The Prime Minister also goes to the Governor General to dissolve Parliament and call a general election. As such, Canada does not have fixed election dates like the United States. In a situation where a minority government exists (where the party in question has the most amount of seats but not a 50+1% majority), the Prime Minister must go to Governor General after losing a vote of no confidence in the hous, which is typically on a budget.
In the case, I imagine Mirai would have a system similar to Germany where the head of the state in the President because I assume there is no monarch as the case is for the UK (and some Commonwealth countries) and Japan. If that is the case this is how I could see the selection for the President of Mirai:
The president is elected by secret ballot, without debate, by the Federal Convention which mirrors the aggregated majority situation of the Bundestag and the parliaments of the 16 German federal states. The convention consists of all Bundestag members as well as an equal number of delegates chosen by the legislatures of the Länder (states). The delegates of each Land to the Federal Convention are elected by the members of the state legislature under a form of proportional representation. However it is not required that Land delegates themselves be members of a legislature; often prominent citizens are chosen.
In total, the Federal Convention numbers more than one thousand members. The German constitution, the Basic Law, requires that it be convened no later than thirty days before the expiration of the term of office of the president (which is five years). The body is convened and chaired by the President of the Bundestag.
Replace "Bundestag" with "Diet"and "federal states" with "prefectures" and you get the idea.
For Albert Pendragon to become Prime Minister he would probably have to resign as mayor of Cyan City and become the leadership candidate for the party opposing Mr. Sayokyoku's. It should not be too hard for with to win it with his track record of running the city. A quick by-election with ensure him a seat in the Diet of Mirai. For example, Jim Prentice, the premier of Alberta (equivalent to a state governor) became leader of province before winning a seat in the provincial legislature in a by-election. Then it would be all a matter of convincing the President to appoint him prime minister with the public's support, hence the campaign.
Just a thought because the Parliamentary system (Westminister or Presidential) is quite different than the federal republic that is the United States of America. I had this image in my mind where Jace commandeers a civics class to school the teacher who has a poor grasp of the Westminister system. >_>