To pass an amendment, you need...13.7 percent minimum

Economics Political Theory
1

Here are my calculations for the naive estimate:

To pass an amendment, you need 75% of states in agreement. Looking within each state (assuming a simple majority vote), you need 51% of the legislators. Looking at each legislator, he needs 51% of his constituents. Looking at the people who actually vote, let’s say 70% of eligible voters vote (which is very high).

Multiplying this out, 0.750.510.51*0.7 = 13.66% of the US population must support your cause.

This model is flawed, as I am not sure that simple majorities within each state are the procedure for ratifying amendments. Furthermore, the size of different states should affect the outcome (yet this just might work both ways, as small states are just as powerful as large ones when it comes to amendments, so this limits the converts you need).

Yet you get the idea. Perhaps I will get more data and run better calculations. This is fun!

2

Good point. So to amend the Articles of Confederation, about 17.5% would be sufficient (assuming that all States were of equal size and that 70% of the people voted in State elections).