Semi-parliamentary system

In a prime-ministerial system, as in standard parliamentary systems, the prime minister can still be dismissed by a vote of no confidence, this however effectively causes a snap election for both the prime minister and the legislature (a rule commonly expressed by the brocard aut simul stabunt aut simul cadent, Latin for "they will either stand together, or fall together").

Parliamentary systems originated in constitutional monarchies, in which the government was dually accountable to the parliament and the king: the plurality of opinions of elected assemblies was then balanced by the direction of the monarch.

[dubious – discuss] The attitude of parliaments towards governments is essentially oppositive, as elected assemblies are often incapable of taking energetic decisions whose advantages will only be perceived in the future, but whose disadvantages are immediately experienced by the electors.

[dubious – discuss] Under Charles de Gaulle, France adopted a different rationalization of parliamentary government called semi-presidential system.

During the thirteenth Knesset (1992–1996), Israel decided to hold a separate ballot for Prime Minister modeled after American presidential elections.

Democratic Design and the Separation of Powers", Ganghof gives this abstract definition of semi-parliamentarism: Under semi-parliamentary government, no part of the executive is elected directly.

The prime minister and cabinet are selected by an assembly with two parts, only one of which can dismiss the cabinet in a no-confidence vote even though the other has equal or greater democratic legitimacy and robust veto power over ordinary legislation.This form of Semi-Parliamentary government has also been further explored by Tarunabh Khaitan, who coined the phrase "Moderated Parliamentarism" to describe a form of Semi-parliamentarism with several distinctive features: mixed bicameralism, moderated (but distinct) electoral systems for each chamber, weighted multipartisanship, asynchronous electoral schedules, and deadlock resolution through conference committees.

World's states coloured by systems of government :
Parliamentary systems : Head of government is elected or nominated by and accountable to the legislature
Constitutional monarchy with a ceremonial monarch
Parliamentary republic with a ceremonial president

Presidential system : Head of government (president) is popularly elected and independent of the legislature
Presidential republic

Hybrid systems:
Semi-presidential republic : Executive president is independent of the legislature; head of government is appointed by the president and is accountable to the legislature
Assembly-independent republic : Head of government (president or directory) is elected by the legislature, but is not accountable to it

Other systems:
Theocratic republic: Supreme Leader holds significant executive and legislative power
Semi-constitutional monarchy : Monarch holds significant executive or legislative power
Absolute monarchy : Monarch has unlimited power
One-party state : Power is constitutionally linked to a single political party
Military junta : Committee of military leaders controls the government; constitutional provisions are suspended
Provisional government : No constitutionally defined basis to current regime
Dependent territories or places without governments

Note: this chart represents the de jure systems of government, not the de facto degree of democracy.
The Semi-Parliamentary System as explained by Steffen Ganghof