Divided government is not only a political phenomenon, but also becomes one of the most salient issues in the study of politics. When two elections are held at the same time, whether divided government appears depends on how many voters split their votes. If voters prefer divided government to unified government, then they split their votes in order to make divided government possible. If split-ticket voting is a phenomenon instead of a mean, then divided government is just the result of that voters prefer different parties in elections held at the same time.
If each political party has one position in the policy space when two elections are held at the same time, then sincere and strategic voting can only provide partial explanations for split-ticket voting. If political parties should have, and in fact they do, two positions in two elections, it is spatial theory that can explain the relationship between split-ticket voting and divided government. The reason for split-ticket voting is that voters do not prefer the same party in different elections. Therefore, divided government is just a phenomenon and has nothing to do with the idea of checks and balances.