Game-Based Schemes for Prime Minister Selection in Multi-Party Semi-Presidential Systems

1. Introduction

In [1], which was written by the present author, it was proposed a game-based scheme for approving prime ministers for a type of presidential systems. The original purpose of that scheme was to address gridlocks between the president and parliament, a challenge typically found in presidential systems with prime ministers. However, we now realize that, with appropriate modifications, this scheme may also be applied to semi-presidential systems. Furthermore, given the similarities in government structure between semi-presidential and parliamentary systems, this paper also examines parliamentary systems for the potential application of the game-based scheme.

To be sure, the game-based scheme is not so useful in semi-presidential or parliamentary systems that purely use the FPTP (First-Past-The-Post) electoral system, such as those found in the UK, Canada, India, and Pakistan, where typically only two dominant parties exist, and one party usually secures an outright parliamentary majority. However, in semi-presidential or parliamentary countries that primarily use the PR (proportional representation) electoral system, parliaments typically feature many small parties. In France, a distinctive two-round system is employed, fostering political diversity and allowing smaller parties a chance to advance to the second round, where they can shape the outcome through strategic alliances. When parliament is fragmented – characterized by no clear majority and a multitude of smaller parties – the resulting government is typically a coalition.

But forming a coalition government is often challenging, due to ideological differences, party fragmentation, and bargaining complexity [2]. When coalition talks fail, a minority government may form, or new elections will be called.

As pointed out in [3,4,5,6], minority governments often face greater difficulties in functioning effectively compared to majority governments, primarily because they struggle to pass key legislation needed to implement their agenda. However, a minority government can rely on the president’s support [7]. When the president holds significant real power and shares political alignment with the prime minister, the ruling camp can leverage this advantage to negotiate with opposition parties and secure the passage of their laws. This dynamic does not apply when the president’s role is purely ceremonial. Therefore, the existence of minority governments as a normal case depends on the president having real power [8]. In the game-based scheme, the president can nominate a candidate for prime minister with only minority support, and as discussed, this power is meaningful only when the president has real power.

It is now clear that for semi-presidential or parliamentary systems, a game-based scheme is useful, and useful only, for multi-party semi-presidential systems. Under such a scheme, even with a fragmented parliament, the president can still appoint a prime minister with possibly mere minority support, thus avoiding new elections and potential constitutional crises. In the following sections, we will explore how the game-based scheme proposed in [1] can be adapted to create a balanced and effective constitutional framework.

2. A Review of Existing Semi-Presidential or Parliamentary Systems

Our exploration aims to develop a package of constitutional reform proposals. To effectively achieve this, it is beneficial to base our discussion on a specific existing constitution, as is done in [1]. However, it seems to us that no particular existing constitution perfectly fits our purpose. Therefore, we instead try to draw inspirations from a range of living semi-presidential or parliamentary constitutions, capitalizing on their proven resilience and effectiveness over time. We will use the constitutions of various European countries, along with a few others, as foundational references. Specifically, they include: Albania, Andorra, Armenia, Austria, Belgium, Bulgaria, Croatia, Czech Republic, Estonia, Finland, France, Georgia, Germany, Greece, Hungary, Italy, Latvia, Lithuania, Malta, Moldova, Montenegro, Netherlands, Poland, Portugal, Romania, Russia, Serbia, Slovakia, Slovenia, Spain, Ukraine, as well as India, Japan, Kazakhstan, Madagascar, Malaysia, Pakistan, Peru, Singapore, and Sri Lanka. An investigation of the aspects covered in this section is also provided in [9].

In this paper, the term “parliament”, when referring to a specific country, denotes the entire legislative body in a unicameral system or the lower house in a bicameral system.

2.1. How the Prime Minister Is Selected

In nearly all the aforementioned countries, the prime minister is formally appointed by either the president or the monarch. However, the prime minister is typically elected by parliament, or who to be prime minister is jointly determined by the president and parliament. Therefore, this paper will use the neutral term “select”, which encompasses “elect”, “appoint”, and any other means. The following table summarizes how the prime minister is selected in the aforementioned countries when a vacancy occurs.

Class	Countries	Procedure
PAR1	Albania, Armenia, Bulgaria, Croatia, Czech Republic, Estonia, Georgia, Greece, Latvia, Moldova, Montenegro, Netherlands, Romania, Serbia, Slovakia, Ukraine, Pakistan	The prime minister is elected through a process that may involve multiple rounds of voting. In each round, the president/monarch, after consulting parliamentary factions, nominates a candidate, and if the candidate secures the confidence of more than half of the parliament members, they are elected as prime minister-designate; otherwise, an additional round is required. If a prime minister-designate is elected within a specified time frame, the president appoints them as prime minister. If no candidate succeeds within this period, parliament is dissolved, and new elections are called.
PAR2	Germany	The prime minister is elected through a process comprising two potential phases. In the first phase, which may involve multiple rounds of voting, the president, after consulting parliamentary factions, nominates a candidate in each round. If the candidate secures the confidence of more than half of the parliament members, they are elected as prime minister-designate; otherwise, a further round is held. If a prime minister-designate is elected within a specified time frame, the president appoints them as prime minister. If no candidate succeeds within this period, the process advances to a second phase. In this phase, parliament elects a candidate by relative majority (the most votes among candidates), and the president then decides either to appoint this candidate as prime minister or to dissolve parliament and call for new elections.
PAR3	Poland, Slovenia	The prime minister is elected through a process comprising three potential stages. The president nominates a candidate, who seeks an absolute majority confidence vote in parliament. If this fails, parliament appoints a candidate by absolute majority. If unsuccessful, the president nominates again, needing only a simple majority (more votes for than against, with at least half present) confidence vote. Success at any stage leads to formal appointment; failure after all three attempts triggers parliamentary dissolution and new elections.
PAR4	Hungary, Spain, Lithuania	The prime minister is elected through a process that may involve multiple rounds of voting. In each round, the president/monarch, after consulting parliamentary factions, nominates a candidate, and if the candidate secures a simple majority (more votes in favor than against), they are elected as prime minister-designate; otherwise, an additional round is required. If a prime minister-designate is elected within a specified time frame, the president/monarch appoints them as prime minister. If no candidate succeeds within this period, parliament is dissolved, and new elections are called.
PAR5	Andorra, Finland	The parliament elects a prime minister-designate with relative majority (the most votes among candidates). Subsequently, the president/monarch formally appoints the prime minister-designate as prime minister.
PAR6	Japan	The Prime Minister is elected by the National Diet, which consists of the House of Representatives and the House of Councillors. Each house conducts its own election, which may involve two rounds. In the first round, candidates are proposed by the political parties. If a candidate receives more than half of the total votes, they are elected. If no candidate achieves absolute majority, the two candidates with the highest votes proceed to the second round. In the second round, the candidate with the most votes wins. If both houses elect the same candidate, that individual becomes the Prime Minister-designate. However, if the two houses elect different candidates, a joint committee is formed to resolve the disagreement. If the committee fails to reach an agreement, the decision of the House of Representatives prevails. Finally, the Emperor formally appoints the Prime Minister-designate as Prime Minister.
DIR1	Austria, Belgium, France, Malta, India, Madagascar, Malaysia, Singapore, Sri Lanka	The president/monarch directly appoints a prime minister, normally the one considered to command parliamentary majority.
DIR2	Italy, Portugal, Peru	The president directly appoints a prime minister, but the prime minister needs to pass vote of confidence within a specified time after appointment to retain their position.
RU	Russia, Kazakhstan	Seemingly similar to PAR4. But the president in this case has greater discretion in nominating candidates for prime minister, and the constraints on this process are typically defined by the number of voting rounds rather than a specific time frame. The president’s discretion often lies in having a limited pool of acceptable candidates, chosen based on their political agenda, even against parliamentary majorities.

In classes PAR1–PAR6, the prime minister is elected by parliament with minimal presidential participation. The only essential distinction among these classes is the standard for either accepting a minority government or dissolving parliament. Countries in these classes are parliamentary, except for Lithuania, Poland, Romania, and Ukraine. Countries in the DIR1 and DIR2 classes can be either parliamentary or semi-presidential, depending on other factors. Countries in the RU class are semi-presidential.

2.2. How the Prime Minister Can Be Removed

The table below outlines the conditions on which a prime minister may be removed from office. In addition to these, the prime minister may also leave office due to voluntary resignation, death, or permanent incapacity. Removal through impeachment should be included in the table, but we choose not to include it, as it is a common procedure across all the countries studied and not central to the focus of this study.

Country	Removal by No-Confidence	Mandatory Resignation on New Parliament	Dismissal by President	Mandatory Resignation on New President
Albania	CVNC	No	No	No
Andorra	Yes	Yes	No	No
Armenia	Yes	Yes	No	Yes
Austria	Yes	No	No	No
Belgium	CVNC	No	No	No
Bulgaria	Yes	Yes	No	No
Croatia	Yes	No	No	No
Czech Republic	Yes	Yes	No	No
Estonia	Yes	Yes	No	No
Finland	Yes	No	No	No
Georgia	CVNC	Yes	No	No
Germany	CVNC	Yes	No	No
Greece	Yes	No	No	No
Hungary	CVNC	Yes	No	No
Italy	Yes	No	No	No
Latvia	Yes	No	No	No
Malta	Yes	Yes	No	No
Moldova	Yes	No	No	No
Montenegro	Yes	Yes	No	No
Netherlands	Yes	No	No	No
Serbia	Yes	Yes	No	No
Slovakia	Yes	Yes	No	No
Slovenia	CVNC	Yes	No	No
Spain	CVNC	Yes	No	No
India	Yes	No	No	No
Japan	Yes	Yes	No	No
Malaysia	Yes	No	No	No
Pakistan	Yes	No	No	No
Singapore	Yes	No	No	No
Poland	CVNC	Yes	No	No
Romania	Yes	Yes	No	No
Lithuania	Yes	Yes	DP_Lithuania	Yes
Portugal	Yes	Yes	DP_Portugal	No
Sri Lanka	Yes	No	No	No
France	Yes	No	No	No
Ukraine	Yes	Yes	No	No
Peru	Yes	No	Yes	No
Madagascar	NC_Madagascar	No	Yes	No
Kazakhstan	NC_Russia	Yes	Yes	No
Russia	NC_Russia	No	Yes	Yes

NE: Not explicitly mentioned in the constitution.

CVNC: Constructive vote of no-confidence. A constructive vote of no-confidence is a parliamentary procedure to possibly remove the prime minister. It requires a motion to remove the incumbent prime minister to name a successor candidate. For the motion to pass, the successor must secure the support of more than half of the parliament members. If successful, the current prime minister is required to resign immediately, and the nominated successor is appointed as the new prime minister. If the successor fails to gain a parliamentary majority, the motion is defeated, and the status quo remains unchanged.

DP_Lithuania: The president may dismiss, upon the assent of the Seimas, the Prime Minister.

DP_Portugal: The President of the Republic may only remove the Government when it becomes necessary to do so in order to ensure the normal functioning of the democratic institutions and after first consulting the Council of State.

NC_Madagascar: The motion of no-confidence is adopted if it is voted by two-thirds of the members of the National Assembly. If it is adopted, the prime minister must resign.

NC_Russia: If a motion of no-confidence is adopted, the president must either dismiss the government or dissolve parliament and call new elections.

2.3. How Parliament Can Be Dissolved

In parliamentary and semi-presidential systems, parliament can be dissolved under several scenarios, guided by constitutional rules and political dynamics. Systematic discussions on dissolution triggers can be found in [10,11,12]. Below are the key possibilities:

• Governmental Deadlock: When no stable government can be formed after elections or the existing one collapses without a viable replacement, dissolution resolves the crisis by calling for new elections.
• Loss of Confidence: Members of parliament may introduce a motion of no-confidence, and the government itself can bring a motion of confidence before parliament. If the government loses either a no-confidence vote or a confidence vote, and if the prime minister is confident in their party’s popularity, they may strategically request the dissolution of parliament and call for new elections in order to seek a fresh mandate from the people.
• Legislative Deadlock: If parliament cannot pass essential legislation, such as a budget or key reforms, dissolution may be triggered to break the stalemate and seek a fresh mandate.
• Discretionary Call: The prime minister or president may initiate a dissolution without a specific trigger, often for strategic reasons, such as capitalizing on favorable public opinion that could shift over time.

The following table summarizes the current practices of the reviewed countries in this regard. While the dissolution of parliament is subject to various constitutional limitations, such as timing, they are considered less significant details, and are therefore omitted from the table.

Country	Dissolution for Failure to Elect or Approve PM	Dissolution as PM’s Countermeasure Against No-Confidence	Dissolution as PM’s Countermeasure Against Rejection of Confidence or Bill	Other Reasons for Dissolution
Albania	Yes	No	Yes(Conf)	FEP
Andorra	NA	No	No	PM_Request
Armenia	Yes	No	No	OR_Inactive
Austria	NE	No	No	HS_Dissol+Self_Dissol
Belgium	Yes	No	No	OR_Belgium
Bulgaria	Yes	No	No
Croatia	Yes	No	No	Self_Dissol
Czech Republic	PD	No	PD(Conf+Bill)	Self_Dissol
Estonia	Yes	PD	PD(Conf+Bill)	HS_Dissol
Finland	NA	NE	NE	HS_Dissol
Georgia	Yes	No	RC_Georgia
Germany	PD	No	RC_Germany
Greece	Yes	No	No	PM_Request
Hungary	PD	No	PD(Budget)	Self_Dissol
Italy	NE	NE	NE	HS_Dissol
Latvia	NE	NE	NE	OR_Latvia
Malta	NE	NE	NE	PM_Request
Moldova	PD	No	No
Montenegro	Yes	No	No	HS_Dissol
Netherlands	NE	NE	NE	HS_Dissol
Serbia	Yes	No	No	PM_Request
Slovakia	PD	No	No
Slovenia	Yes	No	No
Spain	Yes	No	NE	PM_Request
India	NE	NE	NE	HS_Dissol
Japan	NA	Yes	Yes(Conf+Bill)	HS_Dissol
Malaysia	NE	NE	NE	HS_Dissol
Pakistan	NE	NE	NE	PM_Request
Singapore	NE	NE	NE	PM_Request
Poland	Yes	No	PD(Budget)	Self_Dissol
Romania	PD	No	PD(Conf)
Lithuania	PD	PD	NA	OR_Lithuania
Portugal	NE	NE	NE	HS_Dissol
Sri Lanka	NE	NE	NE	PM_Request
France	NE	NE	NE	HS_Dissol
Ukraine	PD	No	No	OR_Inactive
Peru	NE	NC_RC_Peru	NC_RC_Peru
Madagascar	NE	No	No	HS_Dissol
Kazakhstan	NE	NE	NE	HS_Dissol+Self_Dissol
Russia	FA_Russia	NC_Russia	RC_Russia

NA: Not applicable. In some countries, parliament cannot fail to elect a prime minister, so the reason for parliamentary dissolution from failure to elect a prime minister is not applicable to them. In Lithuania, the constitution does not have a provision about the issue of confidence raised by the prime minister.

NE: Dissolution for this particular case is not explicitly mentioned in the constitution, but other reasons can be used to achieve the same purpose.

FEP: Failure to elect a president.

PD: Presidential discretion. The president shall decide whether to dissolve parliament in this particular case.

PM_Request: The prime minister can request dissolution for political or strategic reasons—e.g., to seek a stronger mandate, consolidate power, or resolve a political crisis. This is subject to presidential approval and the restrictions noted (no war/emergency, timing limits).

Self_Dissol: The parliament can vote its own dissolution before its expiry.

HS_Dissol: The head of state (president or monarch) may from time to time dissolve parliament.

RC_Germany: If a motion of the Federal Chancellor for a vote of confidence is not supported by the majority of the Members of the Bundestag, the Federal President, upon the proposal of the Federal Chancellor, may dissolve the Bundestag within twenty-one days. The right of dissolution shall lapse as soon as the Bundestag elects another Federal Chancellor by the vote of a majority of its Members.

RC_Georgia: If parliament rejects confidence and fails to elect and give confidence to a new prime minister within 7 days after the rejection, then the president shall dissolve parliament.

OR_Inactive: The parliament may be dissolved for long time inactivity reasons.

OR_Belgium: the King may, in the event of the resignation of the Federal Government, dissolve the House of Representatives after having received its agreement expressed by the absolute majority of its members.

OR_Latvia: The President shall have the right to propose the dissolution of the Saeima. Following this proposal, a national referendum shall be held. If in the referendum more than half of the votes are cast in favour of dissolution, the Saeima shall be considered dissolved, new elections called, and such elections held no later than two months after the date of the dissolution of the Saeima. The President shall be entitled to nominate the Prime Minister. In the event of the Saeima being dissolved, the previous Cabinet shall continue to exercise its functions until a new Saeima has assembled and a new Cabinet has been appointed.

OR_Lithuania: The President can call early elections if the Seimas proposes it by a three-fifths majority, though this requires Presidential consent and is rare.

NC_RC_Peru: The President of the Republic is empowered to dissolve Congress if it has censured or denied confidence to two Councils of Ministers during his term.

FA_Russia: After the State Duma thrice rejects the candidatures for the Chairman of the Government of the Russian Federation submitted by the President of the Russian Federation, the President of the Russian Federation shall appoint the Chairman of the Government of the Russian Federation, dissolve the State Duma, and call new elections.

NC_Russia: Should the State Duma within three months repeatedly express no-confidence in the Government of the Russian Federation, the President of the Russian Federation shall announce the resignation of the Government or dissolve the State Duma and call new elections.

RC_Russia: The Chairman of the Government of the Russian Federation may raise before the State Duma the issue of confidence in the Government of the Russian Federation. If the State Duma refuses confidence, the President shall, within seven days, decide on the resignation of the Government of the Russian Federation or dissolve the State Duma and call new elections.

2.4. Presidential Powers

As previously mentioned, the powers held by the president can serve as leverage in negotiations with opposition parties to pass legislation crucial for advancing their agenda. One of the most significant of these powers is the veto power over laws. And, in a semi-presidential system, the president typically exercises direct control over defense and foreign affairs. Additionally, the president may possess other powers, such as granting pardons, bestowing honors, and appointing key positions outside the government. The table below provides a quick overview of the presidential powers in the reviewed countries.

Country	President’s Veto and the Parliamentary Majority Required to Override It	President’s Role in Military and Defense Affairs	President’s Role in Foreign Affairs	President’s Power of Issuing Self-Initiated Decrees
Albania	No	Ceremonial	Ceremonial	No
Andorra	No	Ceremonial	Ceremonial	No
Armenia	$>1/2$ all	Ceremonial	Ceremonial	No
Austria	No	Ceremonial	Ceremonial	No
Belgium	No	No	No	No
Bulgaria	$>1/2$ all	Ceremonial	Ceremonial	No
Croatia	No	Ceremonial	Ceremonial	No
Czech Republic	$>1/2$ all	Ceremonial	Ceremonial	No
Estonia	No	Ceremonial	Ceremonial	No
Finland	No	Ceremonial	Ceremonial	No
Georgia	$>1/2$ all	Ceremonial	Ceremonial	No
Germany	No	No	Ceremonial	No
Greece	No	Ceremonial	Ceremonial	No
Hungary	No	Ceremonial	Ceremonial	No
Italy	No	Ceremonial	Ceremonial	No
Latvia	No	Ceremonial	Ceremonial	No
Malta	No	Ceremonial	Ceremonial	No
Moldova	No	Ceremonial	Ceremonial	No
Montenegro	No	Ceremonial	Ceremonial	No
Netherlands	No	No	No	No
Serbia	No	Ceremonial	Ceremonial	No
Slovakia	$>1/2$ all	Ceremonial	Ceremonial	No
Slovenia	No	Ceremonial	Ceremonial	No
Spain	No	No	No	No
India	No	Ceremonial	Ceremonial	No
Japan	No	No	No	No
Malaysia	No	No	No	No
Pakistan	No	Shared Control	Ceremonial	No
Singapore	No	Ceremonial	Ceremonial	No
Poland	$>3/5$ present of at least 1/2 total	Ceremonial	Ceremonial	No
Romania	No	Shared Control	Ceremonial	No
Lithuania	$>1/2$ all	Ceremonial	Ceremonial	No
Portugal	Important laws: $>1/2$ all and $>2/3$ present. Other laws: $>1/2$ all.	Ceremonial	Ceremonial	No
Sri Lanka	No	Shared Control	Shared Control	DE_Sri_Lanka
France	No	Dominant	Dominant	DE_France
Ukraine	$\ge 2/3$ all	Dominant	Dominant	DE_Ukraine
Peru	$>1/2$ all	Dominant	Dominant	DE_Peru
Madagascar	No	Dominant	Dominant	DE_Madagascar
Kazakhstan	No	Dominant	Dominant	DE_Russia
Russia	$\ge 2/3$ all, for both chambers	Dominant	Dominant	DE_Russia

DE_Sri_Lanka: The president of Sri Lanka can issue decrees independently in: emergency declarations and regulations (public security, crises), military command and deployment (as Commander-in-Chief), pardons and clemency, key appointments (military, judiciary, diplomats) and dismissals, parliamentary dissolution (within limits), foreign affairs (diplomatic actions, treaty preliminaries), regulatory implementation (where delegated).

DE_France: The president of France can issue decrees independently in: foreign affairs (treaty negotiation, diplomatic appointments), military command (deployments, defense policy), emergency measures, dissolution of the Assembly, certain appointments (e.g., Constitutional Council), pardons, referendums.

DE_Ukraine: The president of Ukraine can issue decrees independently in: foreign affairs (treaty negotiation, diplomatic appointments), military command (mobilization, appointments), national security and emergencies (martial law, sanctions), certain appointments (e.g., SBU head, governors), pardons, citizenship and honors, legislative actions (vetoes, proposals).

DE_Peru: The president of Peru can issue decrees independently in: foreign affairs (diplomacy, treaties), military and defense (command, emergencies), emergency powers (states of emergency/siege), legislative delegation (delegated laws), economic/financial emergencies (urgent measures), appointments/dismissals (ministers, officials), pardons, regulatory/administrative matters (law execution), citizenship and honors.

DE_Madagascar: The president of Madagascar can issue decrees independently in: emergency measures (state of emergency, martial law), military command and organization (especially in crises), pardons and clemency, some appointments (e.g., military officials) and foreign affairs actions (e.g., ambassador accreditation), though countersignature is common.

DE_Russia: The president can issue decrees independently in: foreign affairs (diplomacy, treaties), military and defense (mobilization, command), national security and emergencies (martial law, sanctions), appointments/dismissals (government, judiciary, security), pardons, legislative actions (vetoes, referendums), economic/administrative regulation, citizenship and honors, constitutional oversight.

2.5. How Ministers Are Selected and Removed

In the countries reviewed, the prime minister is typically a member of parliament, as are most ordinary ministers in many of these nations. This parliamentary composition offers a key advantage: ministerial roles can be used as incentives to draw other political parties into a governing coalition, thereby bolstering alliance stability. However, it also presents a drawback, as individuals with specialized expertise and experience in relevant fields are often excluded from government. When a parliament member assumes a ministerial position, the handling of their seat differs across countries, each approach carrying its own benefits and challenges. Furthermore, some nations permit parliament to initiate a vote of no-confidence against individual ministers – a practice that, too, comes with its own set of advantages and disadvantages.

Country	Whether Ministers Are Usually Chosen from Parliament	Whether MPs Retain/Suspend/Resign Their Seats to Be Ministers	Whether Individual Ministers Can Be Removed by No-Confidence
Albania	Yes	Retain	No
Andorra	Yes	Suspend	No
Armenia	Yes	Retain	No
Austria	No	Retain	Yes
Belgium	Yes	Suspend	No
Bulgaria	Yes	Retain	No
Croatia	Yes	Retain	NCM_Croatia
Czech Republic	Yes	Retain	No
Estonia	Yes	Retain	Yes
Finland	Yes	Retain	Yes
Georgia	Yes	Retain	No
Germany	Yes	Retain	No
Greece	Yes	Retain	No
Hungary	Yes	Retain	No
Italy	Yes	Retain	No
Latvia	Yes	Retain	Yes
Malta	Yes	Retain	No
Moldova	No	Retain	No
Montenegro	Yes	Retain	No
Netherlands	Yes	Suspend	Yes
Serbia	No	Retain	Yes
Slovakia	Yes	Retain	Yes
Slovenia	Yes	Suspend	Yes
Spain	Yes	Retain	No
India	Yes	Retain	No
Japan	Yes	Retain	Yes
Malaysia	Yes	Retain	No
Pakistan	Yes	Retain	No
Singapore	Yes	Retain	No
Poland	No	Suspend	No
Romania	No	Suspend	No
Lithuania	Yes	Suspend	Yes
Portugal	No	Suspend	No
Sri Lanka	Yes	Retain	Yes
France	No	Suspend	No
Ukraine	No	Resign	No
Peru	No	Resign	Yes
Madagascar	No	Resign	No
Kazakhstan	No	Resign	No
Russia	No	Resign	No

NCM_Croatia: If a vote of no-confidence is carried with respect to a minister, the prime minister may put forward a successor for a vote of confidence, or the prime minister and the government may resign.

3. Game-Based Scheme for Semi-Presidential Systems Without Presidential Bias

In the scheme proposed in [1], which will be referred to as the “original scheme” in the sequel, a candidate nominated by parliament must surpass a cohabitation threshold, which is by design higher than absolute majority, to become prime minister. This threshold is a parameter of the scheme. In this paper, we propose two new schemes adapted from that scheme. The two schemes share many elements. To an extent, they can be viewed as two variants of a single scheme with different values of a parameter, called presidential bias, whose meaning will be explained later. In this section, we outline the first adapted scheme, Scheme A. It has a presidential bias of zero, meaning no bias from the president. In the next section, we will present the second, Scheme B, where the presidential bias is nonzero.

We describe a scheme by presenting its provisions, accompanied by explanations for them. When a provision is complete and independent enough to stand on its own, we call it an article. Additionally, as in [1], the term “National Assembly” is used as the name of parliament in the provisions.

3.1. Main Provisions

The main provisions of the scheme are about the process for selecting a prime minister in the event of a vacancy.

Article A1

During a vacancy in the office of Prime Minister, the National Assembly and the President may each nominate one candidate, who must meet the eligibility criteria for the office of Prime Minister. Such nominations, if made, shall be publicly announced. The candidate nominated by the National Assembly is termed the Legislative Candidate, and the candidate nominated by the President is termed the President’s Candidate. If the National Assembly nominates first, the President’s nomination, if any, must follow within one day. If the President nominates first, the National Assembly’s nomination, if any, must follow within fourteen days.

No nomination for Prime Minister, whether by the National Assembly or by the President, may be made:

• while a motion of no-confidence in the Prime Minister is pending a vote in the National Assembly;
• while the National Assembly is electing a Successor to the Prime Minister.

At the conclusion of the nomination phase, if only one candidate is nominated or both candidates are the same individual, the President shall immediately appoint that candidate as Prime Minister, who shall be deemed to have formal legislative confidence.

If the Legislative Candidate and the President’s Candidate are different individuals, the National Assembly shall hold a vote of confidence in the Legislative Candidate within three days of both nominations being made. If the Legislative Candidate secures the support of more than half of the Members of the National Assembly, the President shall immediately appoint the Legislative Candidate as Prime Minister, who shall be deemed to have formal legislative confidence. Otherwise, the President shall, after consulting both candidates within two days, immediately appoint either candidate as Prime Minister, who shall be deemed not to have formal legislative confidence.

Provision A2

During any period in which the office of Prime Minister is vacant, the President may appoint a Caretaker Prime Minister, who must be eligible to serve as Prime Minister. Where the office of Prime Minister becomes vacant due to resignation or dismissal, the outgoing Prime Minister shall automatically assume the role of Caretaker Prime Minister.

The Caretaker Prime Minister is authorized to exercise the powers of the Prime Minister except the power to initiate Request for Successor, and shall perform the duties of the Prime Minister, until this mandate is terminated when a Prime Minister is appointed, a new Caretaker Prime Minister is appointed, the Caretaker Prime Minister resigns, or the Caretaker Prime Minister becomes ineligible to serve as Prime Minister.

Provision A3

A Member of the National Assembly shall not hold any office in the executive branch, except that of Prime Minister. While serving as Prime Minister, a Member of the National Assembly shall suspend their functions as a Member, and the number of Members of the National Assembly shall be reduced by one during his or her tenure as Prime Minister.

The above provisions warrant some explanation.

• In the original scheme, a timeframe was set from the occurrence of the vacancy within which the president must announce their nomination, and an article defined when the vacancy occurs. However, in this scheme (Scheme A), no such timeframe exists, making that article unnecessary.
• Under the original scheme, the president’s nomination is mandatory, but under this scheme, neither nomination is mandatory. This represents a clear departure from the original scheme. Additionally, under this scheme, the president and parliament conduct the nomination process in parallel, which also contrasts sharply with the original scheme, where the process is carried out sequentially, with parliament waiting for the president’s nomination before formally beginning its nomination process. We believe that a parallel process is more efficient than a sequential one, as it helps reduce time wastage.
• In the original scheme, parliament elects a “quasi-candidate”, who gets nominated only when they receive more than half of the votes. However, we have now determined that this is an unnecessary complication. As a result, in the adapted schemes, a quasi-candidate is directly a nominated candidate, and hence the term “quasi-candidate” is eliminated altogether.
• Under the original scheme, if the legislative candidate fails to secure a majority, they are not even nominated, let alone appointed. However, under the adapted schemes, the president is granted some discretion, allowing for the possibility that the legislative candidate may still be appointed. This shift is based on two key reasons: (1) The original scheme was designed for presidential systems, where a parliamentary majority is not as crucial for the formation of the government. (2) Parliament members who do not vote for the legislative candidate are not necessarily supporters of the president’s candidate. Therefore, the failure of the legislative candidate to secure an absolute majority does not automatically indicate that the president’s candidate has gained majority support, particularly in cases where the legislative candidate loses by a narrow margin, or there are a considerable number of absent members and/or abstention votes. In light of this, the article requires the president to consult both candidates before making a final decision. The factors for consideration in this decision-making process primarily include: (1) The potential for a subsequent motion of no-confidence and the likelihood of its success. (2) The readiness of the candidate to face potential challenges. Finally, the final discretion granted to the president effectively compensates for the rigidity of other parts of the article.
• Failure to identify a candidate who enjoys the confidence of an absolute parliamentary majority is not uncommon in multi-party systems, and this issue is addressed in nearly all the constitutions we reviewed. The PAR1-PAR3 countries test candidates one by one to determine whether they have the confidence of an absolute majority. While all or many of the candidates are nominated by the president, the president’s primary role here is simply to decide the order in which potential candidates are nominated. The PAR4 countries seek a simple majority, and the possibility of failure is much lower but still exists. The PAR5-PAR6 countries go a step further by directly electing a prime minister without requiring any absolute majority, a process that cannot fail – similar to how the people of a country cannot fail to elect a president. The philosophy behind the PAR1-PAR3 constitutions is that a candidate who fails the confidence test is unlikely to govern effectively as prime minister. As a result, Their constitution designers prefer not to give such a candidate a chance, opting to dissolve parliament if no candidate passes the test. In contrast, the philosophy behind the PAR5-PAR6 constitutions is that a candidate who is most acceptable to parliament is likely to govern effectively as prime minister. Their constitution designers are then willing to give this candidate a try, as they can be removed through a vote of no-confidence if they are later found to be ineffective in governing. This scheme partially adopts the philosophy of the PAR5-PAR6 models, but with an additional step of competition. In this scheme, parliament nominates a legislative candidate, not directly the prime minister. There is also a key difference: In PAR5-PAR6 countries, the procedure for electing the prime minister is enshrined in the constitution, whereas in this scheme, the procedure for electing the legislative candidate is dictated solely by parliament itself, affording significant flexibility.
• Under Scheme A, the president’s influence is very limited. The confidence vote is solely conducted by parliament, and the president’s candidate has a chance to win only if parliament is fragmented, with several faction leaders holding comparable influence, and the president’s candidate being one of them. As a result, we can expect that, in most cases, there will be no contest between two candidates. The situation will be different under Scheme B, which we propose later.
• A key feature of the original scheme was its fixed timeframe for completing the prime minister selection process, considered a significant advantage over traditional methods in many semi-presidential systems. The adapted schemes eliminate an absolute timeframe starting from a vacancy’s occurrence, which some may perceive as a regression. However, this is not the case. An indefinite vacancy is only a theoretical possibility, as indefinite delay requires both parliament and the president to intentionally stall the process. Typically, either the president or parliament benefits from securing their preferred prime minister, and the advantaged party will almost always seek to expedite the appointment. Even if both parties delay, they risk political backlash and potential vote losses in future elections.
• The parliament has little incentive to delay the prime minister nomination process, as under Provision A2, the president may appoint a caretaker prime minister at their discretion during a vacancy, rendering parliamentary delay almost harmless to the president. However, if a vacancy occurs when parliament is in recess, it may be unable to convene within the permitted nomination period, unless an extraordinary session is called, potentially forfeiting its right to nominate a candidate. But this poses no significant issue, as parliament can subsequently remove the appointed prime minister through a vote of no-confidence.
• Nominating a prime minister candidate is significantly more resource-intensive for parliament than for the president. Consequently, if the president has already nominated a candidate, parliament is allowed a longer delay to respond with its nomination than the president is allowed if parliament nominates first. A one-day delay is sufficient for the president, who likely has a candidate prepared at that stage.
• According to Article A1, a prime minister is always appointed with the constitutional status whether they have formal legislative confidence. The term “formal legislative confidence” is coined in this paper, and has not appeared in the literature or any constitution. It serves as a criterion for determining whether a prime minister can be dismissed by the president, a topic we will elaborate on later. The standard for initially granting formal legislative confidence is as follows: (1) When the legislative candidate succeeds in the vote of confidence, they have formal legislative confidence upon appointment. (2) When the legislative candidate is not contested by a different president’s candidate, they become prime minister without a confidence vote, but are nonetheless deemed to have formal legislative confidence upon appointment. This is why the term “formal” is used, as no actual confidence vote takes place in the latter case. According to this standard, a president’s candidate who is not also a legislative candidate will not have formal legislative confidence upon appointment. This is because the confidence vote applies only to the legislative candidate, and, as mentioned earlier, those members of parliament who do not support the legislative candidate are not necessarily supporters of the president’s candidate.
• In the original scheme, we included a requirement for the legislative candidate to be a member of parliament, but not for the president’s candidate. This requirement was intended to facilitate prompt nomination of the legislative candidate. However, with the removal of an absolute timeframe in the adapted scheme, the stipulation for the legislative candidate to be a member of parliament has been eliminated. Nonetheless, both candidates are still permitted, and likely, to be members of parliament. So there is still the issue of how to address their seat if a member of parliament becomes prime minister. We still prefer the suspension option for the prime minister and the resignation option for other ministers, though alternative approaches are also viable. Therefore, if you prefer an alternative approach, you may replace Provision A3 with a different provision. Please note that this provision is not a key element of the scheme.

3.2. The CVNC Article

In typical semi-presidential countries, the president does not possess the unilateral authority to dismiss the prime minister, and consequently, the prime minister is primarily removed through a vote of no-confidence. There are two types of no-confidence votes: ordinary and constructive. Of the 40 countries reviewed, 32 have adopted the ordinary vote of no-confidence, while 8 have adopted the constructive version. In the original scheme, neither type of no-confidence is used on a daily basis, as presidential dismissal is predominantly relied upon. In Scheme A, however, the constructive vote of no-confidence (CVNC) is the primary method for removing the prime minister. This approach is chosen for the following reasons:

• In this scheme, the selection of the prime minister primarily reflects the political orientation of parliament, and as such, parliament should play a more crucial role in their removal as well.
• A constructive vote of no-confidence enhances governmental stability by making it harder to remove the prime minister than an ordinary no-confidence vote [13,14,15]. Indeed, an ordinary no-confidence vote is incompatible with the game-based scheme, designed to support viable minority governments. A minority government is prone to collapse under an ordinary no-confidence vote.
• It creates a striking consistency in the system that both the confidence vote for the investiture of a new prime minister during a vacancy and the vote of no-confidence against an incumbent prime minister involve a direct comparison between two individuals. In retrospect, it can be said that the main article of the original scheme (Article N2) was a creative attempt to integrate game theory with the concept of constructive vote of no-confidence (CVNC) into the procedure for confirming a new prime minister.

The CVNC article is presented as follows:

Article A4

A motion of no-confidence in the Prime Minister may be submitted in writing to the National Assembly. To be admissible, the motion must:

• Be submitted when the office of Prime Minister is not vacant;
• Designate an eligible Successor Candidate for Prime Minister, distinct from the incumbent;
• Be submitted when the National Assembly is not electing a Successor to the Prime Minister;
• Be submitted when at least sixty days have elapsed since the appointment of the Prime Minister;
• Be submitted when at least forty days have elapsed since a previous no-confidence vote;
• Bear valid signatures of at least one-sixth of the total Members of the National Assembly.

The definition of a valid signature on a motion of no-confidence shall be prescribed by a resolution of the National Assembly, subject to the restriction that no Member of the National Assembly may contribute a valid signature to an admissible motion of no-confidence more than once in any ninety-day period within the current term of the National Assembly.

Upon submission of an admissible motion of no-confidence, the National Assembly shall schedule a vote no earlier than five days and no later than ten days after submission. The vote shall be canceled only if another motion of no-confidence passes during the pending period.

A motion shall be deemed passed if it receives the support of more than half of the Members of the National Assembly. Upon passage, the incumbent Prime Minister shall immediately resign, and the President shall immediately appoint the designated Successor Candidate as Prime Minister, who shall be deemed to have formal legislative confidence.

This article is worth a few remarks.

• Frivolous no-confidence motions could disrupt parliamentary operations. This article uses the measures of cooling-off period and minimum support threshold [13,14,15] to discourage frivolous motions. Additionally, it restricts parliament members from signing multiple motions within 90 days, limiting the number of motions that parliament can simultaneously admit. Alternative measures, such as consequences for failed motions, could be considered if these restrictions prove inadequate. However, these restrictions are not a central element of the proposed scheme.
• What happens if the office of prime minister becomes vacant while a no-confidence motion is pending a vote? The second paragraph of Article A1 prohibits nominations for prime minister during this pending period, preventing the initiation of the standard vacancy-filling process of Article A1. This prioritizes a direct resolution through the no-confidence vote to appoint a successor, avoiding the more complex nomination and appointment procedures in Article A1. However, if the no-confidence motion fails, the Article A1 vacancy-filling process will be initiated.
• This article does not explicitly address the exceptional circumstance of a successor candidate’s death or incapacitation prior to the vote or appointment, consistent with common constitutional practice.

3.3. The Request for Successor Article

In Section 2.3, we have listed various reasons in the 40 reviewed countries for parliament to be dissolved before its term expires. It is striking to find that in Scheme A, one reason is enough for all cases of dissolution.

Article A5

The Prime Minister may submit a written Request for Successor to the National Assembly, subject to the written approval of the President. Prior to submission, the Prime Minister shall consult the Speaker of the National Assembly. Such consultation shall be advisory and non-binding.

No Request for Successor may be submitted while a motion of no-confidence in the Prime Minister is pending a vote in the National Assembly.

Upon receiving a Request for Successor, the National Assembly shall initiate an election of a Successor to the Prime Minister, to be completed within fifteen days. During the election, one or more rounds of voting shall be conducted. In each round, a candidate eligible to serve as Prime Minister, distinct from the incumbent, shall be nominated and subjected to a vote of confidence. If a candidate secures the support of more than half of the Members of the National Assembly, he or she shall be deemed elected as the Successor, and the election shall conclude. The election shall also conclude if fifteen days have elapsed since the submission of the Request for Successor.

By the conclusion of the election, if a Successor is elected, the incumbent Prime Minister shall immediately resign, and the President shall immediately appoint the elected Successor as Prime Minister. Otherwise, the President may dissolve the National Assembly within two days, provided such dissolution complies with other provisions of this Constitution. Unless the National Assembly is dissolved, the Prime Minister, whether he or she is newly appointed or not, shall be deemed to have formal legislative confidence.

Request for Successor will sometimes be abbreviated as RFS hereafter. About RFS, several points need to be explained.

• The game-based scheme prioritizes parliamentary continuity by requiring parliament to attempt to elect a successor before dissolution. This ensures dissolution is a last resort, used only when parliament cannot form a government.
• During the election of a successor, the ruling party may strategically vote against all candidates to trigger dissolution. A comparable mechanism exists in Germany, where the Chancellor submits a motion of confidence to the Bundestag to confirm parliamentary support. Ruling party members then deliberately vote against their own Chancellor, causing the motion to fail, enabling the Chancellor to propose the Bundestag’s dissolution.
• Why should the incumbent be excluded from the election of a successor? If the incumbent were included, the process would be better named “Request for Successor or Confidence”, with the election of the incumbent as successor signifying confidence. The reasons for exclusion are threefold. (1) By issuing an RFS, the incumbent expresses their willingness to step down and their frustration with the current parliament. (2) RFS aims to trigger parliamentary dissolution. The inclusion would only make a difference if the incumbent is ultimately elected, but this would occur only if the incumbent has backed down, abandoning the push for dissolution and instead instructing their party members to vote for them to retain their position as if nothing had changed. Allowing this practice would encourage the prime minister to frivolously initiate an RFS, undermining its original intent. (3) Confidence is indeed granted if the president does not dissolve parliament after its failure to elect a successor (see the last sentence of Article A5). We will elaborate on this shortly.
• Should we establish a separate “Request for Confidence” mechanism? Both options are viable, and we remain neutral on this matter. Such a request should not require presidential approval, and securing an absolute majority should grant the prime minister formal legislative confidence. However, failing to achieve this majority should not be grounds for dissolving parliament – unlike in Germany, where a failed vote of confidence is a legitimate reason for dissolving the Bundestag. Why is this difference? Under a game-based scheme, the government may not hold a majority or may not even be the strongest minority. Therefore as prime minister, you cannot assume that if you fail to secure an absolute majority, no other candidate could do so either. In Germany, the government, during its formation, was either the majority or the strongest minority faction when no clear majority exists, and therefore the Basic Law assumes that the government remains the strongest faction, which is why a failed vote of confidence there is considered valid grounds for dissolving the Bundestag.
• Failure to elect a successor suggests two possibilities: (1) only the incumbent has parliamentary confidence, or (2) no one has parliamentary confidence. Meanwhile, regarding the incumbent’s intention, there are also two possibilities: (1) the incumbent wishes to stay in office with the current parliament, or (2) the incumbent does not wish to stay in office with the current parliament. Unless the president interprets the situation as the (1-1) combination, they should dissolve parliament, provided the constitution allows. Otherwise, the incumbent should retain their position and be recognized for securing confidence. This is why Article A5 includes a provision to grant the prime minister formal legislative confidence.
• RFS impacts the president in two ways: (1) It could lead to the president’s opponent assuming power. (2) Unless parliament is dissolved, the president loses the authority to dismiss the prime minister. But the key reason for RFS to require presidential approval is that only the president has the authority to dissolve parliament, and without this, the prime minister’s objective in initiating an RFS is generally unachievable. Finally, if the president has approved an RFS, it can be reasonably inferred that they have decided to dissolve parliament if a successor (to the prime minister) is not elected, as not doing so would result in their loss.
• An alternative option is to adopt a “Request for New Prime Minister” (RFNPM) mechanism, initiated by the president during a vacancy in the prime minister’s office. In this process, the president relinquishes their right to nominate a candidate but sets a deadline for parliament to elect a new prime minister with absolute majority support, and failure to do so would lead to parliamentary dissolution. So, why choose RFS over RFNPM? (1) Opting for RFNPM would overly complicate the vacancy-filling process for the prime minister’s office and result in a longer period without an official prime minister. (2) If the situation justifies initiating an RFNPM, the president should have the ability to appoint a prime minister of their choosing, who would then be willing to initiate an RFS as desired by the president. So essentially, RFS can achieve the same result as RFNPM. (3) For successful parliamentary dissolution, ruling party members of parliament must vote against all candidates, which requires a collective effort and strong party organization. It is inappropriate for the president to lead such an initiative, as they are expected to maintain a fair distance from party politics.
• RFS replaces the need for ad-hoc dissolution reasons by providing a unified, structured process that addresses all major scenarios requiring parliamentary dissolution. A prime minister may initiate RFS to resolve governance challenges, seek a fresh mandate, or preempt a no-confidence vote. This covers the full spectrum of dissolution triggers – gridlock, strategic elections, government formation failures, and crises – without relying on vague or subjective reasons like “political crisis” or “national interest” found in other constitutions.
• The process for parliament to nominate a candidate for prime minister under Article A1 differs from the election of a successor under Article A5 in three aspects. (1) Article A1 provides for a single nomination opportunity (though parliamentary rules may dictate multiple rounds of deliberation), whereas Article A5 permits multiple voting rounds within a structured process to elect a successor. (2) Article A1 imposes no specific timeframe for the nomination process, while Article A5 mandates a 15-day limit to ensure urgency.
• If a prime minister decides to initiate an RFS, they must be hopeless in effective governance, as no one would voluntarily relinquish power when capable of effective governance. The incumbent prime minister must carefully assess the likelihood of their position being taken over by a successor, ensuring that the benefits outweigh the risks. In most cases, the incumbent will proceed only if they judge a successor cannot be elected. In such instances, the 15-day period would seem excessive and appear wasted. However, this “waste” is necessary, as this period is essential to convince the public that parliamentary dissolution is really the last resort.
• What happens if the office of prime minister becomes vacant while parliament is electing a successor? The second paragraph of Article A1 prohibits nominations for prime minister during this period, preventing the initiation of the standard vacancy-filling process of Article A1. This prioritizes a direct resolution through the successor election to appoint a successor, avoiding the more complex nomination and appointment procedures in Article A1. However, if no successor is elected, the Article A1 vacancy-filling process will be initiated.
• What happens if parliament “elects” a successor after the 15-day deadline for the election of a successor? Legally, such an election lacks constitutional recognition. Specifically, a vote of confidence must be recognized under the constitution, and a vote after the deadline is not valid. However, if the president does not dissolve parliament thereafter, and the prime minister chooses to resign, then parliament may nominate the “elected successor” as legislative candidate under Article A1, who will likely be appointed as the next prime minister.
• Many countries allow their prime minister to tie a legislative bill with a vote of confidence or no-confidence. While the specifics may differ, the underlying principle remains the same. Under Scheme A, a bill could be linked to an RFS, and drafting a provision to implement this is not particularly challenging. However, we choose not to pursue this approach here, for two reasons. (1) The same outcome can be achieved by threatening parliament with, “If this critical bill fails, I will issue an RFS.” Both the bill proposal and the initiation of the RFS can take place during the cooling-off period. (2) The effectiveness of this linkage remains to be seen, as securing a successful RFS outcome may even be more challenging than passing the bill itself.

3.4. The Presidential Dismissal Provision

The presidential dismissal provision is presented as follows:

Provision A6

The President may dismiss the Prime Minister only if the Prime Minister does not have formal legislative confidence. The President shall not dismiss the Prime Minister while a motion of no-confidence in the Prime Minister is pending a vote in the National Assembly, nor while the National Assembly is electing a successor to the Prime Minister.

Below are the reasons for including this provision.

• In-depth analyses of presidential dismissal powers are provided in [8,16,17]. These studies primarily examine the effects of existing constitutional provisions on government stability, with limited discussion on the design of new constitutional frameworks for dismissal powers. It is our belief that neither of the two extreme options: (1) the president has full dismissal power and (2) the president has completely no dismissal power, is ideal. The former hurts government stability while the latter lacks flexibility.
• It is clearly reasonable that a prime minister supported by an absolute parliamentary majority should not be dismissed. Conversely, a prime minister with only minority support is typically aligned with the president, who then acts as a guardian of the prime minister. In such cases, the president should have some control over the government, which is best exercised through the power to dismiss the prime minister.
• The president should have the authority to dismiss a prime minister nominated by a previous president but not nominated by parliament, as such a personnel decision reflects the political orientation of the former president rather than that of the current one. Provision A6 permits this dismissal because the prime minister in question lacks formal legislative confidence.

3.5. Other Presidential Power Provisions

Our game-based scheme seeks to minimize parliamentary dissolution by fostering stable minority governments through a strategic partnership between the government and a president endowed with enhanced powers. To ensure the success of a minority government, which lacks stable support from parliament, it must secure the president’s support. In addition to powers typically held by presidents in semi-presidential systems, the president in this scheme should also be granted:

Legislative Veto Power: The authority to veto legislation, comparable to the veto powers of the presidents of Poland, Portugal, and Ukraine, allowing the president to check parliamentary decisions and strengthen the ruling camp’s position of negotiation with parliamentary factions.

Control Over Defense and Foreign Affairs: Final discretion in appointing the minister of defense, minister of foreign affairs, high-ranking defense officials, and ambassadors to major countries, ensuring the president’s influence over critical policy areas to stabilize government operations.

The presidential powers described in this subsection and the provisions proposed in previous subsections facilitate cooperation between the president and the minority government, reducing the likelihood of dissolution. To accommodate diverse cultural, historical, and institutional contexts, we here avoid prescribing specific constitutional provisions for these presidential powers, allowing flexibility in their implementation.

Similarly, the scheme is designed to function effectively across various electoral systems, and thus includes no specific electoral provisions.

4. Game-Based Scheme for Semi-Presidential Systems with Presidential Bias

In a game-based scheme, two scenarios involve comparing individuals: (1) the legislative candidate versus the president’s candidate during a vacancy, and (2) the successor candidate versus the incumbent prime minister during a constructive no-confidence vote. In Scheme A, outlined in the previous section, comparisons rely solely on parliamentary votes. In Scheme B, to be described in this section, comparisons also hinge on parliamentary votes but incorporate a presidential bias. This core distinction leads to significant differences across multiple aspects, justifying their classification as distinct schemes rather than mere variants of one scheme.

4.1. Main Provisions

Again, the main provisions of the scheme are about the process for selecting a prime minister in the event of a vacancy.

Article B1

During a vacancy in the office of Prime Minister, the National Assembly and the President may each nominate one candidate, who must meet the eligibility criteria for the office of Prime Minister. Such nominations, if made, shall be publicly announced. The candidate nominated by the National Assembly is termed the Legislative Candidate, and the candidate nominated by the President is termed the President’s Candidate. If the National Assembly nominates first, the President’s nomination, if any, must follow within one day. If the President nominates first, the National Assembly’s nomination, if any, must follow within fourteen days.

No nomination for Prime Minister, whether by the National Assembly or by the President, may be made:

• while a motion of no-confidence in the Prime Minister is pending a vote in the National Assembly;
• in the final thirty days of the term of office of the President.

At the conclusion of the nomination phase, if only one candidate is nominated or both candidates are the same individual, the President shall immediately appoint that candidate as Prime Minister, who shall be deemed to have formal legislative confidence.

If the Legislative Candidate and the President’s Candidate are different individuals, the National Assembly shall hold a vote of confidence in the Legislative Candidate within three days of both nominations being made. If the Legislative Candidate secures the support of more than nine-sixteenth of the Members of the National Assembly, the President shall immediately appoint the Legislative Candidate as Prime Minister, who shall be deemed to have formal legislative confidence. Otherwise, the President shall, after consulting both candidates within two days, immediately appoint either candidate as Prime Minister, who shall be deemed to have formal legislative confidence only if he or she was the Legislative Candidate and secured the support of more than half of the Members of the National Assembly in the confidence vote.

Provision B2

During any period in which the office of Prime Minister is vacant, the President may appoint a Caretaker Prime Minister, who must be eligible to serve as Prime Minister. Where the office of Prime Minister becomes vacant due to resignation or dismissal, the outgoing Prime Minister shall automatically assume the role of Caretaker Prime Minister.

The Caretaker Prime Minister is authorized to exercise the powers of the Prime Minister, and shall perform the duties of the Prime Minister, until this mandate is terminated when a Prime Minister is appointed, a new Caretaker Prime Minister is appointed, the Caretaker Prime Minister resigns, or the Caretaker Prime Minister becomes ineligible to serve as Prime Minister.

Provision B3

A Member of the National Assembly shall not hold any office in the executive branch, except that of Prime Minister. While serving as Prime Minister, a Member of the National Assembly shall suspend their functions as a Member, and the number of Members of the National Assembly shall be reduced by one during his or her tenure as Prime Minister.

Provision B3 is identical to Provision A3. Provision B2 is identical to Provision A2 except for the deletion of the RFS clause. Article B1 closely resembles Article A1, but there are key differences between the two. These differences are explained below.

• In Scheme B, a threshold of 9/16 is set for the legislative candidate to be mandatorily appointed as prime minister, compared to a 1/2 threshold in Scheme A. In the original scheme, a 3/5 threshold was used without the confidence theory described here, and the denominator used was the number of present members, not all members as used here. As a general rule across both schemes, the legislative candidate is selected over the president’s candidate if and only if their parliamentary confidence exceeds the president’s candidate’s overall confidence.

  $$\mathrm{l}\mathrm{e}\mathrm{g}\mathrm{i}\mathrm{s}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e} \mathrm{c}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{e}’\mathrm{s} \mathrm{p}\mathrm{a}\mathrm{r}\mathrm{l}\mathrm{i}\mathrm{a}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{y} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{f}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e}={\displaystyle \frac{\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r} \mathrm{o}\mathrm{f} \mathrm{p}\mathrm{o}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{f}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{v}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{s}}{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l} \mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r} \mathrm{o}\mathrm{f} \mathrm{p}\mathrm{a}\mathrm{r}\mathrm{l}\mathrm{i}\mathrm{a}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{m}\mathrm{e}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{s}}},$$

  $$\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{t}’\mathrm{s} \mathrm{c}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{e}’\mathrm{s} \mathrm{o}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{l}\mathrm{l} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{f}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e}=$$

  $$\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{p}\mathrm{a}\mathrm{r}\mathrm{l}\mathrm{i}\mathrm{a}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{y} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{f}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{t}’\mathrm{s} \mathrm{c}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{e}+\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l} \mathrm{b}\mathrm{i}\mathrm{a}\mathrm{s},$$

  $$\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{p}\mathrm{a}\mathrm{r}\mathrm{l}\mathrm{i}\mathrm{a}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{y} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{f}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{t}’\mathrm{s}\mathrm{c}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{e}\in$$

  $$[0,1-\mathrm{l}\mathrm{e}\mathrm{g}\mathrm{i}\mathrm{s}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e} \mathrm{c}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{e}’\mathrm{s}\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{l}\mathrm{i}\mathrm{a}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{y} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{f}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e}],$$

  $$\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l} \mathrm{b}\mathrm{i}\mathrm{a}\mathrm{s}\in [0,\underset{={\displaystyle \frac{1}{8}}\mathrm{i}\mathrm{n} \mathrm{S}\mathrm{c}\mathrm{h}\mathrm{e}\mathrm{m}\mathrm{e} \mathrm{B}}{\underbrace{\mathrm{m}\mathrm{a}\mathrm{x} \mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l} \mathrm{b}\mathrm{i}\mathrm{a}\mathrm{s}}}].$$
  In Scheme A, the presidential bias is fixed at 0, resulting in a 1/2 threshold for the legislative candidate’s mandatory appointment. In Scheme B, the presidential bias ranges from 0 to 1/8, necessitating a 9/16 threshold to ensure the legislative candidate’s parliamentary confidence always surpasses the president’s candidate’s overall confidence, regardless of the president’s estimation and assigned bias. This theory also explains why any outcome is possible in the adapted schemes (Schemes A and B) if the legislative candidate fails to meet the respective threshold. It is due to the president’s freedom in estimating their candidate’s parliamentary confidence and assigning a presidential bias, allowing flexibility in the appointment decision.
• However, the standard for granting formal legislative confidence remains unchanged, fixed at more than half of all members in both schemes.
• In Article B1’s second paragraph, the second sentence no longer references the Request for Successor (RFS), as the RFS mechanism is entirely removed in Scheme B. We will elaborate on this later.
• The second paragraph of Article B1 prohibits nominations in the final 30 days of the president’s term. While nominations are barred during this period, votes of confidence and appointments are not. This ban prevents late-in-term nominations from extending into the next term. In other words, this ban aims to ensure that any nomination made in a presidential term undergoes its appointment within the same presidential term. A side effect of this ban is that it sometimes deprives of the president or parliament’s ability to nominate. For instance, if the president nominates a candidate just before the 30-day window, parliament may not be able to nominate another candidate while meeting simultaneously the constitutional ban and timelines. However, this is not a significant issue, because the appointed prime minister will be in office only for several days, as a separate provision will enforce this limit.
• Why does Scheme A permit nomination and appointment across different presidential terms, while Scheme B does not? This question will be addressed in a later subsection.

4.2. The CVNC Article

The CVNC article of Scheme B is presented as follows:

Article B4

A motion of no-confidence in the Prime Minister may be submitted in writing to the National Assembly. To be admissible, the motion must:

• Be submitted when the office of Prime Minister is not vacant;
• Designate an eligible Successor Candidate for Prime Minister, distinct from the incumbent;
• Be submitted when at least sixty days have elapsed since the appointment of the Prime Minister;
• Be submitted when at least forty days have elapsed since a previous no-confidence vote;
• Bear valid signatures of at least one-sixth of the total Members of the National Assembly.

The definition of a valid signature on a motion of no-confidence shall be prescribed by a resolution of the National Assembly, subject to the restriction that no Member of the National Assembly may contribute a valid signature to an admissible motion of no-confidence more than once in any ninety-day period within the current term of the National Assembly.

Upon submission of an admissible motion of no-confidence, the National Assembly shall schedule a vote no earlier than five days and no later than ten days after submission. The vote shall be canceled only if another motion of no-confidence passes during the pending period.

A motion shall be deemed passed if it receives the support of more than nine-sixteenth of the Members of the National Assembly. Upon passage, the incumbent Prime Minister shall immediately resign, and the President shall immediately appoint the designated Successor Candidate as Prime Minister, who shall be deemed to have formal legislative confidence.

If a motion fails to pass but receives the support of more than half of the Members of the National Assembly, the Prime Minister shall be deemed not to have formal legislative confidence.

Article B4 differs from Article A4 in three aspects.

• Article B4 does not reference RFS, as the RFS mechanism is entirely removed in Scheme B.
• In Scheme B, the replacement threshold is set at 9/16, compared to the 1/2 threshold in Scheme A. This is based on a confidence theory similar to that outlined in the previous subsection, with key differences: (1) The comparison is now between the successor candidate (acting as the legislative candidate) and the incumbent prime minister (acting as the president’s candidate). (2) The president has no discretion in this process. Both the estimated parliamentary confidence and the presidential bias in the incumbent prime minister are set at their maximum values. Consequently, if the replacement threshold is not met, the incumbent prime minister remains in office. This approach is designed to ensure government stability.
• Under Scheme A, the prime minister cannot lose formal legislative confidence but may gain it through an RFS. Under Scheme B, the prime minister cannot gain formal legislative confidence but may lose it due to partially failed motions of no-confidence. The standard for maintaining formal legislative confidence differs from that required to initially secure it. As stipulated in the final paragraph of Article B4, the following rules apply under Scheme B: If a successor candidate receives a parliamentary confidence not exceeding 1/2, then it is possible that the incumbent prime minister’s parliamentary confidence is not below 1/2, and the incumbent’s status of formal legislative confidence keeps unchanged. Otherwise, then the incumbent prime minister’s parliamentary confidence is definitely below 1/2, and the incumbent (if not replaced) loses their formal legislative confidence (their confidence status may or may not change, depending on their prior confidence status). Finally, under the confidence theory, an incumbent prime minister cannot regain formal legislative confidence through a motion of no-confidence, as reflected in this provision.

4.3. No RFS in Scheme B

In Scheme A, the RFS mechanism is highly effective. But this mechanism is no longer useful in Scheme B. Here are the reasons:

• In Scheme B, parliament’s role as the primary source of power is diminished, as the president can appoint a prime minister with clear minority support. Consequently, pursuing parliamentary dissolution holds significantly less importance than in Scheme A.
• If the RFS mechanism were to be implemented in Scheme B, its design must carefully consider the confidence threshold. Should it be set at 1/2 or 9/16? A 1/2 threshold would be ridiculous, as it would allow the ruling camp, which has used the 9/16 threshold to block their opponents, to easily hand over power to their opponents with the much lower RFS threshold. On the other hand, a 9/16 threshold would make electing a successor very challenging. Dissolving parliament for failing to accomplish a challenging task is unconvincing to the public.

4.4. The Resignation and Dismissal Provisions

In Scheme B, there is a prime minister resignation provision and a presidential dismissal provision.

Provision B5

The Prime Minister shall resign upon the assumption of office by a newly elected President.

Provision B6

The President may dismiss the Prime Minister only if the Prime Minister does not have formal legislative confidence. The President shall not dismiss the Prime Minister while a motion of no-confidence in the Prime Minister is pending a vote in the National Assembly.

Provision B6 is nearly identical to Provision A6. However, the necessity of Provision B5 remains unclear. This question, along with some other issues raised earlier, will be addressed below.

• Section 2.2 includes a table identifying which of the 40 reviewed countries mandate the prime minister’s resignation under specific circumstances, such as the convening of a new parliament or the assumption of office by a newly elected president. Neither Scheme A nor Scheme B mandates the prime minister’s resignation upon the convening of a new parliament, as parliament may itself raise a motion of no-confidence to remove the prime minister at its first convening or any time later. Under Scheme A, parliament plays the primary role in selecting the prime minister, and as a result, there is no provision requiring the prime minister to resign when a newly elected president assumes office. In contrast, under Scheme B, the president holds greater influence than parliament in the selection of the prime minister. However, since the president generally cannot dismiss the prime minister, they need a prime ministerial vacancy to exert this influence. The most effective way to create such a vacancy is through the resignation of the prime minister, which is why Scheme B includes a provision for the prime minister’s resignation.
• The prime minister is not required to resign upon the assumption of office by a new president who is not newly elected, as such a president inherits the office from an elected president and does not reflect a new public mandate.
• Under Scheme A, a candidate nominated during a previous presidential term may be appointed as prime minister in the current presidential term, as references to “the President” in a constitutional article do not necessarily denote the same individual. This poses no issue, as the president’s authority to dismiss the prime minister does not depend on the timing of their appointment. Under Scheme B, however, a prime minister nominated in a previous presidential term and appointed in the current term with formal legislative confidence cannot be dismissed by the president. But if the prime minister is appointed in the previous term, they must resign when the current president assumes office, as required by Proposition B5. This is why Scheme B includes a provision in Article B1 to disable nomination and appointment of a prime minister across different presidential terms.

4.5. Other Presidential Power Provisions

Scheme A can be considered to shape a moderate, conventional semi-presidential system. However, while Scheme B still maintains a semi-presidential structure, it is much more presidential-leaning. Therefore, the presidential power provisions outlined in the previous section for Scheme A will also be necessary for Scheme B.

4.6. Governmental Power Provisions

While Scheme A permits minority governments, Scheme B takes it a step further by allowing for even smaller minority governments, i.e., those with fewer seats in parliament. Despite this, a minority government can remain stable in Scheme B due to the high threshold for a vote of no-confidence. However, the bar for passing laws remains unchanged. Therefore, Scheme B should include constitutional provisions that facilitate effective governance with little dependence on new laws or strengthen their bargaining position in negotiations with opposition parties in parliament.

The following constitutional provisions are suggested for consideration, aiming to empower the prime minister and ministers, drawing on models like South Korea, India, and Peru. Constitutional and legal arrangements for the executive powers of prime ministers and ministers in semi-presidential systems are discussed in [18,19,20].

Prime Ministerial Ordinances: Authorize the prime minister to issue ordinances with legal force within existing statutes, effective for some months until repealed or legislated, subject to presidential approval. Modeled on India’s Article 123 and South Korea’s Article 75, this enables policy adjustments (e.g., healthcare or economic regulations) without parliamentary approval.

Budget Power: Grant the prime minister and finance minister authority to reallocate up to 15% of the approved budget without legislative consent, aligning with existing laws, and propose temporary budget measures for 90 days, pending review. Inspired by Peru’s Article 80 and South Korea’s budget execution, this allows prioritization of initiatives (e.g., infrastructure, welfare), enhancing leverage by demonstrating fiscal control.

Emergency Power: The prime minister should recommend presidential emergency orders during crises (e.g., economic collapse, disasters), effective immediately with parliamentary ratification within 30 days. Based on South Korea’s Article 76, this enables swift action (e.g., price controls), with stability ensuring negotiation flexibility with opposition parties.

Trade Negotiation Power: Authorize the prime minister and trade minister to conclude executive trade agreements without parliamentary approval, within existing laws.

Additional Tools: Empower the prime minister to appoint agency heads without parliamentary confirmation (South Korea, Article 87) to align bureaucracy with government goals, and allow ministers to prioritize enforcement of existing laws (e.g., environmental standards), enhancing policy impact. Direct parliamentary access strengthens negotiation by rallying public or opposition support.

These provisions, balanced by judicial review and time-limited parliamentary oversight, enable Scheme B’s minority government to govern effectively within existing laws and leverage unilateral action to secure opposition compromises, ensuring robust governance despite legislative challenges.

4.7. Electoral Provisions

In Scheme B, the absence of a Request for Successor mechanism precludes early dissolution of parliament, necessitating a fixed-term parliament. The constitution should establish a fixed parliamentary term (3-4 years), with elections held on a predetermined date. Several options are available:

Non-Aligned Elections: While the presidential term is typically fixed, the president may leave office before the term ends for various reasons. If a presidential election is called promptly after a presidential vacancy, the election date is not fixed. This is the case in South Korea.

Exactly Aligned Elections: Both presidential and parliamentary elections are held every 4 years on the same day. A 5-year term is excluded, as it would be too long for an indissoluble parliament. This system is used in Brazil, Chile, Colombia, Costa Rica, the Dominican Republic, Ecuador, Ghana, Guatemala, Honduras, and Nigeria.

Argentina Model: Both presidential and parliamentary terms are 4 years. Every 4 years, joint presidential and parliamentary elections are held, with a mid-term parliamentary election in between. Each parliamentary election elects half of the members of parliament. This system is used in Argentina.

Mexican Model: Presidential elections are held every 6 years, while parliamentary elections take place every 3 years. These elections are aligned whenever possible. This model is followed in Mexico and the Philippines.

Cheng’s Model: Presidential elections are held every 5 years. Half of parliamentary elections coincide with presidential elections every 10 years, while the other half (mid-term elections) occur 3 or 2 years after the most recent presidential election, resulting in parliamentary terms of 3 or 4 years. Proposed in [21], this model aims to achieve maximum executive-legislative alignment with appropriate terms for both president and parliament, but remains theoretical, with no adoption in any country.

Finally, to align with Provision B5, Scheme B should also include Inauguration Provisions, ensuring that the gap between the election and the convening of parliament is shorter than the gap between the election and the inauguration of the president, so that if a presidential election and a parliamentary election are held on the same day, the newly elected parliament convenes before the newly elected president assumes office. This is crucial because, when the prime minister resigns as required by Provision B5, the newly elected parliament must already be operational. Fortunately, most real-world constitutions already meet this requirement.

5. Comparative Analysis of the Schemes

This section omits a direct comparison between Schemes A and B, as their similarities and distinctions are easily seen along the way.

5.1. Comparison Between Scheme A and Existing Semi-Presidential Systems

If one were to ask which countries have a constitutional system most similar to Scheme A, the answer would be Poland and Lithuania.

• Poland and Lithuania are semi-presidential republics.
• Poland adopts CVNC.
• Poland’s president has a considerably strong veto power.
• Lithuania’s president has a power of dismissal similar to Scheme A’s.

But there are also several interesting distinctions between Scheme A and typical semi-presidential systems including Poland and Lithuania.

• Of the 40 reviewed countries, only those in the PAR1 class do not accept minority governments. This indicates that most semi-presidential or parliamentary systems are open to minority governments. However, in the reviewed constitutions, excluding those in the RU class, the president’s role is primarily ceremonial. The RU class is unique in that the president holds a pivotal role. Nonetheless, the systems in the RU countries are approval-based rather than game-based. The original game-based scheme [1] was developed to address the limitations of such systems, and the two new game-based schemes proposed here are more refined versions of the original scheme.
• Regarding the president’s power to dismiss the prime minister, all the reviewed countries, except Portugal and Lithuania, either grant no authority or full discretion. Portugal employs a somewhat subjective rationale. Scheme A’s Provision A6 mirrors Lithuania’s relevant provision but is more systematic, as it employs a novel concept of formal legislative confidence, which is based on a coherent confidence theory. Furthermore, Provision A6 offers greater convenience for the president for not needing parliamentary approval, thus avoiding unnecessarily straining relations with the prime minister if approval is withheld.
• All the reviewed countries rely on ad-hoc reasons for the dissolution of parliament. In contrast, Scheme A employs a systematic and unified rationale based on Request for Successor, which makes the system highly consistent and elegant.
• Although not explicitly stated, a “Request for Confidence” (RFC) provision can be incorporated into Scheme A. The RFC is similar to the “in-tenure vote of confidence” – a mechanism commonly observed in many of the reviewed countries, where a vote of confidence takes place after government formation. The key difference between the RFC and the in-tenure vote of confidence is that the former has no legal consequences if it fails, while the latter could result in the government’s resignation or the dissolution of parliament if it fails.

5.2. Comparison between Scheme B and the Original Scheme

Scheme B and the original scheme share the following commonalities.

• The process for selecting a prime minister when the office is vacant is game-based.
• The parliament cannot be dissolved early.
• The rough standard for the prime minister to be immune from dismissal is the support of an absolute parliamentary majority. In Scheme B, it may be lost via of a constructive vote of no-confidence; in the original scheme, it may be lost via an ordinary vote of no-confidence.

What is more important, however, are their differences.

• As for the selection process of the prime minister’s office, the differences between Article B1 in Scheme B and Article N2 in the original scheme, are detailed in the explanation of Article A1. Article A1 and Article B1 are nearly identical as they differ only in the threshold. The threshold (9/16) of Scheme B is lower than the threshold (3/5) of the original scheme, though not significantly so, as the denominator in the former is all members, while the denominator in the latter is present members. From a procedural perspective, Scheme B is much more rigorous than the original scheme.
• Scheme B primarily employs CVNC to remove the prime minister. Conversely, the original scheme relies almost exclusively on presidential dismissal, with the sole exception that a newly elected parliament has a brief window in which it can remove the prime minister through an ordinary vote of confidence.
• Scheme B introduces a novel concept of formal legislative confidence, grounded in the confidence theory articulated in this paper. Under Scheme B, formal legislative confidence may be lost permanently as a result of a partially failed constructive motion of no-confidence. In contrast, under the original scheme, immunity from dismissal of a parliament-nominated prime minister may be temporarily revoked for 30 days due to a successful ordinary vote of no-confidence. This temporary loss of immunity could pressure the president into hastily dismissing the prime minister. Moreover, under Scheme B, formal legislative confidence persists beyond the expiration of parliament, whereas in the original scheme, immunity from dismissal lapses with parliament’s term.

6. Conclusions

This paper draws inspiration from our effort to adapt the game-based scheme, originally developed for Korea-like presidential systems in [1], to semi-presidential systems. Initially, we assumed the prime minister selection procedure for a vacant office could be directly transposed. However, we identified opportunities for improvement, transitioning from the original scheme’s sequential and absolute timing to a parallel process with relative timing, enhancing procedural rigor.

When the game-based concept is applied to the prime minister replacement procedure, we obtain constructive vote of no-confidence. We then developed a detailed procedure and introduced the novel concept of formal legislative confidence, grounded in a theory articulated in this paper. This concept provides a unified standard for determining the president’s authority to dismiss the prime minister. Regarding the selection and replacement of the prime minister, a parameter central to both schemes is the “presidential bias”. When set to zero, the resulting Scheme A resembles a typical semi-presidential system and incorporates a Request for Successor (RFS) mechanism, which unifies parliamentary dissolution processes across all scenarios. In contrast, a nonzero presidential bias yields a presidential-leaning system, termed Scheme B. We selected a maximum bias of 1/8, deemed reasonable, leading to a cohabitation threshold of 9/16, slightly lower than the original scheme’s 3/5 threshold. Scheme B excludes RFS, as it is incompatible with nonzero presidential bias, resulting in an indissoluble parliament.

We recommend Scheme A for those seeking a balanced semi-presidential system robust in fragmented parliaments, and Scheme B for those favoring a presidential-leaning system without parliamentary dissolution. The original scheme is now considered obsolete, as Scheme B represents a refined evolution serving similar objectives.