The executive powers of the President, the Prime Minister, and the Council of Ministers vary significantly depending on the political system in question, particularly in parliamentary versus presidential systems. Here’s an overview of these powers and the mechanisms for their accountability:

President:
In a presidential system (e.g., United States):

1.Executive Powers: The President is the head of state and government and holds significant executive powers, including the authority to enforce laws, command the military, veto legislation, and issue executive orders.

2.Accountability:

• To Parliament: In systems where the President is not directly accountable to parliament, there may be limited mechanisms for oversight unless impeachment or removal processes exist.
  
• To Judiciary: The judiciary can review executive actions to ensure they adhere to constitutional limits.
  Prime Minister and Council of Ministers:
  In a parliamentary system (e.g., United Kingdom):

1.Executive Powers: The Prime Minister is the head of government, chosen from the majority party in the parliament. The Council of Ministers (or Cabinet) collectively exercises executive authority, including policy-making and implementation.

2.Accountability:

To Parliament: The Prime Minister and the Cabinet are accountable to the parliament (House of Commons). They must answer questions, justify policies, and can be removed through votes of no confidence or other parliamentary procedures.
To Judiciary: Judicial review ensures executive actions comply with the constitution and laws.

Debates Surrounding Discretionary Powers:

1.Extent of Powers: There is often debate over how much discretion the executive should have. Critics argue excessive discretion can lead to authoritarianism or misuse of power, while proponents argue it’s necessary for effective governance.

2.Checks and Balances: Systems often include checks and balances to limit executive power. These can include judicial review, parliamentary oversight, separation of powers, and constitutional constraints.

3.Emergency Powers: During crises or emergencies, executives may invoke emergency powers. The legality and extent of these powers are often contentious, balancing the need for decisive action with safeguarding civil liberties.

4.Accountability Mechanisms: Mechanisms like parliamentary oversight committees, judicial review, media scrutiny, and public opinion play crucial roles in holding the executive accountable.

In conclusion, while executives hold significant powers necessary for governance, the extent and exercise of these powers are subject to constitutional and legal constraints. The balance between effective governance and safeguarding against abuse of power is a central theme in the debates surrounding executive discretion.