How did politicians come to rule the roost? First of all, it's not a roost, but a roast, referring to either a council or ruling body of that name or to the role played by the Lord of the manor presiding over dinner — carving and dispensing the roast.
For the origin of those political chickens coming home to roost (c.1810), we return to their inauguration. It began with Ancient Roman soothsayers who studied the movement and formations of birds in order to forecast the success of an enterprise. Combining avis, "bird" and specere, "to see," they created auspicium, a "divination," to describe the process.
When we incorporated auspicium into English, however, we were only interested in signs portending well for us — making an auspicious occasion one where the birds only flew right, were "full of good omens," or "gave promise of success."
Priests called augurs interpreted these auspicious signs, eventually being identified with events heralding new beginnings, making both for our inauguration and our ability to augur or "foretell the future."
The inauguration of new public officials represents one of our more auspicious political events. We like to think that a new administration augurs well for us, but in our heart, we know better.