The Math of Charity

Researchers have found heavy-tailed distributions in many phenomena, from the frequency of words to the sizes of cities. And they've even been found in how people give money to charity, such as how people responded with donations after the 2004 tsunami. These donations obeyed certain probability distributions, but also seemed to have certain features of how an epidemic spreads (I discussed it here).

In a new paper posted to the arXiv, researchers at the University of Vermont decided to compare the patterns in giving to several different types of institutions: educational, health care, the arts, and more. And they found distinctive differences, between institutions and the types of institutions. Here is a figure that provides an overview of the distributions of donations:

The entire paper has a lot of interesting details—including recommendations for fundraisers!—but here's the upshot:

The distribution of gifts received by nonprofit institutions is approximately consistent with a power-law size model. Individual institutions, and possibly broad of categories institutions, have their own characteristic scaling exponent γ. Fundraising projections modeled on power laws may be useful for predicting the success of a given campaign, and for affecting the strategic planning of a campaign.

Check out the full paper here.

Top image:Yukiko Mutsuoko/Flickr/CC