# Who are the most influential cows in a herd of cattle?

You have a herd of cattle moving in different directions. The cows in the herd are more or less always moving, at different direction and in different velocities.When a cow bumps another cow it affects its direction and perhaps its speed so that they would not keep brushing up against each other. If we take a snapshot of this herd of cattle, we can try to predict the eventual direction of the herd by looking at the edges - for example, if all cattle at the bottom of the herd and at the sides are moving up in a forceful manner, we can imagine the cattle in the middle will change their direction upwards as well (because that's the path of least resistance).

We can also think of a different example. We can imagine a group of academic researchers such that each researcher has some degree of influence on others. Each researcher also has his own topic, which could range from biotechnology to environmental science to algebra. When we observe this system over time, we can imagine that researchers (assuming they're not particularly independent) will change their "research direction" over time to fit the direction of the science herd, and we can probably point out the researchers that will have the most "pull" in setting this direction.

My question is, given this sort of setting in the abstract and in a specific moment in time, how do we identify which actors will have the most influence on the eventual direction of the group (Human beings seem to be able to do this quite intuitively!)? Has this problem been studied?

• What you are interested in appears to be similar to the notion of "flocking," for which there is a wide body of literature. See e.g. dtic.mil/dtic/tr/fulltext/u2/a462317.pdf Aug 1, 2014 at 22:28
• BTW, a conclusion of the paper that I referred to above is that "flocks need no leaders." Aug 1, 2014 at 22:29
• I'll definitely have a look at this.
– mich
Aug 1, 2014 at 22:32
• Would you call this 'cow-nian' motion? Aug 2, 2014 at 0:01

Yes they are. Here are 2 articles (1 and 2) about opinion formation and how you can represent that in terms of basic interaction between participants.

I had once read that you can find a very simple process that produces Pareto distribution, which gives you a possible reason for why the distribution wealth in society looks like that.

I'm sure google will give you many more examples.

• Thank you :). You accidentally linked to the same article twice, though.
– mich
Aug 1, 2014 at 22:37
• @Michael They're slightly different but from the same journal. It takes a keen eye to spot the difference (One letter in the title) :) Aug 2, 2014 at 10:29
• Ha! I spotted it now.
– mich
Aug 2, 2014 at 21:50