Ser Jorah frowned. "Princess, hear me. The Dothraki will not follow a suckling babe. Drogo's strength was what they bowed to, and only that." (65 Daenerys 8.49)
We get a few different political systems in A Game of Thrones, from the feudal monarchy of the Seven Kingdoms to the democratic discussion of the Mountain Clans. Here we get a very simple-seeming system: the Dothraki follow whoever is strongest. On one hand, this might seem silly; but on the other, is it any sillier than the system in the Prologue, where the strongest and most experienced person followed the youngest and, well, dumbest?