On the Frequency and Probability of Amendments to the U.S. Constitution

Consider the following chart of amendments to the U.S. Constitution:

The number of times the U.S. Constitution has been amended has been very "bursty" -- there tend to be many amendments in eras of tremendous social upheaval, and then longer spans without any amendments at all. We're currently in one of the long spans basically devoid of amendments being passed. To be specific:
  1. Ten amendments were passed together in 1791 as the Bill of Rights soon after the country was founded, and two more in 1795 and 1804 -- but then no more for a period of 60 years.
  2. Three amendments were passed in the era of the Civil War (in 1865, 1868, 1870) -- but then no more for the next 40 years.
  3. Four amendments were passed near the end of the Progressive Era (1913, 1913, 1919, 1920).
  4. Two were passed in the depths of the Great Depression (both in 1933).
  5. Five were passed around the decade of the Sixties (1951, 1961, 1964, 1967, 1971).
  6. Only one was passed in the last 40 years; and it's a clear outlier, in that this 27th Amendment was first proposed in 1789 and was pending ratification for over 200 years (finally enacted in 1992).

As a possibly related matter, consider how the chance of achieving ratification changes as the country grows (i.e., adds more states). Note that after a two-thirds vote by Congress, amendments require ratification by three-quarters of the States. As a simple model, we'll use the binomial distribution and assume a fixed probability of being ratified by any given state:

Caveat: States don't have just one chance to ratify an amendment; each one can try year after year until it succeeds (so it becomes more like an "or" operator, increasing the chance over time; see the 27th Amendment above, for example).

But what we see here is that, generally speaking, more states means that a greater level of consensus is needed to pass amendments. If the chance per state is 75% (three-fourths), then the chance to ratify is basically fixed at 50%, since the expectation itself is for three-fourths of the states to approve (with some jumpiness in the percents due to granularity of rounding the three-fourths to an integer number of states). If the chance per state is lower (like 60%; a weak majority), then the chance to ratify crashes precipitously with more states; but if the chance per state is higher (like 80%; a stronger majority), then the chance to ratify increases to near-certainty.

Open Document spreadsheet with these calculations.

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