With all due respect Mr. President, the equivalent of our little problems in the US would be if Al Gore boarded a plane for Europe on election night after Bush was declared the winner in Florida and then his supporters destroyed ballot boxes in response. A number of Senators would have to join him in exile also. The US also has never had state secede because of voting irregularities.
You don't think there is going to be complaints of "influence peddeling" of Senators when they elect a Prime Minister?
Also, we must remember that this is not treated as a "game" by many. Seeing how this is a baord full of competitive teenagers we will see complaints and foul play in whatever we do.
What we should do is abolisht he Senate and the government baord and simply have a "President" with no power who runs for reelection every four months just for the fun of it.
But then again I don't concern myself with such matters of reform since this is but a game, like Clue.