My street is a Halloween Mecca.  People flock from neighboring blocks to a section of my street and to the street just North of us.  (Ours is an East-West street as are most of the residential streets in the area.) And I have noticed that in other neighborhoods in the area and in other places I have lived there is usually a local, focal Halloween hub where most of the action is.

And on those blocks where most of the action is the residents expect that they will get most of the action.  They stock more candy, they lavishly decorate their yards, and they host haunted houses.  They even serve beer.  (To the parents)

I think I have figured out why we coordinated on my street.

In a perfectly symmetric neighborhood lattice, trick-or-treating is more or less a random walk. With a town full of randomly walking trick-or-treaters every location sees on average the same amount of traffic.  Inevitably, one location will randomly receive an unusually large amount of traffic, those residents will come to expect it next year, decorate their street, and reinforce the trend.  Then it becomes the focal point.

In this perfectly uniform grid, any location is equally likely to become that focal point.  That is the benchmark model.

But neighborhoods aren’t symmetric.  One particular asymmetry in my neighborhood explains why it was more likely that my street became the focal point.  Two streets to the South is a major traffic lane that breaks up the residential lattice.  In terms of our Halloween random walk, that street is a reflecting barrier.  People on the street just to the South of us will all be reflected to our street.  In addition we will receive the usual fraction of the traffic from streets to the North.  So, even before any coordination takes hold our street will see more than the average density of trick-or-treeters.  For that reason we have a greater chance of becoming the focal point.  And we did.