Celestia - Ruler By Right And Might

In my headcanon, Celestia earns the leadership of the three tribes of Equestria by the sweat of her brow.

To retain the title of Princess Of Princesses, head of the Unicorn Tribe and leader of the aristocratic council, she enters their competition held every seven years. She gets top scores in the Grace and Beauty portion. She demonstrates great skill, strength, and restraint in the Magic portion. And since she's the eldest of unicorns present, she gets a +1 to her score for perfect Ancestry.

Every six years, the earth ponies across Equestria hold an election. Celestia wins the Chancellorship by both popular and electoral vote every time, due to her fairness and civility, the history of her judgments, her upholding of the common law system, and the fairness of her police.

The pegasi are a proud and noble warrior race. Their military government is second to none for fighting readiness, and a squad of the Wonderbolts Special Forces Unit can (usually) take down a lone full-grown dragon. In order to keep their ranks fresh, any officer can be challenged by her immediate subordinate to determine rank; the winner gets the higher rank. (There is a mandatory waiting period of one month between re-challenges.) Every two years, the top four tiers hold a fighting tournament where all ranks are up for grabs. The tournament is six-limbed grappling, no weapons allowed. Broken bones and displaced joints are often the result of their sparring. Celestia removes her crown, breastplate, and shoes, and de-energizes her mane and tail. She binds her hair in the traditional fashion, as do all the competitors, so as not to give purchase to those who would pull on it. Then she fights. Her opponents are not gentle, but they never come away broken. She has not lost the title of Supreme Commander since the first time she earned it.