There is a sophisticated literature on the measurement of socio-cultural complexity that dates mostly to the third quarter of the previous century. Raoul Naroll was one of the most active investigators on that issue. At the bottom of this post you’ll see an index he compiled in the late 1960s . The 50 societies were chosen to represent all geographic areas and represent a standard sample often used in such research
He developed the index using measures for division of labor (how many different occupational specialties?), scale of settlement (size of largest settlement), and social ramification ¬– “more hierarchical levels, more councils of advisors, and more staffs to enhance the organization’s power to enforce its decrees (Teams)” . Once he’d gotten a raw score for he normalized them to the interval between 1 and 100. Those are the scores you see in the middle column below. Note that the lowest normalized score is 12 and the highest is 84. The right-hand column assigns an ordinal rank; where two or more societies had the same score, they’re assigned the same rank.
Now, look at the red numbers, which I added. Starting at the bottom, notice the interval between successive scores. Where that interval is larger than one I’ve indicated the interval distance with a red number, up to a point. That point is the distance between the Amhara, at 43, and the Burmese, at 56, where the difference is 13. That is by far the largest interval distance on the chart. The next largest distance is 4, between the Egyptians and the Irish.
What’s interesting about that place in the chart is that every culture from the Burmese through the Austrians is literate, while everything from the Semang through the Tongans is illiterate. What about the Amhara, you ask? They’re literate.
That is, setting the Amhara aside, all the cultures with complexity values up through 42 are Rank 1 cultures while all those with values of 56 or above are Rank 2 or Rank 3. I asked Naroll about the Amhara and he replied something to the effect, “Oh, they’re a puzzle.” But I forget what he said afterward.
Assuming that there is a good account for the Amhara, what that 13 point gap suggests is that there is an interesting difference between the societies below that interval and the societies above. The difference between Ranks 1 and 2 has a qualitative aspect to it that shows up in this quantitative measure as a dramatic quantitative difference.
 I found it in James M. Schaefer, “A Comparison of Three Measures of Cultural Complexity”, American Anthropologist 71, 1969, 706-708, https://anthrosource.onlinelibrary.wiley.com/doi/pdf/10.1525/aa.1969.71.4.02a00090.
 David G. Hays, The Measurement of Cultural Evolution in the Non-Literate World: Homage to Raoul Naroll, Metagram Press, 1998, p. 28, https://www.academia.edu/37163326/The_Measurement_of_Cultural_Evolution_in_the_Non-Literate_World.