I finally got around to carefully reading “A Theory of the Critical Mass…” by Oliver, Marwell, and Teixeira. Now I’m asking: what took me so long?

The article formalizes the notion of critical mass in collective action. It identifies two main independent variables that can influence the “probability, extent, and effectiveness of group actions in pursuit of collective goods”:

  • The form of the “production function” that relates “contributions of resources to the level of the collective good”. Two important categories of production functions are: (a) decelerating: the “first few units of resources contributed have the biggest effect on the collective good, and subsequent contributions progressively less”; (b) accelerating: “successive contributions generate progressively larger payoffs; therefore, each contribution makes the next one more
  • The “heterogeneity of interests and resources” in the population of potentially interested actors.

The authors then show that the problems and opportunities for collective action are very different for accelerating vs. decelerating production functions and for homogeneous vs. heterogeneous populations of actions. I’m not going to summarize the findings: the paper is a joy to read, so I mostly want to urge you to do that.

However, there were a couple of ideas that I found particularly relevant to issues in open content systems that I care about, so I did want to mention them.

First, this work looks at critical mass in “public” goods, where all the value is created by a group of people. This is true for many open content systems: Wikipedia and OpenStreetMap are two good examples. However, this isn’t true of other systems, including our Cyclopath bicycle routing system. Cyclopath began with a nearly complete transportation map created from Mn/DOT data and with a good objective route-finding algorithm that did not require user input. While we have shown that user input improves route-finding significantly and that algorithms based on user input are better than purely objective algorithms, I think it’s fair to say that most of the value of the Cyclopath “good” already was present before any user contributions were made. It’s interesting to consider how the concepts of this paper can be applied to a system like Cyclopath.

Second, Oliver at al. show that with decelerating production functions, the optimal outcome would be achieved if the *least* interested people contribute first and the *most* interested people contribute later. This obviously isn’t the way it usually works. They point out that one way to make this happen is for the most interested parties to “hold back”; perhaps they can offer “matching contributions” to entice less interested parties to contribute early in the process. This might suggest new strategies for intelligent-task-routing-like strategies to elicit participation in open content communities.

Third, many of the illustrative examples the authors give concern the different opportunities for collective action in “upper middle class” vs. “lower income” neighborhoods. I wonder: what’s the equivalent of an “upper middle class” open content system?

Fourth, the notion of “interest” presumed here is one of direct tangible personal benefit: if I give N dollars, I’m increasing the chances that I’ll receive M dollars (M >> N). However, we know that many contributors to open content systems (and many ‘volunteers’, too) contribute for other types of reasons, e.g., they “believe” in the public good, they are altruistic, or they want to build a reputation. For example, in Cyclopath, our most active editors don’t request many routes. For another example, other researchers have shown that there are many users in discussion forums who just answer questions and don’t ask any of their own.

Fifth, finally, and simply, I’d like to empirically measure the production function in various open content systems. I suspect that in many cases it is decelerating: i.e., early units of contribution are proportionally more valuable. I’d also like to measure this for individual users. Doing this calculation requires a way to measure the global quality of an open content system as well as the quality for a particular user. We can do both of these for Cyclopath. We can do the latter for MovieLens… not sure about the former.

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