The election of leaders is a function of government and not of the sovereignty.
Gist of Idea
The sovereignty does not appoint the leaders
Jean-Jacques Rousseau (The Social Contract (tr Cress) , IV.3)
The point is that the general will only establishes the form of government, and not its content. In Britain we accept leaders who are appointed by their own party, and not by the electorate.
Rousseau,Jean-Jacques: 'The Basic Political Writings', ed/tr. Cress,Donald A. [Hackett 1987], p.207