The Dubious Power of Power Laws
A plethora of things in nature follow a normal distribution. This can be explained via the Central Limit Theorem, which states that the sampling distribution of the sample means approaches a normal distribution as the sample size increases. Following a normal distribution means that the majority of the measurements of independent quantities are centered around the average, with values around the average being large and values far from the mean being small. Some examples include people’s heights, blood pressure, wealth, and even intelligence. However, normal distributions are not the only naturally occurring distribution.
There are also heavy-tailed distributions which are well described by power laws. These arise from the feedback introduced by correlated decisions across a population and as a result are commonly associated with the preferential attachment phenomena which presents itself as the rich get richer phenomena in economics. An issue with power laws is that they exhibit the equifinality – the principle in which the same outcomes can be produced by different processes.
The claim made is “equifinality makes it problematic to infer causes from outcomes, because there is not a one-to-one relationship between formative mechanisms and the resulting statistical distributions.” What this means that power laws alone, unlike the normal distribution, do not reveal anything about nature. They simply represent patterns which can occur via a “number of different causes – equifinality.”
This is interesting to think about. Comparing directly to the rich get richer phenomena taught in class, the articles claim becomes questionable. Power law models are built from “the observable consequences of decision-making in the presence of cascade.” All that means is that people tend to follow the decisions of the people prior to them. In the case of the rich get richer model, it can not only be proved that the model follows a power law, but knowing the model follows a power law gives you more information than just “rich get richer follows a power law”. The evolution of the network over time can be predicted, as well as the actions people are likely to take in relation to the network.
In conclusion, the resource connected to discusses a lot of the material discussed in class on power laws. However, it introduces the claim that while a lot of things do follow a power law, that information doesn’t give you anything except that a power law distribution explains the event. In analysis of this claim, it is determined that it doesn’t appear entirely correct, since power laws do arise naturally in nature.
Sources
https://geography.as.uky.edu/blogs/jdp/dubious-power-power-laws
https://www.definitions.net/definition/equifinality
Easley, David, and Jon Kleinberg. Networks, Crowds, and Markets Reasoning about a Highly Connected World. Cambridge University Press, 2010.