There are (likely) many ways in which tweets allow for collective intelligence. I will offer one example of how this works.
Tweets are made up of text, with an invisible cachet of metadata — I say invisible but that’s not true at all. Geolocation, the source of a Tweet (i.e. the application that is the means of the tweet), the tweet that may have been the source of a tweet-as-response — these are all viewable depending on the manner in which you view a particular tweet.
One study that was conducted by MIT focused on the semantic density on Twitter as medium of “highly emotional words.” They looked at the appearance of words that indicated extreme emotions randomly selected through the main Twitter stream. What the researchers at MIT found was that there was evidence indicating a correlation between the increase of highly emotional words on Twitter and a dip (never, apparently, rise despite the emotions arguably conveyed) a few days later in the DowJones Index.
Read here for more details on this particular study:
What this study did not do, however, is perform a diffusion analysis of words that eminate from “influencers” on Twitter. Twitter users are networked together, and clearly looking only at re-tweets as one crude example of behavior that demonstrates influence could be analyzed for the appearance, in the same problem space as what MIT studied, for the source of highly emotional words and how such messages are amplified. This isn’t necessarily a great study — but it would be an interesting one that examined networked behavior with regards to collective intelligence.
I personally feel there are more interesting studies to be performed with tweets than as an arguable indicator of the DowJones (human migration patterns using census data, time between joblessness and new employment, goal attenuation and networked behavior, how many popular ideas originate when people are tweeting from their bathroom — just to name a few). However, the MIT study is certainly a documented example that supports that tweets do allow for collective intelligence, simply by the fact that there is text that represents an idea that is shared, thus potentially influencing others.