In the first season the politician was a progressive candidate for Mayor of Copenhagen, who was implicated in a murder. He was super-charismatic, and a bit sinister. In this season Thomas Buch is a centre-left politician in a coalition or a hung Parliament. He is suddenly promoted to Minister of Justice when the incumbent Minister attempts suicide in the wake of the murder which Sarah Lund is now investigating.
I am only guessing but I think Buch got the job because he is seen as useless and weak, and the big players want to engineer a cover-up of something the previous Minister did. He's a smashing character, because he does quite brave and reckless things, and then acts mortified when it all goes wrong. He's awkward, overweight, young, not very wily. He spends about 50% of each episode being out-manoeuvred and humiliated by horrid political sharks who despise him as a weakling. I assume he will be vindicated by events in the final two episodes this weekend, and the sharks get their well-deserved come-uppance. Hope so. *Rubs hands in anticipation*