Final answer:
In a parliamentary system, the chief executive, often called the prime minister, is appointed by the legislature, which is usually composed of a majority party or coalition. The prime minister's authority is directly linked to their ability to maintain the confidence of the parliamentary majority.
Step-by-step explanation:
In most parliamentary systems, the executive is chosen by the legislature. Once public elections have taken place and the members of the legislature, typically referred to as parliament, are elected, the majority party or coalition therein has the power to appoint the chief executive. This position is commonly known as the prime minister, though in some countries, the title may vary, such as "chancellor" in Germany. The prime minister is both a member of the legislature and heads the executive, blurring the lines between these two branches of government. However, the structure ensures that the prime minister's ability to govern is directly dependent on retaining the confidence of the majority in the parliamentary system.
The strength of this system lies in the efficiency with which legislation can be passed, given that the executive authority requires legislative majority support. Conversely, its weakness is the potential instability that can emerge from party or coalition conflicts, which may lead to a vote of no confidence. Such occurrences may necessitate fresh elections and the possibility of a new legislature and consequently, a new executive. In some parliamentary systems, there is also a dual executive role, where a ceremonial president coexists with the prime minister, as seen in parliamentary republics with executive presidencies nominated or elected by the legislature.