[Anguirel]

Eomer is most certainly elected; if in a similar way to the Reges Teutonicorum or the Kings of Scotland, or Hungary, or Sweden (or, for that matter, the President of the United States); i. e., the electors will tend to continue to support one dynasty barring really serious disaster. It is repeatedly asserted that the Rohirrim "put their trust in the House of Eorl", and that is why Eowyn is required to rule over them in her uncle's absence.

In addition, as a proto-Anglo-Saxon society it is almost certain that Eomer required the confirmation of some kind of Witanegamot body of elders in order to rule legally.