LitCharts assigns a color and icon to each theme in The Social Contract, which you can use to track the themes throughout the work.
Human Freedom and Society
Sovereignty, Citizenship, and Direct Democracy
Government and the Separation of Powers
National Longevity and Moral Virtue
Summary
Analysis
Government elections can happen either “by choice [through voting] or by lot [randomly],” but Rousseau emphasizes that, either way, elections are the government’s job (not the sovereign’s). In a perfect democracy, random elections would be fairer because serving as a magistrate is “a heavy responsibility” for which it would be unfair to single people out. In an aristocratic government, the governing elites would choose their successors, and voting is the obvious way to ensure they are of high quality. And since there is no “true democracy” whose citizens are all equals, democracies should also vote for some “places that call for special skills, such as military commands.” In monarchies, there are no elections, since the monarch controls the whole government.
While Rousseau believes that the people (that is, the sovereign) should make the laws and magistrates should be elected, he puzzlingly does not think the sovereign people should be the ones to elect those magistrates. But this is not as paradoxical as it seems: as he explained in Book 3, the sovereign has to temporarily turn itself into a democratic government in order to appoint the government that will actually come to rule. This is because the sovereign cannot take “particular acts,” including naming specific people to office. What Rousseau is really saying, then, is that elections by definition have to be conducted by an executive rather than a sovereign body (although both these bodies can be made of the same people). This means that his theory, as presented here, is fully compatible with the possibility of the people democratically voting for their own ministers. That said, he does specifically argue here that the aristocracy should choose its successors on the basis of merit, although he envisions this as a kind of committee vote rather than an appointment process.