Amending the constitution has gotten harder, but it happens anyway
The idea of measuring how little of the United States would be required to veto a constitutional amendment was raised by Antonin Scalia.
It’s very very difficult to amend [the Constitution], infinitely more difficult than it was when that provision was written. … I figured it out once if you took a bare majority in the smallest states by population, something less than 2% of the population could prevent a constitutional amendment.
To restate his point with an example from today, we can imagine that an amendment today would require approval from 38 states (DC is not asked). This means that a veto (metaphorically) would require 13 states to refuse to ratify. These smallest states are, in descending order of population: Idaho, West Virginia, Hawaii, New Hampshire, Maine, Montana, Rhode Island, Delaware, South Dakota, North Dakota, Alaska, Vermont, and Wyoming. The population of these states, as of 2024, is about 15 million, which is about 4.4% of the US. Half of that is about 2.2%.
So in some imaginary scenario in which all these states were on the same side, and somehow in opposition to California, Texas, Florida, New York and so on, then they could stop the amendment from passing.
I wanted to quantify what “infinitely more difficult” meant, so I ran the numbers. Historical state population data can be found on Wikipedia.1 I only counted states that were actually in the union as being part of the population or as being potentially the smallest state. I always included DC in the total population.
It turns out that the union started with a veto percent of about 5%, maxed out at 6%, and then trended downward, before landing at 2%.
Outside of the Bill of Rights, most amendments have become law after the size of the hypothetical veto percent shrank to about 2%.
A lot of these amendments are fairly anodyne and procedural. The 20th, 22nd and 25th are about stating when the president takes office, how many times that person may do so, and who can succeed him.
Others are more controversial, but still not in a way that seems to fit into partisan politics. The 18th amendment (banning alcohol) was ratified by all but two states, and then repealed by 38 of those states.
The 19th amendment, granting women the right to vote, required 36 states’ approval. It was passed by 38 states within two years of its proposal, more than enough to ratify it. The remaining states ratified it in the following decades, with Mississippi holding out until 1984.
Failed amendments include the Child Labor Amendment from 1924 (only 28 states ratified before expiration), the Equal Rights Amendment from 1972 (only 35 states ratified before expiration) and the District of Columbia Voting Rights Amendment (only 16 states ratified before expiration).