[periphrasis]

> instability and violence from a too-powerful government (thus checks and balances)

This is not the argument of the federalist papers. They argue for a government with powers commensurate to its objects. They discuss at great length the dangers of a government being too weak, namely that it forces a series of usurpations because its the only way to get anything done.

> They warned of tyranny of the majority

Nor is this the argument of the federalist papers, for much the same reasons above. Madison and Hamilton are quite explicit that majority rule is the only way to have a functional government, and that the alternative will only lead to dysfunction and the need to seize more power to break the resulting logjams.

[periphrasis]

From Federalist 10

"The inference to which we are brought is that the causes of faction cannot be removed and that relief is only to be sought in the means of controlling its effects.

If a faction consists of less than a majority, relief is supplied by the republican principal, which enables the majority to defeat its sinister views by regular vote."

Madison goes on to discuss the difficulty of the situation in which faction encompasses the majority, which is likely what you're referring to. But he is VERY explicit that majority rule is one of the primary weapons against faction, and the discussion of the failures of articles of confederation and historical leagues and confederacies that occupies multiple papers makes clear that lack of majority rule is one of the great enablers of faction.

edit: The guard against majority faction does NOT come from minority rule or supermajority requirements. It comes from representation, rather than direct assembly, and a large population that is geographically and politically diverse. Those are the mitigations Madison proposes in Federalist 10 for the dangers of majority faction. He's quite clear that majority rule is the only way to run a popular government and any danger it poses must be mitigated by other means, namely representation and large geographic extent.

[patmorgan23]

Remember the historical context here. When the constitution was proposed, the United States was operating under the articles of confederation. The articles created an incredibly weak central government that could not raise a standing army or even impose its own taxation (only request funding from the states). The Constitution represented a significant strength, anything of the central/federal government.