea is patentable?

Each country has a government office which evaluates whether your patent application should be granted. In the US, this is the USPTO (United States Patent and Trademark Office). The USPTO assigns a Patent Examiner to read and evaluate your patent application. You have an opportunity to argue or negotiate with the Examiner, you can appeal internally within the USPTO, and you can ultimately appeal to the Courts. The Courts can also declare an issued patent invalid if the invention is found to be obvious or otherwise unprotectable by law.