This floated around last October -- John Bethencourt simulated group decisionmaking in a group of 40,000 students who were deciding on what date to celebrate Halloween (it fell on a Thursday in 2002.) The key factor was that no one could talk to any more than single digits of other students at the same time, so voting was verboten and consensus would be emergent and time consuming.

As it turns out, for group conversation sizes of between 3 and 8, the graph converges smoothly on on an answer, as one of the three days quickly emerges as a slight front-runner, slowly gathers momentum, and finishes by quickly grows to 95% agreement. The hypothetical process takes 9 days if people can talk in groups of up to 8, while it takes 50 days if people can only talk in groups of 3, as message passing overhead grows with the square of the number of groups, the downisde of Metcalfe's Law.

The most important part of the work, though, is to put our sense that groups are different than pairs (the "3 is a Magic Number" principle) to a simulated test, and indeed, communication in overlapping pairs is very different than communication in even small groups.

The really interesting things happen when we have a maximum friend count of two. That is, each person may consult only one or two others each day (always the same one or two). At this point, the system becomes extremely chaotic and unstable. Although it does eventually reach agreement, it takes a *very* long time.

The dramatic change in the communications graphs between pairwise and group conversation illustrates the same observation.