Percolation analysis 4 (the network is important)
Now I get to the main question I tried to address in this analysis. Given the basic pattern and the qualifications, what is the probability that the Viewer added the Owner's photo as a favorite? How does this probability depend on whether Viewer's contacts faved that photo?
First, some numbers. I observed in my sample almost 680 million instances of the basic pattern - that is, a Viewer having contacted at least one person who faved the Owner's photo. In almost 20 million cases, the Viewer has added the Owner as a contact. In slightly over 3 million cases, the Viewer has faved the image. Finally, the sample includes 961390 cases of the Viewer having both faved the image and added the Owner as a contact. I mention these numbers just to give an indication that the sample used is large.
(Incidentally, if I don't require even one contact of Viewer to have faved the image, the pattern exists some 2.47 10^10 times in my sample, including 40 million in which Viewer contacted Owner, 4 million in which Viewer faved the photo, and 1.34 million in which Viewer did both.)
Now for the interesting part about how it depends on the number of contacts that faved.
If Viewer has not added Owner as a contact (see blue graph), the probability that Viewer faved Owner's photo depends linearly with N: the more of Viewer's contacts that faved the photo, the more likely it is that Viewer will fave it as well. It is striking that this relationship is so strongly linear, but even more striking that if one extrapolates to N=0... the probability is nearly zero. In other words, if the person who posted the photo isn't in your contact list, and none of your contacts faved the photo, it is very unlikely that you faved it.
What if Viewer did add Owner as a contact? (see red graph) Again, the probability of Viewer having faved Owner's photo grows linearly with N, but it does so twice as fast. What about N=0, in this case? If none of your contacts faved the photo, but Owner is in your contact list, the probability you faved the photo is ~2.3%.
One way to account for all this would be the following scenario.
1) Imagine a Viewer that already has a number of contacts and is used to browsing the contacts' favorites. Now and then, Viewer will find a photo of interest and will fave it. Some photos will not capture Viewer's attention the first time they show up among a contact's favorites, but as they show up again and again in other contacts' favorite galleries... eventually they'll capture Viewer's attention, leading to a fave.
2) Viewer also visits the contacts' photostreams, gets exposed to their new photos, and faves some.
3) When browsing favorites, one sees both their thumbnails, and the photographer's flickr name. If the photographer is among Viewer's contacts, Viewer will recognize the name, and pay more attention to the image... and Viewer might have already seen the image in the photographer's photostream. These effects, combined, make it easier for a photo to capture Viewer's attention while browsing contact favorites, leading to more frequent faves.
Under the previous graph, I wrote about the inability to distinguish between "faving after contacting" and "contacting after faving", both of which happen in flickr. In that case, causality was hard to infer. This new graph shows that there is a strong relation between faving and one's contact network, which is not quite the same as with contacting the Owner. To clarify what I mean by this, consider these two statements:
1) "The more contacts of mine that faved an image, the more likely I am to fave it."
2) "When I fave an image, I tend to add as contacts the people that faved it."
The first statement is very intuitive and will happen if people browse their contacts' favorite galleries - and we know people do this.
The second statement is very counterintuitive. While technically possible, I don't think (based on my experience in flickr) that this is something people do.
When considering these results and scenarios like the one I described above, one has to keep in mind that Viewer is an intelligent human being, with a personality and a personal sense of aesthetics. It may sound very strange to claim that, even having no idea what Viewer's aesthetics and interests are, one can predict (in the sense of giving a probability) whether Viewer will fave a photo, solely based on the behavior of Viewer's contact network. Given enough Owners, photos, Viewers and contacts, though, one can make a statistical statement about the general trend. This is not unlike the axioms of Hari Seldon's Psychohistory: you can't predict the behavior of one person, but you can predict the behavior of many people.
In conclusion, information about photos does appear to percolate through the social network, via favorites.
(See the last slide...)