Representatives are appointed by the Emperor by decree but only if their is a vacant seat in the Assembly either because a Representative has passed away or retired. However someone can become a Representative by challenging a sitting Representative which needs the challenger to put forward a petition as well as one billion credits, either their own money or money collected from Patrons who donate for the petition are required. When the petition is received along with the credits then it goes to a vote that lasts for one year which allows the two candidates to campaign and gather support before the vote takes place. If the challenger loses their bid to become the Representative then they or their donators are given back their credits and the sitting Representative can not be challenged again by any one for two years. This is to make sure that the Representative is more focused on serving the empire rather then constantly campaigning to try and stay in office. In the event a Representative loses the challenge for their position then they are unable to petition for two years to try and get back into the assembly.
While the emperor has absolute authority over the empire the Imperial Assembly is responsible for the day to day functions of the empire and making sure that the most important issues are brought to the emperor to prevent more serious issues from having time taken away. The emperor is also the only individual in the empire to declare war and can do so without the approval of the assembly. In the event an issue comes up, before it gets sent to the emperor goes through a vote in the assembly however the vote is not a decision but more of an opinion on the possible decisions that the emperor can consider and get a feel for where the assembly stands.