From most sources I am reading, people like to label Yuan rule as an essential military dictatorship under the Khan. Was there a chancellor, however? Was there some sort of assembly with legislative powers? Also, how did this compare with the Southern Song dynasty at the time? For these answers, presume the year is 1271, right after the creation of the Yuan Empire.
Bonus points to someone who also answers how the vassal Goryeo Kingdom government worked.
According to Marco Polo, Kublai Khan had 12 Barons below him in the political ladder. These Barons are directly below him and are appointed by him, the barons, in turn, appoint governers for the 34 provinces of the Empire of the Great Khan (Yuan Dynasty). The provinces had judges and clerks that resided there. The Barons lived in Beijing (Cambulac) with the Khan and other high ranking political officials. They had control of the armies as well.
Source: The Book of Ser Marco Polo: The Venetian Concerning Kingdoms and Marvels of the East