Researchers in China investigated the question in a study published in the awesomely-named Chaos: An Interdisciplinary Journal of Nonlinear Science. Basically, the researchers harvested a bunch of twitter data from early 2011 through the site’s open API (application programming interface), sorted it all by topic (e.g., “iPhone 4” or “Arab Spring”, and then analysed the opinions of the tweeters as they progressed.
Researchers found that opinion evolves rapidly at first, but levels off quickly, with one opinion becoming dominant. Fluctuations cease, and the dominant opinion is endorsed by larger and larger groups. According to Fei Xiong, the study’s co-author, “Once public opinion stabilizes, it’s difficult to change.”