Researchers Find Innate Correlations Among Different Power Law Phenomena

November 17, 2009 By Lisa Zyga, feature

The Zipf plot of wealth and donation are innately connected. The upper part of the donation distribution follows Zipf’s law, and the Zipf exponent is equal to that of the corresponding wealth distribution. Image credit: Q. Chen, et al.
( -- Studying the patterns that emerge in natural and social phenomena is a popular area of research, although usually individual phenomena are studied separately from each other. In a recent study, researchers have found innate correlations among some of these phenomena, showing that the amount of money that individuals in a society donate to a charity can be used to determine the distribution of personal wealth in that society. The connection between these two topics can also be used for exploring the complexity of a society's economic system.

“The greatest significance of this work is showing that power law phenomena in different references may correlate with each other innately,” Yougui Wang of Beijing Normal University told “Thus, this implies that some power law phenomena should be the derivatives of other basic ones.”

The key to using patterns from one data set to infer the patterns of a different set of data is realizing that both sets share a mathematical principle called Zipf’s law, explained Wang, along with coauthors Qinghua Chen and Chao Wang of Beijing Normal University. Although Zipf’s law was originally proposed in the field of linguistics to explain the distribution of words in a language, it has attracted much more attention because it also describes a wide variety of natural and social phenomena. Zipf’s law quantitatively describes how the most common entities of a set (such as the common word “the”) appear with a high frequency that logarithmically tapers off as entities become less common. The same power law holds true for the distribution of population sizes, Internet traffic, and other phenomena. As researchers have previously found, in some cases the law stems from a competition among individuals for a constraint resource.

In the current study, the scientists show that collective donations follow a particular pattern: the upper part (made of the larger monetary donations) follows Zipf’s law, while the lower part (made of smaller donations) exhibits a uniform distribution. The data comes from donations by Chinese to the Chinese Red Cross Foundation after an earthquake of magnitude 8.0 struck Sichuan province in southwest China in May 2008. The data includes more than 230,000 personal donations, with the donation amount ranging from 0.01 RMB to 2.79 million RMB. Significantly, 205,000 donations (87.5%) of the total sample were 100 RMB or more. This part of the data approximately followed Zipf’s law, while the distribution of donations of less than 100 RMB was basically uniform.

So far, the analysis is yet another phenomenon of human behavior that follows the regularity of Zipf’s law. But the researchers also developed a model to explain this pattern, taking into account the previous finding that wealth distribution has also been known to follow Zipf’s law. Their model shows that only a portion of the individuals in a society have a desire to donate, and of these, each individual donates a portion of his or her overall wealth that is random but uniformly distributed. Even though only a small sample of the donators in the case of the Sichuan earthquake was collected and analyzed, the researchers’ model could generate the distribution of personal wealth throughout China, which is consistent with what has been obtained from the data of the richest 500 individuals in China.

As the researchers explain, donation and wealth, like other power law phenomena, seem to coexist in systems. By showing that power law phenomena can be related to one another, the researchers’ work could be valuable for exploring the correlations among natural patterns in systems.

“Based on the results of our study, the distribution of wealth could be derived from that of donation,” said Qinghua Chen. “Once the link between two variables involved in a complex system is just like the relation between donation and wealth in our case, we can infer the distribution of one variable from the other.”

More information: Q. Chen, C. Wang, and Y. Wang. “Deformed Zipf’s law in personal donation.” Europhysics Letters, 88 (2009) 38001. doi: 10.1209/0295-5075/88/38001

Copyright 2009
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1 / 5 (1) Nov 17, 2009
That's neat, but I'm not too impressed with the ability to develop a model that maps a correlation between two known sets of data. Until they demonstrate that the model can actually predict unknown values, it's just plain not science.
not rated yet Nov 17, 2009
Was this donation organized by Chinese government? Or are rich people altruistic exactly in the same ratio, like these poor ones?
5 / 5 (1) Nov 17, 2009

It is very much science to model data, and to make careful and critical observations. It's by this action, of analysis, that eventually through testing and continued research models which make reliable predictions, such as what you propose, can be realized.

Making progress towards an answer, while not having the answer, is science in action. Science inherently makes no promises about being able to answer any given question, but instead sets the rules and guidelines on how answers can be logically deducded.

You fail at understanding science, and the scientific process.
not rated yet Nov 17, 2009
Did i miss something here?
"each individual donates a portion of his or her overall wealth that is random but uniformly distributed."
Can you explain that seemingly-contradictory statement?
5 / 5 (3) Nov 20, 2009
Sincerely Two;

You misunderstand me. The scientific process is, of course, as you describe. However, the claims that appear to be being made (and perhaps there is an issue with translation, as well as the usual issues with science journalism) are not substantiated by the efforts described within the article. The article headline declares that the researchers have found innate correlations among different power law phenomena. I do not believe that this can be satisfactorily demonstrated by the fit of an 'a posteriori' model to original data. This was the aspect of the information before me which I sought to criticize.

It is important to realize that neither Yougui Wang nor Qinghua Chen seem to have intended to claim this, but they were perhaps excited enough by such a hypothesis to speculate incautiously in front of journalists without ensuring that the latter understood the distinction between what had and had not been proven.
not rated yet Nov 20, 2009

Yea, looks like I did misunderstand. I developed the habit of assuming the journalists just get carried away and just focused on the fact that this kind of data was being collected and analyzed. So... of course, I took your criticisms as being of the researchers and not of the writers. xD my bad. Gotta love those subtle 'context-conflicts', if that's a good way to describe it.
5 / 5 (1) Nov 20, 2009
Suppose one has two sets of data and finds they fit the same mathematical curve. But one cannot take for granted that, there is an innate correlation between the phenomena, unless he is able to logically deduce one set from the other. It is plain that, a mathematical structure underlies quite different phenomena. In physics, examples are ample. Two completely unrelated phenomena can bear the same mathematical structure. For example, one finds 'Dirac particles' in graphene.
not rated yet Nov 20, 2009
hiyok, yea, that should be pretty obvious to any professional scientist/researcher, and people at least with average intelligence. The point of doing that for a living is to actually discern illusion from fact. Unless like in most other careers it's easy for anyone to get the degree and just as easy to poison the field with poor practice. >:\ bleh. I'm sure those researchers are not sitting there saying; "It looks the same, therefore it is the same!"

Then again I could be flawed by so easily biasing on the side of optimism (by nature), and cynicism by choice. ^_^
5 / 5 (1) Nov 22, 2009
Did i miss something here?
"each individual donates a portion of his or her overall wealth that is random but uniformly distributed."
Can you explain that seemingly-contradictory statement?

The statement is not at all contradictory but I can understand how the description of some phenomenon as being both random and uniform may sound counter-intuitive. Consult the "Uniform Distribution" article on Woolfram's Math World for details. The speaker/writer simply means that the distribution of donations vs. wealth (within a certain unspecified range) fits this mathematical model better than the Zipf's Law model (a flat, horizontal line instead of a logarithmic curve). This implies that, among those whose wealth places them in the unspecified range, the number of stingy people is approximately equal to the number of generous people. In other words, (Chinese) people in this range give as much as or as little as they want, regardless of income/assets.
not rated yet Nov 22, 2009
Was this donation organized by Chinese government? Or are rich people altruistic exactly in the same ratio, like these poor ones?

Recent evidence suggests people's political/moral values correlate with donations. Rich, liberal democrats donate less than poorer, conservative republicans who attend church.


You must be joking. How many thousands of people die in the name of religion? Who voted for that last worthless flop of a president that damaged America...
Get off your superiority kick and open your eyes.

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