Stubborn Effectiveness
In lecture we discussed the important relationship between a node’s location in a network and how much power the node can wield. In the most basic examples reviewed in class, all nodes were offering each other very basic, mutually beneficial deals, and were only differentiated by their positions relative to each other. However, the principal applies to more complicated situations, with more variables occasionally swinging the results to heavily favor the connected few. In a study done by Michael Kearns at the University of Pennsylvania, subjects were placed in a network of 36 nodes of varying amounts of interconnectedness. The subjects then had to vote either blue or red, and would each receive payment if the entire group were to reach a consensus within a minute. To vary the results of the experiment, the individual nodes were also given varying specific incentives to swing to one side or another (i.e. they would receive more if a certain color won and less if another color won).
The results showed a surprising effect of powerful individuals. Unsurprisingly, the best connected individuals were the most influential, meaning the nodes with the most connections were disproportionately influential in the final decisions. This allowed those few to force decisions in short time, meaning the entire network voted one way or another in 55 out of the 81 trials. More interesting was the fact that the differences in pay among the subjects made some individuals more stubborn, since they had a far greater incentive to vote one way. Because of this, “Kearns found that the spoils went to those who were most stubborn – but not completely intractable.” Because of the fast nature of the game, the whole group would often benefit from a few subjects tirelessly insisting on one outcome. Ironically, sometimes this would not represent the group’s greatest social welfare: in one instance, six nodes with a greater red incentive convinced the remaining thirty blues to change to red.
Unlike the pairing games demonstrated in class, in the Kearns study there was a much smaller limit on how connected the most powerful nodes could be. On a small scale (five nodes) there is a strong counterbalancing effect; the middle of five linear nodes, though the most connected, is weakened by the stronger ties generated by its neighbors and their neighbors. On the other hand, the Kearns study allowed the most connected to always have a greater advantage, since the larger nature of the network meant a well connected node would not be surrounded by similarly powerful nodes. This seems to be more analogous to any hypothetical real-life situation: someone who is very well connected will always be at a greater advantage, since there are not many nodes who are as well connected to balance them out.
http://phys.org/news156957899.html
-TCP