Question
Article V counts states. At each ratification event, how much of the country did the ratifying states represent, and what range of coalitions does the rule permit? The work answers with computations and counts. It does not argue for or against any amendment or any change to Article V.
Definitions
- Ratification floor
- Population share of the smallest set of states that can ratify: the three-quarters requirement filled with the least populous states.
- Blocking floor
- Population share of the smallest set of states that can block ratification.
- Threshold share
- Population share of the states that had ratified on the day an amendment reached three-quarters.
- Final share
- The threshold share plus states that ratified after adoption.
- Ratification event
- The Bill of Rights (one act, completed by Virginia in 1791) and amendments 11 through 27, for 18 events. The Equal Rights Amendment, which reached 38 states in 2020 after its deadline, is reported separately.
Analytic choices
- Union membership. States enter on their admission dates. The number required is three-quarters of the states then in the union, rounded up.
- Population between censuses. Interpolated linearly; annual series are sampled on July 1. 2026 carries forward the 2020 census.
- Event grain. One record per state, per amendment, per action (ratification, rejection, or rescission). Every aggregate is computed from that ledger.
- Specification range. Threshold shares are recomputed under 24 combinations: two denominators (with or without the ex-Confederate states during Reconstruction), three census interpolations, rescissions counted or not, and two boundary conventions. The fact sheet reports the range; 12 of 18 threshold shares move by less than one point, and the 14th and 15th Amendments move most.
- Legislators. Counts of state legislators needed to ratify or block use a majority-of-all-seats model in each chamber. It does not reproduce each state's own ratification rule. Some nineteenth-century chamber sizes are filled from the nearest record, so those counts may be up to 3% short.
- Comparison measures. Coalitions are also measured by votes cast, eligible electorate, personal income, and land area, where records exist. Series begin when their sources do.
Data sources
| Input | Coverage | Main source |
|---|---|---|
| State population | Censuses 1790–2020 | Census Bureau counts, compiled 1790–2010 from a secondary tabulation; 2020 from the Census Bureau directly |
| Admission dates | 50 states | Secondary compilation of admission dates |
| Ratification ledger | 1,013 state actions | Founding-era ratifications from the U.S. Senate Manual (GovInfo); later amendments mostly from secondary compilations, pending re-sourcing |
| 21st Amendment convention votes | 37 states | 1933 tabulations held by the Library of Congress and Internet Archive |
| Legislature sizes | 1790–2026 | Harvard Dataverse state-legislature data, period almanacs (Internet Archive), and NCSL |
| Eligible electorate | 1980–2024 | University of Florida Election Lab turnout data |
| Votes cast | 1824–2024 | Presidential returns from published datasets and secondary compilations |
| Personal income | 1840–2025 | Bureau of Economic Analysis (state personal income) and NBER historical series |
| Land area | Current | Census Bureau TIGER 2024 |
Every row in the project data carries the URL of the source it was taken from.
Known limitations
- Ratification dates are provisional. Most post-founding ratification, rejection, and rescission dates come from secondary compilations. They are being re-sourced to primary records (state journals, the Congressional Record, and archival notices). Threshold shares, final shares, and the counts of rejections and rescissions may change. The ratification and blocking floors use only populations and admission dates.
- Unrecorded votes. For 7 of 18 ratification events, the decisive state's record contains no vote tally, so vote-margin results cover only the events that have one.
- Convention applications are not covered. State applications for an Article V convention are outside this release; the application data are being rebuilt from primary sources.
- Literature search. The work reproduces and extends Peter Suber, Population Changes and Constitutional Amendments: Federalism versus Democracy, 20 U. Mich. J.L. Reform 409 (1987). A search of HeinOnline and Westlaw for other prior work is not yet complete, so this release makes no claim to be the first computation of any series.
Prior work
Using Suber's convention (states in the union on January 1 of the census year), this work matches 36 of his 40 published floor values to within 0.1 point. The largest difference, 1.5 points in 1900, comes from a 2,000,000-person subtotal error in his appendix.
Replication
The calculation engine has tests that verify the arithmetic on synthetic data independently of the real inputs. Code and data are at github.com/mini-matters/article-v, with instructions to rerun every step. The repository reproduces the fact sheet's numbers exactly. Code is under the MIT license; text, figures, and data are under CC BY 4.0.