The Constitution did this in a number of ways.
First, it limited the influence that people would have over the government. It allowed the people to directly elect the House of Representatives, but it did not allow direct elections of any other part of the government. This would help to inhibit majority rule.
Second, it placed a number of restrictions on what the government could do. It did not give it the right to regulate commerce within any state, regardless of what the majority wanted. It did not give it the right to pass bills of attainder, even if the majority wanted to.
In these ways, the Constitution limited majority rule.
The United States Constitution as written limited majority rule in several ways. First, the concept of majority rule deals with which party controls Congress. Since the Constitution separated the jobs of each branch of government, it is possible that the majority party or group in Congress may not get its way or what it wants. The majority rule of one party or group may be limited if the President, from the executive branch, uses his power to control the legislative branch. With the system of checks and balances, the President could veto a bill passed by the majority in Congress. If the President is from a different party, he could threaten to veto or block a proposed law. This could cause the majority in Congress to consider the views of the President or the minority party.
It is also possible that the courts could restrict the rule of the majority. With the system of checks and balances, the courts could rule that laws passed by the legislative branch are illegal or unconstitutional. If that occurs, the law would not go into effect.
The Constitution also limited the power of people to elect some of their leaders. For many years, we couldn’t elect our United States Senators. They were chosen by the state legislature. We also don’t directly elect the President. We vote for electors who actually choose the President. Thus, it possible that the candidate that receives the majority of the popular vote won't become President.
There were several ways the Constitution limited the rule of the majority.
The primary way in which the U.S. Constitution sought to limit the power of majority rule was based upon the principle of separation of powers and checks and balances as articulated by James Madison in Federalist Papers #10 and #51.
Madison effectively wanted to create a system of government that would prevent any single interest from gaining control of all of government at any one time. Separation of powers meant dividing the powers of government not only between the three branches of government and the national level but also by expressly dividing the powers of government between the national and the state level and then giving explicit powers to the various branches and the various levels of government.
This division of powers, underscored by different constitutional responsibilities of the three branches (legislative, executive, and judicial), meant that even it would be very difficult for a single majority to dominate and control all the branches at once.
The Constitution also divides the legislative branch into two chambers (known as bicameralism) and those two chambers (the House of Representatives and the Senate) represent different majorities and constituencies because of different term lengths and the staggering of elections in addition to terms and different geographic areas (geographic congressional districts and state wide senate seats).
Majority rule is also limited by language in the 9th and 10th Amendments to the Constitution that places meaningful limits on the powers of the national government but reserving all powers not expressly given to those institution to the states and to the people.
One additional way in which majority rule is limited is by the use of supermajorities for amending the Constitution. This means that it takes a supermajority in both houses of Congress (2/3) to approve an amendment to be sent to the states for ratification and it takes a super majority of the states (3/4) to ratify the proposed amendment.