What is the special majority required for constitutional amendments in the United States?

Two-thirds majority

The correct answer is Option 2 - Two-thirds majority

The U.S. Constitution requires a two-thirds majority in both houses of Congress for proposing amendments, illustrating the principle of special majority in its amendment process.

Two principles dominate the various procedures of amending the constitutions in most modern constitutions.

One is the principle of special majority. For instance, the constitutions of U.S., South Africa, Russia, etc. have employed this principle: In the case of constitution of US, it is two-thirds majority, while in South Africa and Russia, for some amendments, three-fourths majority is required.
The other principle that is popular among many modern constitutions is that of people’s participation in the process of amending the constitution. In Switzerland, people can even initiate an amendment. Other examples of countries where people initiate or approve amendment to the constitution are Russia and Italy, among others.