A compressor read 187 constitutions and found the British Empire

A compressor makes a file smaller by noticing that it has seen something before. Give it two documents and that property becomes a measurement: how much does knowing the first help you describe the second? Nothing about law, language or history is involved. We pointed it at every constitution currently in force.

The corpus is all 187 in-force national constitutions from the public Constitute Project, in English, converted to plain text — about 30 MB. Every pair gets one number:

NCD(a,b) = (C(a+b) - min(C(a),C(b))) / max(C(a),C(b))

That is 17,391 pairs, which took 1,329 seconds. The world median came out at 0.923 — most constitutions have essentially nothing in common with most other constitutions, which is what you would hope.

First, check the instrument on something with a known answer

Before measuring anything we did not already know, we measured something we did. Software licences have documented lineage: the AGPL is the GPL version 3 with one extra section bolted on, GPL version 3 was a ground-up rewrite rather than an edit of version 2, and the Apache licence was drafted independently of all of them.

The closest constitutions on Earth

Sorted by distance, the top of the list is startlingly uniform. The fifteen most similar pairs out of 17,391 are all drawn from six small states in the Eastern Caribbean.

0.319  Dominica              St Lucia
0.343  St Lucia              St Vincent & the Grenadines
0.377  Dominica              St Vincent & the Grenadines
0.390  Grenada               St Vincent & the Grenadines
0.437  Grenada               St Lucia
0.452  Antigua & Barbuda     St Lucia
0.461  Dominica              Grenada
0.463  Antigua & Barbuda     St Vincent & the Grenadines

Those six — Dominica, St Lucia, St Vincent & the Grenadines, Grenada, Antigua & Barbuda and St Kitts & Nevis — took their independence constitutions from a common template drafted in London between 1978 and 1983.

That was the result we expected. The full corpus produced a better one.

The family that spans five regions

Clustering on the size-controlled score rather than raw distance produces two dominant families. Neither of them is geographic.

Antigua & Barbuda · Bahamas · Barbados · Belize · Botswana · Dominica · Grenada · Guyana · Jamaica · Kiribati · Lesotho · Mauritius · Nauru · Solomon Islands · St Kitts & Nevis · St Lucia · St Vincent & the Grenadines

Seventeen states across the Caribbean, the Pacific, Southern Africa, the Indian Ocean and South America. They share no geography, no trade bloc, no culture and no language family beyond English. What they share is that all seventeen are former British territories that became independent between 1962 and 1983, with independence constitutions drafted from a common Colonial Office template. Seventeen out of seventeen, with no members that do not fit.

The links that cross oceans are as strong as the ones that do not. The z-score below is how much closer a pair is than other pairs with a similar size ratio; more negative means more related.

z = -7.45   Kiribati  [Pacific]     <-> St Kitts & Nevis [Caribbean]
z = -6.88   Belize    [C. America]  <-> Kiribati         [Pacific]
z = -6.35   Grenada   [Caribbean]   <-> Lesotho          [S. Africa]
z = -5.95   Nauru     [Pacific]     <-> St Kitts & Nevis [Caribbean]

The second cluster is the mirror image: Comoros, Congo, DR Congo, Djibouti, Madagascar, Mauritania, Niger and Senegal. Seven of the eight are former French colonies drafting on the Fifth Republic model. The eighth, DR Congo, was Belgian — francophone and civil-law, so a near-miss rather than a false positive, and we report it as one.

The instrument recovered both imperial drafting traditions and separated them from each other, having been told about neither.

What died on the way, which matters more than the map

Document length is badly confounded with compression distance. Across all 17,391 pairs, the correlation between absolute log size ratio and NCD is +0.515: texts of very different lengths look unrelated whether they are or not. Controlling for it — binning pairs by size ratio and reporting a residual z-score — killed three of our four initial findings.

A France-centred francophone cluster also failed its own control on the pilot corpus: raw distance put France's five nearest neighbours as Côte d'Ivoire, Mali, Benin, Togo and Cameroon, a clean sweep of former colonies, but the size-controlled cluster mean was only z = -0.33. The full corpus does recover a French family — France simply is not at the centre of it. And a set of Iceland pairings that looked strong turned out to sit at size ratios of three to five times, the extreme tail where our own control has too few comparable pairs and over-corrects.

Four patterns appeared. Three were artefacts of document length. The control is the product, not the map.

What this does and does not show

• It is not about legal content. NCD sees shared phrasing, structure and boilerplate. A constitution can be philosophically derivative and textually original, and this method will call it distant.
• Translation convention contributes. The Commonwealth cluster is the safest claim in the set precisely because those texts are originally in English. The French cluster is read in translation, and some of its cohesion may be shared translator convention rather than shared drafting.
• Single-linkage clustering chains. The core of each family is far more solid than its edges.

Reproduce it

Independently, and without anything from us. The corpus is public, normalized compression distance is a standard published metric, and the whole method is four lines. Any NCD implementation over the same texts will land in the same place — that is the point of using a metric nobody has to take on trust.

corpus   constituteproject.org, in-force, ?lang=en, HTML -> text  (187 docs, 30 MB)
metric   at1 ncd distance A B
matrix   17,391 pairs in 1,329 s
control  bin by |log size ratio|, windowed residual z (K=600)

Computing 17,391 pairs through a command line would spend most of its time starting processes, so the matrix was computed in-process using the same metric — and we checked that it agreed with the shipped at1 ncd distance before trusting it, on three pairs chosen across the range: 0.4519 against 0.4519, 0.9510 against 0.9510, 0.8219 against 0.8219.

If you want the pair-level distances rather than recomputing them, ask us and we will send the table.

The same instrument, pointed at a lottery, found nothing and said so. That is the same result as this one: a measurement is only worth reading when the control was run first.