Signal -> Noise in Group Settings

This is a little exploration into something I was thinking about today.

My hypothesis is this:

Over time, the influenial members of a group will become dominant, such that the overall characteristics of the group will take on the properties of the influencers.


A little Mathematical Example To Set It Up:

If you graph a set of random data points it looks like a bumpy random graph.

If you have a bunch of random sets, and sum up the values at each point, you don’t get a random graph anymore. You get a uniform graph.

It’s like “White Noise”. You have a thousand signals all mashing up against each other - and the total sum of all the signals is a uniformly bland mildly randomly fluctuating signal we call white noise.

Now - let’s say you took the same system but introduced signal interference.

Let’s say some signals were “influencers” and others were “influenceable”. The influencers change nearby signals to be more like themselves. They don’t change themselves. The influenceable are dynamic, strongly picking up the properties of their neighbor signals, and weakly changing nearby signals to be more like themselves.

Now, in this system, initially, you’ll get a uniform signal, as you did before.

Again, my hypothesis is this:

Over time, the influencers will become dominant, such that the overall signal will take on the properties of the sum of the influencers.

What are the implications?

If there are lots of random influencers, you’ll get a uniform signal like before.

But if the number of influencers is small, or if the influencers tend to all have similar characteristics, you’ll get a signal that is driven by the influencers.

The original problem I wanted to solve was this:

Can I build a simulation to figure out how much of an impact an influential member of a group had compared to those who prefer to follow?


So I’m going to build something like this:

Take a 100x100 table of data, with each row being a “member” and each column being “some thing that they believe in to a certain extent”. The value of a particular node (x,y) tells us that x person feels F(x,y) about issue y.

Then I’ll put in a correlation of influence. Some people will be big influencers, others will tend to gravitate towards the ideas of others.

Each person x will have a list of “neighbors” that they directly affect. So, an influencer with a lot of neighbors should theoretically cause their values to become much more prominent in the overall system.

The question I want to find out is – how much of the overall signal over time is driven by the top X% of influencers? None? Lots?

How about if influencers operate in a heirarchy? Where some influencers influence other influencers.

Another question: How far away from the original signal can you get simply by selectively crafting the influencers? What if influencers can change the number of others that they influence over time?

hmmmmm..

One more: How simple of a system can you have before the effect is obvious?