Small Worlds Hypothesis

In the 1960’s Stanley Milgram and Jeffrey Travers tried an experiment sending letters.

  1. They sent letters to randomly selected individuals. In each letter was letter explaining the experiment and details of the target person.
  2. If the person receiving the letter knew the target they could forward the letter directly. If they didn’t know the target they were to forward the letter on to to someone they knew who would be more likely to know this person.
  3. Each time to letter was forwarded the forwarder added their name and sent an attached postcard to the researchers. In this way the progress of the letters could be tracked.

The result as its widely spread is the 6 degrees of separation in that on average it took 6 steps between the person who began the process and the person receiving it. So what gets spread about is you are on average 6 people away from anyone else in the world.

Actually it isn’t quite that simple

In fact if you read the experimental paper its not that simple. The target is a stockbroker in Boston of the starting points

  • 196 were solicited by mail in Nebraska of these:
  • 100 were owners of blue chip stocks.
  • 100 volunteers were solicited through a Boston Newspaper

so 296 altogether.

Because the each person forwarding the letter could see who had previously handled it loops were avoided.

217 of 296 letters were sent on of which 64 actually reached the target. Of the completed chains the average distribution of links was 5.2 which is the number that gets rounded up to 6 degrees. So your discounting all the broken or abandoned chains.

To be fair the experimenters spot many of the issues and knowledge them these include

  • The starting points had a strong bias towards being middle class and the target was also middle class.
  • It depends very much on how well the participants were motivated.
  • Your avoiding the odd cases recluses and people who travel constantly for example.

Partly they were interested in how the letters were traveling was it based on geography, or through professional networks.

Failing or incomplete chains

The mean distribution of failed chains in 2.6 there was also a difference between the letters that originated in Boston where the chain was 4.4 and from Nebraska random where the chain length is 5.7 and Nebraska stockholders were 5.5.

Interestingly there was a lot of convergence with people towards the end of the chain occurring repeatedly. Think this is probably one of the more interesting things and linked to ‘super influencers’ and the hubs between networks.

So its interesting but its not so simple as everyone is separated by 6 degrees of separation.