Counting a crowd is not necessarily difficult, even when the numbers are "large": the exact attendance at a football match is known. But at a demonstration, no one is sitting in a numbered seat! Estimating the number of protesters runs into the two main problems statisticians face: deciding what to count and how to count it.
Knowing what to count begins with trying to define the object of study precisely. This is no easy matter, since the concepts of a "protest" and a "protester" can describe a wide variety of situations: a protest may be on the move—such as the traditional Bastille-to-Nation march on May 1st—or stationary—such as the rally in support of François Fillon at the Trocadéro on March 5, 2017. It may also be widely dispersed geographically, like the "yellow vest" protests at roundabouts in the winter of 2018–2019. Likewise, must protesters be present from beginning to end to be counted? What about someone who attends only briefly, or someone who stays on the sidewalk without joining the march but waves a placard? Conversely, what about someone caught up in the flow of the march who simply wants to get home? Establishing a counting method requires assumptions about what constitutes a protest and a protester. Two counts will not produce the same result if they are not based on the same definitions or assumptions.
How to count protesters? -----------------
Several techniques, which are not mutually exclusive, can be used to estimate the size of a demonstration. The simplest is merely to count the people who pass an observer. In practice, two people facing each other use mechanical tally counters to count everyone who passes between them. Allowing for errors and omissions, this produces a figure for the number of protesters… who walked as far as that counting point. To prevent manipulation, such as a protester passing the counters several times, organizers are not told where the observation post is, and observers are generally positioned above ground level for a better view. This technique is relatively effective for marches, although fatigue among the counters can lead to a growing underestimate of the number of protesters over time. An arbitrary adjustment—10%, for example—may be applied to allow for omissions and protesters who bypassed the counting gate. This method has the advantage of requiring very little technical equipment.
Another method is to consider the demonstration as a whole: its occupied area is calculated from a map, then multiplied by a visually estimated density of people per square metre to obtain the number of protesters. This technique is useful for stationary rallies (see box), but is better at detecting implausible estimates than producing a precise figure. The method also works for moving demonstrations if the rear of the march sets off before the front reaches its destination, since an area can then be calculated.