Small percentages, large numbers, and political “events”

Insight from an old article: where there are lots of people, small percentages of people can have a big absolute impact.

Reading Marc Stears’ Demanding Democracy yesterday, I realized that I didn’t know what had happened at Columbia in 1968 (as opposed to Berkeley and Cornell) and decided to chase down one of his footnotes: Allen H. Barton, “The Columbia Crisis” (Public Opinion Quarterly 32 [1968]: 333-51; academic paywall). Three things about it struck me.

1. An article like this would never be published in an academic social science journal today (except maybe PS: Political Science and Politics). Right after the Columbia sit-in and violent police response, Barton designed and sent out a survey on it (funded by a research institute at Columbia, which also probably wouldn’t fund such a thing nowadays); wrote it up and got it published in record time—the events happened in the Spring of ’68 and the article appeared in the Fall—and reported the results as a contribution to a real-life political debate, not a theoretical debate within political science or sociology (Barton’s field). We’ve gained a lot as social science fields have become more professionalized, but we’ve also lost something.

2. Barton was eerily prescient about what might happen if, as seemed likely when he wrote, the parties nominated Nixon and Humphrey in 1968 and left antiwar voters with no outlet for their anger: alienation and mass protest, met by calls for “law and order” on the other side, with the prospect of even-greater polarization and a widening generation gap (full quotation at the bottom of this post). When I was in graduate school, it was common for professors to lament the demise of the old politics in which party elites were able to focus on economic issues and keep “distracting” questions off the agenda. That was wrong, and Garry Wills after the fact, like Barton before it, was right: our politics suffered permanent harm when opponents of the Vietnam War, having become a near-majority of the public, were unable to vote for a candidate who clearly represented that position (as opposed to Humphrey’s late and, it seems, unconvincing evolution).

3. Barton said something about small minorities and large numbers that really matters and that I’ve never seen expressed so well. Slightly misreading one of his own tables showing that only 17 percent of Columbia students thought it was all right for protestors to have broken into President Kirk’s office and copied many of his files, Barton wrote (on p. 337):

    “Here the importance of absolute numbers as compared with proportions must be considered. In a referendum or an election, 19 per cent of the vote does not amount to much. On the other hand, 19 per cent of 17,000 students amounts to 3,250 people—a formidable picket line, sit-in group, or crowd. If the remaining 81 per cent are motivated to take counter-action, the result might be a smashing victory for the majority in a pushing match or a fight. But, as long as the majority remain passive, a minority of 19 per cent can completely tie up a campus; while if part of the majority is activated, or the police are called, the minority can turn the campus into a battleground” (emphasis in original).

Faculty prone to feel intimidated by student protests should note this: if there were Bartons around to survey things and institutes to fund them, we would almost always find that what seem like large numbers of students in favor of some outrageous action, like shouting down a visiting speaker or vandalizing signs, represent small percentages. (This realization might well motivate a certain contempt towards extreme self-styled student leaders, but greater respect towards students as a whole.) 

This also explains why notable political “events” typically occur in places that are populous in absolute terms: for better or worse, a small minority can make a lot of noise in New York, but not so much in Needles. The average New Yorker need not be particularly committed in order for New York to be the center of all sorts of activism. And the same is true of UCLA vis-à-vis Colby College.

In both instances of populous locales, by the way, the chance to have a dramatic impact out of proportion to one’s percentage support might motivate a taste for protest politics—as opposed to the kind based on voting, where those percentages would tell. The problem of collective action may be reversed for this limited purpose: the larger the number of people present in a place, the more sense it makes to stage a confrontational protest rather than running a candidate.

No doubt this insight is familiar to many. It probably even has a name. But it was new to me. And one of the many joys of academe is the constant chance of finding an idea you’ll remember forever in a past work that might seem destined for little influence beyond its own moment.


Here’s the Barton quotation mentioned in point 2 (from p. 351):

“What will happen if the anti-war majority of students and faculty are confronted with a Humphrey-Nixon campaign this fall? … [T]he great majority of Columbia students and faculty, and others like them throughout the country, will be extremely alienated from normal politics.

“Some may withdraw in disgust, but the war and the draft of students make it almost impossible for students or professors to retire into their ivory towers. There is a distinct possibility that the massive civil disobedience practiced by a campus minority this spring may be transferred to the national political arena this fall, with widespread support from students and faculty. Massive confrontations and illegal demonstrations against the candidates, the draft, and the war would in turn bring demands for stern enforcement of ‘law and order,’ which would carry the process of alienation further in a vicious circle, widening the ‘generation gap’ and the political divisions in the country. The effect of alienation a generation of students and a large section of the intellectuals from normal political channels can be very serious both for universities and for nations, as demonstrated in other countries as well as the United States.”


Author: Andrew Sabl

Andrew Sabl, a political theorist, is Associate Professor of Political Science at the University of Toronto. He is the author of Ruling Passions: Political Offices and Democratic Ethics and Hume’s Politics: Coordination and Crisis in the History of England, both from Princeton University Press. His research interests include political ethics, liberal and democratic theory, toleration, the work of David Hume, and the realist school of contemporary political thought. He is currently finishing a book for Harvard University Press titled The Uses of Hypocrisy: An Essay on Toleration. He divides his time between Toronto and Brooklyn.

7 thoughts on “Small percentages, large numbers, and political “events””

  1. For other examples, see the Bolsheviks in 1917-18 and the Nazi party in Germany in 1933.

  2. How do you fit McGovern into this paradigm? His nomination for president in 1972 surely gave the anti-war vote the opportunity to be heard? Yet it was Nixon’s “Silent Majority” that again won the day. I’ve often wondered whether “pro-peace/anti-war” was a bridge too far.

    1. You’re missing the point. Barton’s saying that large-scale unrest follows when a widely-held view isn’t represented on election day. Are you perhaps thinking that he’s suggesting that unrest followed when a widely-held view is merely defeated on election day?

      Nixon won both elections, but 1972 wasn’t anything like 1968. This fits entirely within Barton’s “paradigm” when you consider that the anti-war view wasn’t represented in 1968 and was in 1972.

  3. Was this triggered by the latest Supreme Court ruling?

    “Barton was eerily prescient about what might happen if, as seemed likely when he wrote, the parties nominated Nixon and Humphrey in 1968 and left antiwar voters with no outlet for their anger” seems somewhat relevant to a Republican Party hellbent on (and with the way forward opened up by Roberts et al) disenfranchising anyone it can who doesn’t vote Republican…

  4. “opponents of the Vietnam War, having become a near-majority of the public” — it’s probably OK to stipulate this, and it makes sense when connected with the (unmeasurable) alienation Barton mentioned. What else can explain the crushing defeat by Nixon of an explicitly antiwar candidate four years later? What I never heard from the antiwar coalition was anything about how the war should be ended, apart from a (presumed) unconditional American withdrawal. What Nixon delivered was, beginning within a year of his inauguration, a steady decline in US casualties and some cosmetic improvements in the South Vietnamese political situation (an end to revolving-door military coups, token land reform, etc.). In the fall of 1972 he was able to claim that “peace is at hand,” a peace that would preserve the South Vietnamese regime — one clearly-understood objective that brought us into the war nearly a decade earlier. Whatever fraction of Nixon’s “silent majority” had opposed continuing the war four years earlier, had clearly jumped ship at the prospect of a negotiated peace on terms that were outwardly not unlike what we had achieved in the Korean War.

  5. On the publication turnaround, I had my study of the Dixie Chicks blacklist in the mail about six weeks after the event occurred. It got a first round conditional accept and appeared in print about 18 months after the precipitating event. That’s the left-tail of publication lag. Like most of us, it usually takes me about 3 or 4 years to go from conception to publication if I’m actively working on it the whole time. This is one of the reasons I’m excited about Sociological Science, which is promising expedited up-or-down reviews with no R+Rs and immediate pre-prints. If it proves successful we could very well see poli sci journals adopt the model.

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