the 3.5% rule

In a 2013 TED talk, Harvard political scientist Erica Chenoweth (born 1980) focused on what she calls a “3.5% rule”— “the notion that no government can withstand a challenge of 3.5% of its population without either accommodating the movement or (in extreme cases) disintegrating”.

“Researchers used to say that no government could survive if five percent of its population mobilized against it. But our data reveal that the threshold is probably lower. In fact, no campaigns failed once they’d achieved the active and sustained participation of just 3.5% of the population—and lots of them succeeded with far less than that. Every single campaign that did surpass that 3.5% threshold was a nonviolent one.”

My Talk at TEDxBoulder: Civil Resistance and the “3.5% Rule”

The “3.5% rule” of Ms Chenoweth has been picked up by the media, and transmitted widely on the web, most recently (14 May 2019) by BBC News

In response to a July 2017 query, Ms Chenoweth said “It’s not in the book. I calculated the 3.5% rule based on the data in the book for a workshop for activists a few years after the book was published. I cited this figure in my TED Talk, which is the only published source for the claim.” See this and other exchanges of comments here.

The book, written with US State Department political scientist, Maria J. Stephan, titled Why Civil Resistance Works: The Strategic Logic of Nonviolent Conflict, was published by Columbia University Press in 2011. An appendix (pp. 233-242) contains a list of 325 resistance campaigns that took place from 1900 to 2006. Of the total, 106 were classified as non-violent and 219 as violent. More than half (54.8%) of the non-violent campaigns were successful; 24.5% were partially successful and 21.7% were failures. Violent campaigns fared worse: only 26.5% were successful, 12.8% partially successful and 60.7% failures. For purposes of statistical analysis, the ‘partial success’ outcome was eliminated, but there is no indication of whether the authors placed them in the successful group or in the failure group. There is a more detailed appendix online, but I was unable to locate it.

This is a difficult book to understand, because little information is provided regarding the statistical analysis used. The technique is known as logit analysis; the dependent variable is unusual in that it takes only two values, 0 or 1 (in this case failure or success). The only thing the book contains that is close to the 3.5% rule is the following graph. Since the “probability of success” is calculated but never observed, this must be a logit curve. A true logit curve is simply a curve, not a scatter of observations. Possibly the scatter appears from calculation of probability, with adjustment for other variables. Otherwise all points would lie on the same logistic curve.

The chart below, from Wikipedia, provides an example of a logit (logistic) curve. All observations lie on the horizontal lines for success (1) or  failure (0). The S-shaped curve is simply the function estimated using the data shown by points on the graph.

Look again at figure 2.1 above. The horizontal axis measures the logarithm (presumably base 10) of campaign participants per thousand population. The number 0.5, then, represents 3.2, the square root of 10. Similarly, the number 1 represents 10, 1.5 is equal to 31.6 and 2 is 100 (10 squared). The 3.5% participation rate would then be equal to 35 participants per thousand population (1.54 in log form), predicting probability of success of about 85%. None of the participation rates come even close to 10% (2 on the horizontal axis of figure 2.1).

It is interesting that the authors found non-violent campaigns to be more successful, on average, than violent campaigns. Non-violent resistance can be successful, but success depends on many factors, so this work is a call for further research. I, for one, would like to see how figure 2.1 was constructed, in order to better understand what it shows. A good start would be for the authors to provide us with access to the now-hidden online appendix that “introduces and discusses the data compiled for this book and the various robustness checks performed to test the findings reported in the text” (p. 233).

Measurement is a problem with this research. Campaigns often contain both violent and non-violent activity. How do we measure success? Campaigns for resistance and change can be for good or for evil, and their worth is a subjective valuation. The Tea Party in the USA was a campaign of non-violent resistance that brought us the current government of Donald Trump. His support exceeds 40% – much higher than the 3.5% rule. Does this mean that, for the foreseeable future, we will have to live with the most powerful country in the world governed by Donald Trump and others like him?

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