The word elite is used in two ways.
It is used to mean "snob", and it is used to mean "more capable person".
By definition, all societies are ruled by their elites, because the people in charge always have more power than those who do not.
For years, England was ruled by a noble class that simply ruled by virtue of being members of the nobility.
Many of these individuals (George III, notably) were not really up to the chore of running anything. George III was barking mad for a period. Some attribute this to his eating odd pewter plates with a high lead content. Heavy pewter was supposed to be superior.
Eventually, some of the nobility actually took advantage of their superior educations and became industrialists. More often, the smarter of their middle class classmates were hired to run his lordship's businesses.
On the US, especially in New England where there was no plantation aristocracy, the ideal was that the society be ruled by a meritocracy: a rule of the most capable.
Plato was probably the first major writer to come up with rule by a more capable elite in his work The Republic. The Republic was a utopian state on some remote island somewhere undisturbed by the rest of the world. It was ruled by Philosopher Kings, an elite who were identified as children as being the best and the brightest and given the best education the Republic had to offer.
The Republicans use the word "elite" to mean "snobs": people who have a better than average grasp on education, sociology and politics than the businessmen who tend to be self-taught and somewhat deficient in their education. They might not know as much as the OSHA inspector, but they refuse to admit this because they have more money than he or she does. They will bow down to the demands of an insurance company inspector, because the insurance company has more money than they do.
In an ideal society, people with the best qualifications should be identifiable and identified by the voters, who would freely elect them based on their knowledge of how the government works, ignoring irrelevant details, which might include their ability to kill a moose or survive in a Vietnamese prison camp, since these are activities that never are likely to be useful when leading a country. Certainly Joe Biden knows acres more about foreign policy that McCain or Palin put together. Other differences could be based on ideology, I suppose, since there is a basic difference between the world view of traditional Christians, who believe that Man is born corrupt from the stench of the diaper to the reek of the shroud and must be controlled, and the Liberal view that people can be rational beings who can be persuaded to not be corrupt. In any event, the best qualified people ideally should be the leaders. It is rather imperative that the leader of any society have some idea of the direction in which he wishes to lead. This was clearly lacking in Juniorbush's prosecution of the Iraq War, since he, Cheney, Rumsfeld and a gaggle of Neocons had no clue of what to do once they had toppled Saddam. Colin Powel could have told them, but they had decided to ignore him despite his deep understanding, and he was disposed to obey them because he was first a good soldier.