Each candidate must choose a Running Mate to be Vice-President.
Let's say Bruce Wins.
His VP would be...Alfred...who else? He's the behind the scenes man...who keep up Wayne Manor and the Bat Cave. He's loyal and trustworthy....very intelligent. He'd probably end up actually running the country.
Sec. of Defense....Deathstroke...hell, yeah
Sec. of State....Clark Kent...he's honorable...and a diplomat
Sec. of Treasury...Lex Luthor...he's a wealthy man...he has a thorough knowledge of economics...and Bruce can keep a good eye on him in this position.
Sec. of Homeland Security...Joker. Hell, if some terrorrists try to invade...let Joker run wild with his laughing gas...or whatever the hell else he has. And Batman can keep a good eye on him.