What type of government requires the executive branch to maintain the support of a majority in the legislative branch to govern?

The correct answer is responsible government, which is characterized by the necessity for the executive branch to maintain the confidence and support of the legislative branch, typically a majority. This system is fundamental in parliamentary democracies, where the head of government, such as a prime minister, is usually a member of the legislature and must have the backing of the majority of lawmakers to pass legislation and remain in power. If the executive loses this support, it may lead to a vote of no confidence, potentially resulting in their resignation or a call for new elections.

In contrast, absolute monarchy is a form of government where the monarch has complete control and is not required to align with a legislative body, thus lacking the checks and balances found in a responsible government. A dictatorship similarly centralizes power in the hands of a single leader or a small group, circumventing the need for legislative support. Oligarchy refers to a government controlled by a small group of people, which does not inherently require majority support from a larger legislative body for the executive to govern effectively. This makes responsible government unique in its structure and accountability to the legislature.