December 14, 2008

Six Degrees of Separation says, everyone is not that far from a random stranger in the world, the shorted path from one person to some stranger only has 6 hops.

While this sounds quite exciting, esp. to those Social Network System owners, the “dark side” of this idea is quite depressing: The trust between friends decreases at a very fast pace as the number of hops increases. In other words, you don’t trust their friends as you trust your frinds.

The question is: How fast does this trust thingy decrease as number of hops increases?

Let’s define trust as the probability you believe what one person says. People’s trust to themselves is 100%, and people don’t give a damn of whatever a stranger says, that’s 0. So trust is a value between 1 and 0.

Now we got 2 data points: Hop, or Degree of Separation is 0 (self), Trust is 1; Degree of Separation is 6 (stranger), Trust is 0. How about a linear function like this:

Frankly speaking, it’s more depressing than this. Instead of being linear, I believe it’s decreasing exponentially. Since you’ve being trusting me and followed this far in this post, why not bear with me for a couple of more formulars?

Let’s say the average trust between people is μ.If your friend Andy told you 100 stories today ( This Andy dude is quite talkative ) then you only believe 100 * μ stories. Let’s say you then pass those 100 * μ stories on to your friend Betty, how many stories will Betty believe? Only 100 * μ² stories.

Then what is the value of μ? I don’t know, some people trust their friends more than others do, people trust some of their friends more than other friends. One average, it is safe to say μ is ½. The graph below also confirms ½ is a good number: If a stranger (Degree of Separation is 6) told you 100 stories, you may believe 1 or so. In the graph below, μ is ½, Trust drops to 1.56% when Degree of Separation is 6, that’s “1 stories or so”.

Note that Turst drops to around 10% when Degree of Separation is 3. Trust does not go very far.


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