Illinois State Representative Michael Madigan holds up a photo of Donald Trump after he was re-elected as Speaker of the House, Springfield, Ill., January 11, 2017. (Joshua Lott/Reuters) Democrats have always been a party of special-interest factions without a lot in common, who work together by trading favors that each wants. This morning’s Politico Illinois Playbook perfectly captures the strange-bedfellow dynamic. The first item is about Illinois’ notoriously corrupt House speaker, Michael Madigan, an old-timey machine pol who for decades has been…