The range of estimates for last weeks march is 15,000 (LAPD, LA Times) to 50,000 (ANSWER organizers) pretty wide range
The following is a repost from http://www.sciencenet.org.uk/news/2003/0203/crowds.html that might help explain the range
This scale of discrepancy between estimates from different sources is nothing new and is almost an intrinsic part of any march or demonstration. Generally, supporters will give the higher estimates whilst those that disapprove give the lower figures. Although it might make sense to assume that the ‘real’ figure lies somewhere in the middle, developing accurate methods of estimating crowd sizes would eliminate the need to make huge assumptions that are open to manipulation.
Currently, there are two main methods used to obtain crowd size estimates – both built on their own particular assumptions. Data can be obtained using a grid system, where aerial snapshots are taken and divided into squares so that the area occupied by the crowd can be established. By multiplying the average number of people per square metre by the total area of the crowd, a rough total can be estimated. The second method estimates the number of people marching by looking at flow rates. If the march has a defined route, CCTV and manual counters can be used to estimate the number of people passing one point in a period of time, so that an average can be used to estimate the final numbers.
But many factors can make these methods inaccurate. The grid system assumes a certain number of people standing in a square metre and this value, just as with the totals, can differ depending on who does the calculations. Furthermore, reality is much more complex as parts of the crowd will be much more crowded than others. The problem with flow measurements is that it assumes that the majority of people will march past those points being monitored – it doesn’t take into account those that join the march after the control points. On last Saturday’s march, for instance, it would have missed those people that went directly to Hyde Park.
Although combining the two methods can improve accuracy, scientists are striving to find better alternatives. Computer modelling programs are being developed to analyse and predict crowd dynamics. And interestingly, studies on the behaviour of social insects such as ants are providing scientists with valuable clues. It seems that when large numbers of us are concentrated in small areas we move pretty much like ants. Just as they follow each other to food sources so we seem to follow each other, but are then repelled when the crowd becomes too dense.
Although integrating this kind of information with the existing methods could be the solution to accurately estimating crowd numbers these studies are still in the early stages. It seems that for the time being we will have to agree to disagree on the number of people attending demonstrations.