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Researchers who generate data often optimize efficiency and robustness by choosing stratified over simple random sampling designs. Yet, all theories of inference proposed to justify matching methods are based on simple random sampling. This is all the more troubling because, although these theories require exact matching, most matching applications resort to some form of ex post stratification (on a propensity score, distance metric, or the covariates) to find approximate matches, thus nullifying the statistical properties these theories are designed to ensure. Fortunately, the type of sampling used in a theory of inference is an axiom, rather than an assumption vulnerable to being proven wrong, and so we can replace simple with stratified sampling, so long as we can show, as we do here, that the implications of the theory are coherent and remain true. Properties of estimators based on this theory are much easier to understand and can be satisfied without the unattractive properties of existing theories, such as assumptions hidden in data analyses rather than stated up front, asymptotics, unfamiliar estimators, and complex variance calculations. Our theory of inference makes it possible for researchers to treat matching as a simple form of preprocessing to reduce model dependence, after which all the familiar inferential techniques and uncertainty calculations can be applied. This theory also allows binary, multicategory, and continuous treatment variables from the outset and straightforward extensions for imperfect treatment assignment and different versions of treatments.

We discuss a method for improving causal inferences called "Coarsened Exact Matching" (CEM), and the new "Monotonic Imbalance Bounding" (MIB) class of matching methods from which CEM is derived. We summarize what is known about CEM and MIB, derive and illustrate several new desirable statistical properties of CEM, and then propose a variety of useful extensions. We show that CEM possesses a wide range of statistical properties not available in most other matching methods but is at the same time exceptionally easy to comprehend and use. We focus on the connection between theoretical properties and practical applications. We also make available easy-to-use open source software forR, Stata, andSPSSthat implement all our suggestions.

The growing usage of social media by a wider audience of citizens sharply increases the possibility of investigating the web as a device to explore and track political preferences. In the present paper we apply a method recently proposed by other social scientists to three different scenarios, by analyzing on one side the online popularity of Italian political leaders throughout 2011, and on the other the voting intention of French Internet users in both the 2012 presidential ballot and the subsequent legislative election. While Internet users are not necessarily representative of the whole population of a country's citizens, our analysis shows a remarkable ability for social media to forecast electoral results, as well as a noteworthy correlation between social media and the results of traditional mass surveys. We also illustrate that the predictive ability of social media analysis strengthens as the number of citizens expressing their opinion online increases, provided that the citizens act consistently on these opinions.