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Is it at all realistic that the legislature of a successful country could require a supermajority (e.g., three-fifths or two-thirds) in order to pass laws, rather than a simple (one-half) majority? Maybe a group of constitution-writers would want to put checks on the legislature, but without having to deal with the extra back-and-forth of having to vote twice on the same bill--once with a simple majority to pass the bill, and again with a supermajority to override an executive veto.

Amendments to the country's constitution might require an even larger supermajority--e.g., 3/5 for laws and 3/4 for constitutional amendments, or 2/3 and 4/5.

Wikipedia has the following information on the current use of legislative supermajorities in the IRL USA:
A Senate rule requires an absolute supermajority of three fifths to move to a vote through a cloture motion, which closes debate on a bill or nomination, thus ending a filibuster by a minority of members. In current practice, the mere threat of a filibuster prevents passing almost any measure that has less than three-fifths agreement in the Senate, 60 of the 100 senators if every seat is filled.
One common provision of so-called "taxpayer bill of rights" laws (either in state statutes or state constitutions) is a requirement of a supermajority vote in the state legislature to increases taxes. The National Conference of State Legislatures reported in 2010 that fifteen states required a supermajority vote (either a three-fifths, two-thirds or three-fourths majority vote in both chambers) to pass some or all tax increases. Supermajority requirements for tax increases have been criticized as "deeply flawed" by a Center on Budget and Policy Priorities report, since such requirements make it difficult to close tax loopholes, empower a minority of legislators, make it difficult to fund transportation infrastructure, and may encourage pork-barrel spending as a trade-off to ensure passage of a tax increase.
The National Conference of State Legislatures says this:
Supermajorities are intended to prevent a "tyranny of the majority," and also encourage deliberation and compromise as proponents attempt to gather enough votes to reach a supermajority. Supermajorities in the legislature often are required for constitutional amendments because of the belief that constitutions should not be amended without careful deliberation. Many states also require a supermajority vote of the legislature to increase taxes.

In most states, however, the initiative constitutional amendment process is not subject to the same supermajority vote requirement as the legislature. Some experts question why supermajorities are required of the legislature but not of the people. They point out that the initiative process lacks checks found in the legislature that promote compromise and consensus and suggest that a supermajority vote requirement might help to prevent the passage of initiatives that are supported only by a narrow majority.
usgovinfo.about.com cites The Federalist:
In general, the Founding Fathers favored requiring a simple majority vote in legislative decision making. Most of them, for example, objected to the Articles of Confederation's requirement for a supermajority vote in deciding such questions as coining money, appropriating funds, and determining the size of the army and navy.

However, the framers of the Constitution also recognized the need for supermajority votes in some cases. In Federalist No. 58, James Madison noted that supermajority votes could serve as a "shield to some particular interests, and another obstacle generally to hasty and partial measures." Hamilton, too, in Federalist No. 73 highlighted the benefits of requiring a supermajority of each chamber to override a presidential veto. "It establishes a salutary check upon the legislative body," he wrote, "calculated to guard the community against the effects of faction, precipitancy, or of any impulse unfriendly to the public good, which may happen to influence a majority of that body."
Does anyone have any opinions on this topic?
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