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Math Trek

Probing Wikipedia editors’ hive mind for rules on cooperative behavior

Wikipedia, Encyclopedia, cooperation

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Wikipedia acts a bit like one big brain. Similar to how independently firing neurons somehow in aggregate produce thought, independently operating editors together produce the vast online encyclopedia, which, it has been argued, has an accuracy approaching that of the carefully curated Encyclopedia Brittanica. Taken as a whole, the system performs a sort of enormous computation, taking in the collective knowledge of the Internet and spitting out encyclopedia articles.

So just as neuroscientists look for rules that explain how the individual firing of neurons comes together to create the large-scale phenomenon of thought, Simon DeDeo of the Santa Fe Institute is looking for rules that explain how zillions of individual edits come together to produce encyclopedia articles. Those articles can be remarkably different from what any individual editor would produce. The entry for George W. Bush, for example, is the most heavily edited on Wikipedia, with 45,000 changes. Though each editor likely had strong opinions about him, the entry reads as a dispassionate exposition. Somehow the system was able to channel partisan discord into a single, generally coherent article. How? What rules underlie the group’s behavior?

These, of course, are such broad questions that scientists will be chewing on them for a long time to come — especially because DeDeo really wants to divine these types of driving rules for a wide variety of social systems. But Wikipedia made an especially good target for an initial stab at the questions because it makes so much data available, recording every last edit. DeDeo’s challenge was to figure out how to get a handle on the emergent dynamics, not just the individual behavior of editors.

The degree of cooperation between editors was one key behavior to analyze. A notable noncooperative behavior on Wikipedia is reversion, when an editor cancels a previous editor’s changes, returning the article to its earlier incarnation. This can lead to “revert wars” with individual editors insisting on their preferred version.

DeDeo analyzed data on the 10 most edited pages on Wikipedia, and he found that the longer the editors had worked together cooperatively, without reverts, the lower the likelihood the next edit would be a revert. It seems logical enough: Cooperation begets cooperation. But in addition, he found that the likelihood of a revert fell predictably according to a consistent mathematical law: On each of the pages, the probability of a revert declined as the square root of the length of time since the last revert. So the longer it’s been since the last revert, the lower the chance that the next edit will be a revert — but the probability falls quickly at first and more slowly later on. DeDeo described his results in July at the Santa Fe Institute and online at arXiv.org.


From one perspective, this is a surprisingly pessimistic result. Many standard models of reasoning would imply that people believe that there will be about as much cooperation in the future as they’ve seen in the past. DeDeo, together with Seth Lloyd of MIT, have realized that the square root law implies that although cooperation begets cooperation, it doesn’t beget quite that much: The square root law means that people believe that they will see less cooperation in the future than they have so far.

DeDeo has an intriguing hint that this square-root law might describe something fundamental to social systems. Together with Drew Cabaniss of the University of North Carolina, he has performed a similar analysis of revolutions in ancient Greece, figuring out the probability of revolution given how long a ruler has been in power. He has found preliminary evidence of the same thing: A revolution was less likely the longer a ruler had been in power, and the probability fell in proportion to the square root of the current ruler’s longevity.

DeDeo points out that his work has another implication: “Somehow the group itself has a memory.” The amount of time since the last revert influences the behavior of current editors, even though editors change over time and it’s possible that none have been actively editing the page the entire time since the last revert. DeDeo wants to understand how this institutional memory functions. One possibility is that editors assiduously read through the entire history of edits, but that is sufficiently time-consuming — particularly for the very heavily edited entries DeDeo studied — to make it unlikely. Another possibility is that the information is stored in the entry itself: A long period of cooperation may smooth out the issues that might attract a revert. A final possibility is that the community of editors might be affected by extended cooperation, forming a culture that makes them disinclined to revert.

DeDeo’s results give just a glimpse into how Wikipedia works at a deeper, hidden level, but it’s a tantalizing view. Our lives are increasingly influenced by social systems whose properties emerge from the loosely constrained behavior of many individuals, and we’re just beginning to develop the tools necessary to understand them. DeDeo’s work gives a glimmer of how mathematicians and scientists might proceed in untangling the workings of the hive mind.  

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