I came across this article about the data mining team in Obama's reelection campaign. Unfortunately, the article is very fuzzy about the actual machinery of the statistical algorithms. However, it sounded as if the general techniques are known in social and political sciences. Since this is not my area of expertise, can anyone point me at (overview) literature about these kind of techniques?
That area is called microtargeting (if you would like to google for it). Campaigns are pretty secretive about their tools and procedures, so to my knowledge there is not that much published work except Hal Malchow's Political Targeting (2008) or Green & Gerber's (2008) Get out the Vote: How to Increase Voter Turnout (the latter deals more with social science aspects like what ads are effective and such).
On more technical matters the literature is even scarcer, but see, e.g, Murray & Scime (2010), the Political Analysis paper by Imai & Strauss (2011) (postprint) or the recent Annals of Applied Statistics paper by Rusch, Lee, Hornik, Jank & Zeileis (2013) (postprint). What they all have in common is that they make use of data mining techniques, mostly tree based.
Murray & Scime use standard classification trees like CART.
Rusch et al. use classification trees, logistic models and a hybrid of trees and logistic regression. They also use (among others) random forests, neural networks, support vector machines and Bayesian Additive Regression trees to compare with their tree hybrids, as is described in the rejoinder to their paper. Their hybrid trees performed on par with those other methods on their data sets and offer increased interpretability (they also share their code and data, which is nice).
Imai & Strauss is interesting insofar as they present a comprehensive decision theoretic framework for optimal campaign planning, not just tools for microtargeting as the others do. Thus they are very much focusing on aspects of operational research about how to get the most out of every dollar put into a the campaign. In the aspect of their framework where they employ statistical techniques for microtargeting and turnout estimation, they again rely on classification trees.
So, there seems to be some consensus that the usage of tree based methods work well in this area.